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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 .
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emely has an even number between 10 and 85 the sum of the digits is an even number less than 10 what is her number ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place .
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hi people does money take place in the world ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place .
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in the number 335 the 3 in the hundreds place is ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ?
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what the value of the 3 in the tens place ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 .
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how do you know that the 2 in 25,430 is 20,000 ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 .
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what is the value of the 2 in the number 42,341 ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 .
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will the difference between place value always be a number that ends with a 0 such as 1000 and 100000 ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 .
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is n't the second 7 suppose to be of a larger value than the first one because the first place is the ones place , second place is the tens place , etc ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place .
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what is the importance of place value and what jobs would you use it in ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 .
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what happens if the numbers go more than ones place ?
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the 4 in the number 5,634 is blank times blank than the 4 in the number 12,749 . so let 's think about what they 're saying . so the 4 in the number 5,634 , that 's literally in the ones place . it literally just represents 4 . now , the 4 in the number 12,749 , that 4 is in the tens place . it represents 40 . so this 4 , it 's a 10 times smaller value than this 4 . or this 4 , i should say . this 4 right over here represents 4 , while this represents 40 . so it is 10 times smaller than the 4 in 12,749 . 4 by itself is 10 times smaller than 40 . make sure i got the right answer . let 's do another one . in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place . it literally represents 70,000 , 7 ten thousands , or 70,000 , while this represents 700 thousands , or 700,000 . so the second 7 is 1/10 the value of the first 7 . or another way of thinking , it 's 10 times less . this is 70,000 , and this is 700,000 . so the value of the second 7 is 10 times less than the value of the first 7 . let 's do one more . this is fun . fill in the following blanks to complete the relationships between 25,430 and 2,543 . all right , so 25,430 is 10 times larger than 2,543 . literally , you take this , you multiply it by 10 , you 're going to get 25,430 . the digits in 25,430 are one place to the blank of the digits in the number 2,543 . well , let 's think about it . here you have a 2 in the thousands place . here you have a 2 in the ten thousands place . here you have a 5 in the hundreds place . here you have a 5 in the thousands place . and we could keep going . but what we see is a corresponding digit . in 25,430 , they 're one place to the left of the digits right over here . now , finally , we 're going to take 25,430 and divide it by 2,543 . well , we already know that the first number is 10 times larger than this number right over here . so literally , if you divide the smaller number into the larger one , you 're going to get 10 . this right over here is 10 times larger than this . so that was the first part of the question , and we are done .
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in the number 3,779,264 , how many times less is the value of the second 7 than the value of the first 7 ? how many times less is the value of the second 7 than the value of the first 7 ? so the second 7 right over here , that 's in the ten thousands place .
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why do we need place value ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have two positive numbers . let me draw a number line . so let me draw a number line .
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is there an easy way to do this in your head without a number line ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it 's pretty straightforward . we have two positive numbers . let me draw a number line .
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whoever put `` sal said 'integers ' but meant 'numbers ' '' would n't integers mean the same as numbers ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 .
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if i am doing a prime tree , how am i supposed to know how many 3 's or 2 's can be used ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 .
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lets say 3 numbers give me 3 3 's 2 2 's and 1 5. how am i supposed to know when i maxed out on my 3 or 2s ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier .
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what do i do if i want to divide fractions with same signs and different signs ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have two positive numbers . let me draw a number line . so let me draw a number line .
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what is a negitive number ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like .
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can you turn a negative number into positive number ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 .
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how are the number 25/8 + 6/8 = 31/8 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have two positive numbers . let me draw a number line . so let me draw a number line .
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why do i have to use a number line when adding fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ?
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what is the point of the orange arrow 4 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it 's pretty straightforward . we have two positive numbers . let me draw a number line .
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what is the point of mixed numbers ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 .
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how do you convert the mixed number to an improper fraction ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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can you have a denominator that is negative ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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whats the key to addng or subtracting a negative fraction with a positive fraction i know negative ad negative agualls a negative and the same for positive but how do you determine what the sign is if their different ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it 's pretty straightforward . we have two positive numbers . let me draw a number line .
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do you need to make mixed numbers into fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 .
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so would n't it be 31/8 x -11/6 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have two positive numbers . let me draw a number line . so let me draw a number line .
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is it necessary to use a number line ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we can just add them . we just have to find a like denominator . so we have 25 over 8 .
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like a good neighbor state farm is there with what ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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well , both of these are positive integers . so we can just add them . we just have to find a like denominator .
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do you add the fractions together or is there something that must be done ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have two positive numbers . let me draw a number line . so let me draw a number line .
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can a number line just keep going ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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well , both of these are positive integers . so we can just add them . we just have to find a like denominator .
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why do u need to add fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 .
