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welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | i 'm going to do it in different colors now . 5 plus 6 . so if you want , you could pause the video and try this . | why is 5+6 = 11 ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | what is the origin of the word addition ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | let 's say i have 3 avocados -- 1 , 2 , 3 . and let 's say you were to give me 4 more avocados . so let me put this 4 in yellow so you know that these are the ones you 're giving me . | how to give proper blowjob ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | so you know the first number is 0 , which is nothing . maybe you do n't know , but now you know . and then you go to 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 . | do you know what 111111111111+888888888888888 equals ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | so let me put this 4 in yellow so you know that these are the ones you 're giving me . 1 , 2 , 3 , 4 . so how many total avocados do i have now ? | 3 feet length & 2 feet wide what is it 's area ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | so you know the first number is 0 , which is nothing . maybe you do n't know , but now you know . and then you go to 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 . | how do you know what do do ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | and actually , i think this is how i do it in my head when i forget -- if i do n't have it memorized . so number line , i just write all the numbers in order . and i go high enough just so all the numbers i 'm using are kind of in it . | general question - what input device is sal using to write ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | where does the word addition come from ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | what makes addition `` addition '' ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | i 'm going to do it in different colors now . 5 plus 6 . so if you want , you could pause the video and try this . | why is the addition ( plus ) sign a cross ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | but if we look at the number line you start at 8 and you add 1 . 8 plus 1 is equal to 9 . let 's do some harder problems . | is b x x equal to one ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | so let 's start at 6 . ignore the yellow for now and add 5 to it . 1 , 2 , 3 , 4 , 5 . | @ hankinstaylor how do you add a mixed fraction ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | how to operated diesel engine ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | and now i 'm going to introduce you to another way of thinking about this . it 's called the number line . and actually , i think this is how i do it in my head when i forget -- if i do n't have it memorized . | do we use the number line ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | so 1 plus 1 is equal to 2 . now , i know what you 're thinking . that was too easy , so let me give you something a little bit more difficult . | at the bottom of the screen are the words , `` i know what your thinking ... '' is there a way to fix the spelling of the word `` your '' ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | i 'm going to do it in different colors now . 5 plus 6 . so if you want , you could pause the video and try this . | is 5 plus 20 twenty2 ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | maybe you do n't know , but now you know . and then you go to 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 . keeps going -- 11 . | if a train stops am and another train arrives pm , whats the difference ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | what is the root of addition ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | who wants to join the anti-revouloution on keeping the leaf system ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | well let 's say i start with an old classic . 1 plus 1 . and i think you already know how to do this , but i 'll kind of show you a way of doing this in case you do