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how do you get 25/8 out of 3 1/8 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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what is the denominators had a negative sign , how would you add or subtract the fraction ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have two positive numbers . let me draw a number line . so let me draw a number line .
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why do you use the number line ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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what do you do when multiplying negative fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have two positive numbers . let me draw a number line . so let me draw a number line .
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how are we supposed to use a number line when we do n't have much time is there a shorter method ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 .
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why do you need to find common denominator ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well .
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when you add or subtract fractions without like denoms , in a problem like : -4/8+7/4 , do you get a positive or a negative ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier .
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is n't negative fractions considered improper ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier .
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how do we subtract fractions with unlike signs ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear .
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how do you get a common denominator so that you could add easier ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear .
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where did the 24 common denominator came from ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we can just add them . we just have to find a like denominator . so we have 25 over 8 .
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when one denominator is 5 and the other one is 10 you would put the denominator as ten then how do i figure out the numerators ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it 's pretty straightforward . we have two positive numbers . let me draw a number line .
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is there a pattern with negative and positive numbers ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 .
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do negetive numbers have to always be subtracted , or can you deal with them in another way ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier .
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how do you add and subtract fractions with different signs without using a numberline ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first .
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3 1/8 a negative fraction ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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how would you solve a negative fraction plus a negative fraction ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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why do we need to learn how to add and/or subtract negative fractions already ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier .
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do you have to simplify the fractions when adding/subtracting the negatives and positive fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 .
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so what would 1/6+ -7/9 be ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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can a negative fraction subtract a negative fraction and still get a positive ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here .
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so my question is why does the minus sign turn to an addition ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 .
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how do i get oh noes the error charecter ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 .
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-what was the absolute value ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 .
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do the same rules of adding and subtracting negative numbers apply with fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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also , do of multiplying and dividing negative numbers apply with fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have two positive numbers . let me draw a number line . so let me draw a number line .
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how to number lines work ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ?
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what is 3,000,000,000,000 divided by 9 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first .
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what is a integer anyway ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 .
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do you think that the answer is 1 17/24 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 .
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ca n't you just switch the 93 here as in 31 ( 3 ) =93 so 13 ( 3 ) is 39 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point .
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how 'd you get the 25 over 8 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 .
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what is 1/6 as a fraction ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 .
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what is 1/7 as a fraction ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 .
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what is 1/8 as a fraction ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ?
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is 3/4 the same as 75 % or 0.75 % ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier .
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how do you add three fractions that have unlike denominators ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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how do you add and subtract negative fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like .
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how can you add a negative number to two big numbers ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive .
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what is negative 5 over 13 plus 5 over 52 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like .
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how do you know which way to add or subtract a negative number to a fraction ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw .
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how would i solve a negative addition/subtraction problem ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we can just add them . we just have to find a like denominator . so we have 25 over 8 .
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can only a numerator or only a denominator of a fraction have a different sign that the rest or does the whole fraction have to be solidly one sign ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here .
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how do you add/minus the mixed numbers ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right .
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why is 3 1/8 right by the three ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first .
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what is a integer anyway ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it 's pretty straightforward . we have two positive numbers . let me draw a number line .
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what happens when you subtract two negatives together ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 .
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why do we need to find a common denominator ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 .
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why do we need to find a common denominator ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here .
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ca n't we just add 25/8 + 3/4 directly ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well .
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why do n't u stick with one color ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 .
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how do i find a common denominator ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier .
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do you use greatest common factor when adding negative fractions by positive fractions ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it 's pretty straightforward . we have two positive numbers . let me draw a number line .
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whats the difference between integers and numbers ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like .
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nur do you alias write a negative number in brockest ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 .
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i am confused with mixed fraction : +2 3/5 - ( -2/4 ) why negative fractions change to positive and vice versa ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here .
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this is what i find odd 40-60 = -20 8-3 = 5 thus 48 - 63 should equal -25 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 .
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how is 3 ( 1/8 ) equals 25/8 ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 .
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how do you write the fraction sign on the computer ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 .
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what is -3/5+- ( 8/2 ) ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 .
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the problem is 1/2 + n = 0 what is n ?
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find the sum 3 and 1/8 plus 3/4 plus negative 2 and 1/6 . let 's just do the first part first . it 's pretty straightforward . we have two positive numbers . let me draw a number line . so let me draw a number line . and i 'll try to focus in . so we 're going to start at 3 and 1/8 . so let 's make this 0 . so you have 1 , 2 , 3 , and then you have 4 . 3 and 1/8 is going to be right about there . so let me just draw its absolute value . so this 3 and 1/8 is going to be 3 and 1/8 to the right of 0 . so it 's going to be exactly that distance from 0 to the right . so this right here , the length of this arrow , you could view it as 3 and 1/8 . now whenever i like to deal with fractions , especially when they have different denominators and all of that , i like to deal with them as improper fractions . it makes the addition and the subtraction , and , actually , the multiplication and the division a lot easier . so 3 and 1/8 is the same thing as 8 times 3 is 24 , plus 1 is 25 over 8 . so this is 25 over 8 , which is the same thing as 3 and 1/8 . another way to think about it , 3 is 24 over 8 . and then you add 1/8 to that , so you get 25 over 8 . so this is our starting point . now to that , we are going to add 3/4 . we are going to add 3/4 . so we 're going to move another 3/4 . we are going to move another 3/4 . it 's hard drawing these arrows . we 're going to move another 3/4 to the right . so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ? well , both of these are positive integers . so we can just add them . we just have to find a like denominator . so we have 25 over 8 . we have 25 over 8 plus 3/4 . that 's the same thing as we need to find a common denominator here . the common denominator , or the least common multiple of 4 and 8 is 8 . so it 's going to be something over 8 . to get from 4 to 8 , we multiply by 2 . so we have to multiply 3 by 2 as well . so you get 6 . so 3/4 is the same thing as 6/8 . if we have 25/8 and we 're adding 6/8 to that , that gives us 25 plus 6 is 31/8 . so this number right over here , this number right over here , is 31/8 . and it makes sense because 32/8 would be 4 . so it should be a little bit less than four . so this number right over here is 31/8 . or the length of this arrow , the absolute value of that number , is 31/8 , a little bit less than 4 . if you wanted to write that as a mixed number , it would be what ? it would be 3 and 7/8 . so that 's that right over here . this is 31/8 . that 's that part right over there . now to that , we want to add a negative 2 and 1/6 . so we 're going to add a negative number . so think about what negative 2 and 1/6 is going to be like . so let me do this in a new color , do it in pink . negative 2 and 1/6 . so we 're going to subtract , or i guess we 're going to say we 're going to add a negative 1 . we 're going to add a negative 2 and then a negative 1/6 . so let me draw . so negative 2 and 1/6 , we could literally draw like this . negative 2 and 1/6 we could draw with an arrow that looks something like that . so this is negative 2 and 1/6 . now , there 's a couple ways to think about it . you could just say , hey , look , when you add this arrow , this thing that 's moving to the left -- we could put it over here , and you would get straight to negative 2 and 1/6 . but we 're adding this negative 2 and 1/6 . it 's the same thing as subtracting a positive 2 and 1/6 . we 're moving 2 and 1/6 to the left . and we 're going to end up with a number whose absolute value is going to look something like that . and it 's actually going to be to the right . so it 's not going to only be its absolute value . well , its absolute value is going to be the number since it 's going to be a positive number . so let 's just think about what it is . this value right here , which is going to be the answer to our problem , is just going to be the difference of 31/8 and 2 and 1/6 . and it 's the positive difference because we 're dealing with a positive number . so we just take 31/8 . and from that , we will subtract 2 and 1/6 . so let 's do this . so this orange value is going to be 31/8 minus 2 and 1/6 . so 2 and 1/6 is the same thing as 6 times 2 is 12 plus 1 is 13 . minus 13/6 . and this is equal to , once again , we need to get a common denominator over here . and it looks like 24 will be the common denominator , 24 . and let me make it very clear . this is the 31/8 . and this is the 2 and 1/6 . this right here is the 2 and 1/6 . so 31/8 over 24 . you have to multiply by 3 to get to the 24 over here . so we multiply by 3 on the 31 . that gives us 93 . and then to go from 6 to 24 , you have to multiply by 4 . we do that in another color . you have to multiply it by 4 , so we have to multiply by 4 up here as well . so 4 times 13 , let 's see . 4 times 10 is 40 . 4 times 3 is 12 . so that 's 52 . so this is going to be equal to 93 minus 52 over 24 . and that is -- so 93 minus 52 . 3 minus 2 is 1 . 9 minus 5 is 4 . so it is 41/24 and positive . and you can see that here just by looking at the number line . this right here is 41 over 24 . and it should be a little bit less than 2 because 2 would be 48 over 24 . so this would be 48 over 24 . and it makes sense that we 're a little bit less than that .
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so this right here , the length of this that we 're moving to the right is 3/4 . so plus 3/4 . now where does this put us ?
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is 3/4 the same as 75 % or 0.75 % ?
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we 're told to solve and graph the solution for the system of equations right here . and the first thing that jumps out at me , is that we might be able to eliminate one of the variables . and if we just focus on the x , we have a 4x here and we have a 2x right here . if we were to just add them right now , we would get a 6x . so that would n't eliminate it . but if we can multiply this 2x by negative 2 , it 'll become a negative 4x , and then when you add it , they would cancel out . so let 's multiply this equation , this second equation , by negative 2 . so i 'm going to multiply both sides of this equation by negative 2 . and the whole motivation is so that this 2x becomes a negative 4x . and , of course , i ca n't just multiply only the 2x . anything i do to the left-hand side of the equation i have to do to every term , and i have to do to both sides of the equation . so the second equation becomes negative 4x -- that 's negative 2 times 2x -- plus -- we have negative 2 times negative y -- which is plus 2y is equal to 2.5 times negative 2 , is equal to negative 5 . i just rewrote the second equation , multiplying both sides by negative 2 . now , this top equation -- i 'll write it on the bottom now -- we have 4x minus 2y is equal to positive 5 . and now we can eliminate it . we can say , hey , look , the negative 4x and the positive 4x should cancel out , or they will cancel out . so let 's add these two equations . let 's add the left side to the left side , the right side to the right side , and we can do that because these two things are equal . we 're doing the same thing to both sides of the equation . so what do we get ? if we take our negative 4x plus our 4x , well , those cancel out . so you 're left with nothing . maybe i could write a 0 there . 0x if you want . and then you have your plus 2y and your negative 2y . those also cancel out . so you 're also left with 0y . and then that equals negative 5 plus 5 is equal to 0 . so this just simplifies to 0 equals 0 , which is true , but it 's kind of bizarre . we had all these x 's and y 's . everything canceled out . so let 's explore this a little bit more . let 's graph it and see what this 0 equals 0 is telling us when we try to solve this system of equations . so let me graph this top guy . i 'll do it in blue . so right now it 's in standard form . let 's put it in slope-intercept form . so we have 4x minus 2y is equal to 5 . let 's subtract 4x from both sides . i want the x terms on the right-hand side . so then i 'm left with negative 2y is equal to negative 4x plus 5 . now we can divide both sides by negative 2 . and we are left with y is equal to positive 2x , right , that 's positive 2x , minus 2.5 . so let 's graph that . the y-intercept is negative 2.5 . so negative 2.5 right there , and then it has a slope of 2 . so if we move up 1 , if we move up in the x-direction , if we move to the right 1 in the positive x-direction , we will move up 2 . so 1 , 2 . right there . and if we were to do it again , we move up 1 , 2 . just like that . so the line 's going to look something like this . i 'll try my best to draw a straight line . this is the hardest part about a lot of these problems . there you go . so that 's the top equation . now , let me draw the bottom equation . let me draw and i 'll do it in this green color . so this bottom equation was 2x minus y is equal to 2.5 . and we can subtract 2x from both sides . the left-hand side becomes negative y is equal to 2x plus -- or is equal to negative 2x plus 2.5 . now let 's multiply or divide both sides by negative 1 . and you get y is equal to positive 2x minus 2.5 . and let 's try to graph this , and you already might notice something interesting about these two equations . you try to graph this , the y-intercept is at negative 2.5 , right there . the slope is 2 . so it 's going to be this exact same line . and you saw that algebraically . i did n't have to graph it . these two lines have the exact same equation when you put them in slope-intercept form . that 's the first equation . that 's the second equation . so what this 0 equals 0 is telling us is actually that these are the same line . that these actually have an infinite number of solutions . any point on this line , which is both of those lines , will satisfy both of these equations . you give me an arbitrary y , solve for x in the top equation , that x and y will also satisfy the bottom equation . so this actually has an infinite number of solutions . these are the same line .
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i 'll do it in blue . so right now it 's in standard form . let 's put it in slope-intercept form .
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what is the point of standard form ?
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we 're told to solve and graph the solution for the system of equations right here . and the first thing that jumps out at me , is that we might be able to eliminate one of the variables . and if we just focus on the x , we have a 4x here and we have a 2x right here . if we were to just add them right now , we would get a 6x . so that would n't eliminate it . but if we can multiply this 2x by negative 2 , it 'll become a negative 4x , and then when you add it , they would cancel out . so let 's multiply this equation , this second equation , by negative 2 . so i 'm going to multiply both sides of this equation by negative 2 . and the whole motivation is so that this 2x becomes a negative 4x . and , of course , i ca n't just multiply only the 2x . anything i do to the left-hand side of the equation i have to do to every term , and i have to do to both sides of the equation . so the second equation becomes negative 4x -- that 's negative 2 times 2x -- plus -- we have negative 2 times negative y -- which is plus 2y is equal to 2.5 times negative 2 , is equal to negative 5 . i just rewrote the second equation , multiplying both sides by negative 2 . now , this top equation -- i 'll write it on the bottom now -- we have 4x minus 2y is equal to positive 5 . and now we can eliminate it . we can say , hey , look , the negative 4x and the positive 4x should cancel out , or they will cancel out . so let 's add these two equations . let 's add the left side to the left side , the right side to the right side , and we can do that because these two things are equal . we 're doing the same thing to both sides of the equation . so what do we get ? if we take our negative 4x plus our 4x , well , those cancel out . so you 're left with nothing . maybe i could write a 0 there . 0x if you want . and then you have your plus 2y and your negative 2y . those also cancel out . so you 're also left with 0y . and then that equals negative 5 plus 5 is equal to 0 . so this just simplifies to 0 equals 0 , which is true , but it 's kind of bizarre . we had all these x 's and y 's . everything canceled out . so let 's explore this a little bit more . let 's graph it and see what this 0 equals 0 is telling us when we try to solve this system of equations . so let me graph this top guy . i 'll do it in blue . so right now it 's in standard form . let 's put it in slope-intercept form . so we have 4x minus 2y is equal to 5 . let 's subtract 4x from both sides . i want the x terms on the right-hand side . so then i 'm left with negative 2y is equal to negative 4x plus 5 . now we can divide both sides by negative 2 . and we are left with y is equal to positive 2x , right , that 's positive 2x , minus 2.5 . so let 's graph that . the y-intercept is negative 2.5 . so negative 2.5 right there , and then it has a slope of 2 . so if we move up 1 , if we move up in the x-direction , if we move to the right 1 in the positive x-direction , we will move up 2 . so 1 , 2 . right there . and if we were to do it again , we move up 1 , 2 . just like that . so the line 's going to look something like this . i 'll try my best to draw a straight line . this is the hardest part about a lot of these problems . there you go . so that 's the top equation . now , let me draw the bottom equation . let me draw and i 'll do it in this green color . so this bottom equation was 2x minus y is equal to 2.5 . and we can subtract 2x from both sides . the left-hand side becomes negative y is equal to 2x plus -- or is equal to negative 2x plus 2.5 . now let 's multiply or divide both sides by negative 1 . and you get y is equal to positive 2x minus 2.5 . and let 's try to graph this , and you already might notice something interesting about these two equations . you try to graph this , the y-intercept is at negative 2.5 , right there . the slope is 2 . so it 's going to be this exact same line . and you saw that algebraically . i did n't have to graph it . these two lines have the exact same equation when you put them in slope-intercept form . that 's the first equation . that 's the second equation . so what this 0 equals 0 is telling us is actually that these are the same line . that these actually have an infinite number of solutions . any point on this line , which is both of those lines , will satisfy both of these equations . you give me an arbitrary y , solve for x in the top equation , that x and y will also satisfy the bottom equation . so this actually has an infinite number of solutions . these are the same line .
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i 'll do it in blue . so right now it 's in standard form . let 's put it in slope-intercept form . so we have 4x minus 2y is equal to 5 .
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instead of changing 4x - 2y = 5 to slope-intercept form in order to graph it , how ( if you even can ) would you graph the equation while keeping it in standard form ?
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we 're told to solve and graph the solution for the system of equations right here . and the first thing that jumps out at me , is that we might be able to eliminate one of the variables . and if we just focus on the x , we have a 4x here and we have a 2x right here . if we were to just add them right now , we would get a 6x . so that would n't eliminate it . but if we can multiply this 2x by negative 2 , it 'll become a negative 4x , and then when you add it , they would cancel out . so let 's multiply this equation , this second equation , by negative 2 . so i 'm going to multiply both sides of this equation by negative 2 . and the whole motivation is so that this 2x becomes a negative 4x . and , of course , i ca n't just multiply only the 2x . anything i do to the left-hand side of the equation i have to do to every term , and i have to do to both sides of the equation . so the second equation becomes negative 4x -- that 's negative 2 times 2x -- plus -- we have negative 2 times negative y -- which is plus 2y is equal to 2.5 times negative 2 , is equal to negative 5 . i just rewrote the second equation , multiplying both sides by negative 2 . now , this top equation -- i 'll write it on the bottom now -- we have 4x minus 2y is equal to positive 5 . and now we can eliminate it . we can say , hey , look , the negative 4x and the positive 4x should cancel out , or they will cancel out . so let 's add these two equations . let 's add the left side to the left side , the right side to the right side , and we can do that because these two things are equal . we 're doing the same thing to both sides of the equation . so what do we get ? if we take our negative 4x plus our 4x , well , those cancel out . so you 're left with nothing . maybe i could write a 0 there . 0x if you want . and then you have your plus 2y and your negative 2y . those also cancel out . so you 're also left with 0y . and then that equals negative 5 plus 5 is equal to 0 . so this just simplifies to 0 equals 0 , which is true , but it 's kind of bizarre . we had all these x 's and y 's . everything canceled out . so let 's explore this a little bit more . let 's graph it and see what this 0 equals 0 is telling us when we try to solve this system of equations . so let me graph this top guy . i 'll do it in blue . so right now it 's in standard form . let 's put it in slope-intercept form . so we have 4x minus 2y is equal to 5 . let 's subtract 4x from both sides . i want the x terms on the right-hand side . so then i 'm left with negative 2y is equal to negative 4x plus 5 . now we can divide both sides by negative 2 . and we are left with y is equal to positive 2x , right , that 's positive 2x , minus 2.5 . so let 's graph that . the y-intercept is negative 2.5 . so negative 2.5 right there , and then it has a slope of 2 . so if we move up 1 , if we move up in the x-direction , if we move to the right 1 in the positive x-direction , we will move up 2 . so 1 , 2 . right there . and if we were to do it again , we move up 1 , 2 . just like that . so the line 's going to look something like this . i 'll try my best to draw a straight line . this is the hardest part about a lot of these problems . there you go . so that 's the top equation . now , let me draw the bottom equation . let me draw and i 'll do it in this green color . so this bottom equation was 2x minus y is equal to 2.5 . and we can subtract 2x from both sides . the left-hand side becomes negative y is equal to 2x plus -- or is equal to negative 2x plus 2.5 . now let 's multiply or divide both sides by negative 1 . and you get y is equal to positive 2x minus 2.5 . and let 's try to graph this , and you already might notice something interesting about these two equations . you try to graph this , the y-intercept is at negative 2.5 , right there . the slope is 2 . so it 's going to be this exact same line . and you saw that algebraically . i did n't have to graph it . these two lines have the exact same equation when you put them in slope-intercept form . that 's the first equation . that 's the second equation . so what this 0 equals 0 is telling us is actually that these are the same line . that these actually have an infinite number of solutions . any point on this line , which is both of those lines , will satisfy both of these equations . you give me an arbitrary y , solve for x in the top equation , that x and y will also satisfy the bottom equation . so this actually has an infinite number of solutions . these are the same line .
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anything i do to the left-hand side of the equation i have to do to every term , and i have to do to both sides of the equation . so the second equation becomes negative 4x -- that 's negative 2 times 2x -- plus -- we have negative 2 times negative y -- which is plus 2y is equal to 2.5 times negative 2 , is equal to negative 5 . i just rewrote the second equation , multiplying both sides by negative 2 .
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if -3x-6y=-63 , how do you know if the `` 6y '' is negative ?
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we 're told to solve and graph the solution for the system of equations right here . and the first thing that jumps out at me , is that we might be able to eliminate one of the variables . and if we just focus on the x , we have a 4x here and we have a 2x right here . if we were to just add them right now , we would get a 6x . so that would n't eliminate it . but if we can multiply this 2x by negative 2 , it 'll become a negative 4x , and then when you add it , they would cancel out . so let 's multiply this equation , this second equation , by negative 2 . so i 'm going to multiply both sides of this equation by negative 2 . and the whole motivation is so that this 2x becomes a negative 4x . and , of course , i ca n't just multiply only the 2x . anything i do to the left-hand side of the equation i have to do to every term , and i have to do to both sides of the equation . so the second equation becomes negative 4x -- that 's negative 2 times 2x -- plus -- we have negative 2 times negative y -- which is plus 2y is equal to 2.5 times negative 2 , is equal to negative 5 . i just rewrote the second equation , multiplying both sides by negative 2 . now , this top equation -- i 'll write it on the bottom now -- we have 4x minus 2y is equal to positive 5 . and now we can eliminate it . we can say , hey , look , the negative 4x and the positive 4x should cancel out , or they will cancel out . so let 's add these two equations . let 's add the left side to the left side , the right side to the right side , and we can do that because these two things are equal . we 're doing the same thing to both sides of the equation . so what do we get ? if we take our negative 4x plus our 4x , well , those cancel out . so you 're left with nothing . maybe i could write a 0 there . 0x if you want . and then you have your plus 2y and your negative 2y . those also cancel out . so you 're also left with 0y . and then that equals negative 5 plus 5 is equal to 0 . so this just simplifies to 0 equals 0 , which is true , but it 's kind of bizarre . we had all these x 's and y 's . everything canceled out . so let 's explore this a little bit more . let 's graph it and see what this 0 equals 0 is telling us when we try to solve this system of equations . so let me graph this top guy . i 'll do it in blue . so right now it 's in standard form . let 's put it in slope-intercept form . so we have 4x minus 2y is equal to 5 . let 's subtract 4x from both sides . i want the x terms on the right-hand side . so then i 'm left with negative 2y is equal to negative 4x plus 5 . now we can divide both sides by negative 2 . and we are left with y is equal to positive 2x , right , that 's positive 2x , minus 2.5 . so let 's graph that . the y-intercept is negative 2.5 . so negative 2.5 right there , and then it has a slope of 2 . so if we move up 1 , if we move up in the x-direction , if we move to the right 1 in the positive x-direction , we will move up 2 . so 1 , 2 . right there . and if we were to do it again , we move up 1 , 2 . just like that . so the line 's going to look something like this . i 'll try my best to draw a straight line . this is the hardest part about a lot of these problems . there you go . so that 's the top equation . now , let me draw the bottom equation . let me draw and i 'll do it in this green color . so this bottom equation was 2x minus y is equal to 2.5 . and we can subtract 2x from both sides . the left-hand side becomes negative y is equal to 2x plus -- or is equal to negative 2x plus 2.5 . now let 's multiply or divide both sides by negative 1 . and you get y is equal to positive 2x minus 2.5 . and let 's try to graph this , and you already might notice something interesting about these two equations . you try to graph this , the y-intercept is at negative 2.5 , right there . the slope is 2 . so it 's going to be this exact same line . and you saw that algebraically . i did n't have to graph it . these two lines have the exact same equation when you put them in slope-intercept form . that 's the first equation . that 's the second equation . so what this 0 equals 0 is telling us is actually that these are the same line . that these actually have an infinite number of solutions . any point on this line , which is both of those lines , will satisfy both of these equations . you give me an arbitrary y , solve for x in the top equation , that x and y will also satisfy the bottom equation . so this actually has an infinite number of solutions . these are the same line .
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let 's put it in slope-intercept form . so we have 4x minus 2y is equal to 5 . let 's subtract 4x from both sides .
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what is the solution of 4x+y=57 and 7x-2y=21 ?
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we 're told to solve and graph the solution for the system of equations right here . and the first thing that jumps out at me , is that we might be able to eliminate one of the variables . and if we just focus on the x , we have a 4x here and we have a 2x right here . if we were to just add them right now , we would get a 6x . so that would n't eliminate it . but if we can multiply this 2x by negative 2 , it 'll become a negative 4x , and then when you add it , they would cancel out . so let 's multiply this equation , this second equation , by negative 2 . so i 'm going to multiply both sides of this equation by negative 2 . and the whole motivation is so that this 2x becomes a negative 4x . and , of course , i ca n't just multiply only the 2x . anything i do to the left-hand side of the equation i have to do to every term , and i have to do to both sides of the equation . so the second equation becomes negative 4x -- that 's negative 2 times 2x -- plus -- we have negative 2 times negative y -- which is plus 2y is equal to 2.5 times negative 2 , is equal to negative 5 . i just rewrote the second equation , multiplying both sides by negative 2 . now , this top equation -- i 'll write it on the bottom now -- we have 4x minus 2y is equal to positive 5 . and now we can eliminate it . we can say , hey , look , the negative 4x and the positive 4x should cancel out , or they will cancel out . so let 's add these two equations . let 's add the left side to the left side , the right side to the right side , and we can do that because these two things are equal . we 're doing the same thing to both sides of the equation . so what do we get ? if we take our negative 4x plus our 4x , well , those cancel out . so you 're left with nothing . maybe i could write a 0 there . 0x if you want . and then you have your plus 2y and your negative 2y . those also cancel out . so you 're also left with 0y . and then that equals negative 5 plus 5 is equal to 0 . so this just simplifies to 0 equals 0 , which is true , but it 's kind of bizarre . we had all these x 's and y 's . everything canceled out . so let 's explore this a little bit more . let 's graph it and see what this 0 equals 0 is telling us when we try to solve this system of equations . so let me graph this top guy . i 'll do it in blue . so right now it 's in standard form . let 's put it in slope-intercept form . so we have 4x minus 2y is equal to 5 . let 's subtract 4x from both sides . i want the x terms on the right-hand side . so then i 'm left with negative 2y is equal to negative 4x plus 5 . now we can divide both sides by negative 2 . and we are left with y is equal to positive 2x , right , that 's positive 2x , minus 2.5 . so let 's graph that . the y-intercept is negative 2.5 . so negative 2.5 right there , and then it has a slope of 2 . so if we move up 1 , if we move up in the x-direction , if we move to the right 1 in the positive x-direction , we will move up 2 . so 1 , 2 . right there . and if we were to do it again , we move up 1 , 2 . just like that . so the line 's going to look something like this . i 'll try my best to draw a straight line . this is the hardest part about a lot of these problems . there you go . so that 's the top equation . now , let me draw the bottom equation . let me draw and i 'll do it in this green color . so this bottom equation was 2x minus y is equal to 2.5 . and we can subtract 2x from both sides . the left-hand side becomes negative y is equal to 2x plus -- or is equal to negative 2x plus 2.5 . now let 's multiply or divide both sides by negative 1 . and you get y is equal to positive 2x minus 2.5 . and let 's try to graph this , and you already might notice something interesting about these two equations . you try to graph this , the y-intercept is at negative 2.5 , right there . the slope is 2 . so it 's going to be this exact same line . and you saw that algebraically . i did n't have to graph it . these two lines have the exact same equation when you put them in slope-intercept form . that 's the first equation . that 's the second equation . so what this 0 equals 0 is telling us is actually that these are the same line . that these actually have an infinite number of solutions . any point on this line , which is both of those lines , will satisfy both of these equations . you give me an arbitrary y , solve for x in the top equation , that x and y will also satisfy the bottom equation . so this actually has an infinite number of solutions . these are the same line .
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now we can divide both sides by negative 2 . and we are left with y is equal to positive 2x , right , that 's positive 2x , minus 2.5 . so let 's graph that .
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how do i solve : 8x-7y=21 2x=3y+4 using addition/elimination ?
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we 're told to solve and graph the solution for the system of equations right here . and the first thing that jumps out at me , is that we might be able to eliminate one of the variables . and if we just focus on the x , we have a 4x here and we have a 2x right here . if we were to just add them right now , we would get a 6x . so that would n't eliminate it . but if we can multiply this 2x by negative 2 , it 'll become a negative 4x , and then when you add it , they would cancel out . so let 's multiply this equation , this second equation , by negative 2 . so i 'm going to multiply both sides of this equation by negative 2 . and the whole motivation is so that this 2x becomes a negative 4x . and , of course , i ca n't just multiply only the 2x . anything i do to the left-hand side of the equation i have to do to every term , and i have to do to both sides of the equation . so the second equation becomes negative 4x -- that 's negative 2 times 2x -- plus -- we have negative 2 times negative y -- which is plus 2y is equal to 2.5 times negative 2 , is equal to negative 5 . i just rewrote the second equation , multiplying both sides by negative 2 . now , this top equation -- i 'll write it on the bottom now -- we have 4x minus 2y is equal to positive 5 . and now we can eliminate it . we can say , hey , look , the negative 4x and the positive 4x should cancel out , or they will cancel out . so let 's add these two equations . let 's add the left side to the left side , the right side to the right side , and we can do that because these two things are equal . we 're doing the same thing to both sides of the equation . so what do we get ? if we take our negative 4x plus our 4x , well , those cancel out . so you 're left with nothing . maybe i could write a 0 there . 0x if you want . and then you have your plus 2y and your negative 2y . those also cancel out . so you 're also left with 0y . and then that equals negative 5 plus 5 is equal to 0 . so this just simplifies to 0 equals 0 , which is true , but it 's kind of bizarre . we had all these x 's and y 's . everything canceled out . so let 's explore this a little bit more . let 's graph it and see what this 0 equals 0 is telling us when we try to solve this system of equations . so let me graph this top guy . i 'll do it in blue . so right now it 's in standard form . let 's put it in slope-intercept form . so we have 4x minus 2y is equal to 5 . let 's subtract 4x from both sides . i want the x terms on the right-hand side . so then i 'm left with negative 2y is equal to negative 4x plus 5 . now we can divide both sides by negative 2 . and we are left with y is equal to positive 2x , right , that 's positive 2x , minus 2.5 . so let 's graph that . the y-intercept is negative 2.5 . so negative 2.5 right there , and then it has a slope of 2 . so if we move up 1 , if we move up in the x-direction , if we move to the right 1 in the positive x-direction , we will move up 2 . so 1 , 2 . right there . and if we were to do it again , we move up 1 , 2 . just like that . so the line 's going to look something like this . i 'll try my best to draw a straight line . this is the hardest part about a lot of these problems . there you go . so that 's the top equation . now , let me draw the bottom equation . let me draw and i 'll do it in this green color . so this bottom equation was 2x minus y is equal to 2.5 . and we can subtract 2x from both sides . the left-hand side becomes negative y is equal to 2x plus -- or is equal to negative 2x plus 2.5 . now let 's multiply or divide both sides by negative 1 . and you get y is equal to positive 2x minus 2.5 . and let 's try to graph this , and you already might notice something interesting about these two equations . you try to graph this , the y-intercept is at negative 2.5 , right there . the slope is 2 . so it 's going to be this exact same line . and you saw that algebraically . i did n't have to graph it . these two lines have the exact same equation when you put them in slope-intercept form . that 's the first equation . that 's the second equation . so what this 0 equals 0 is telling us is actually that these are the same line . that these actually have an infinite number of solutions . any point on this line , which is both of those lines , will satisfy both of these equations . you give me an arbitrary y , solve for x in the top equation , that x and y will also satisfy the bottom equation . so this actually has an infinite number of solutions . these are the same line .
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any point on this line , which is both of those lines , will satisfy both of these equations . you give me an arbitrary y , solve for x in the top equation , that x and y will also satisfy the bottom equation . so this actually has an infinite number of solutions .
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how do i solve : x+3y-z=10 2x+5y+4z=57 3x-y+2z=15 using elimination ?
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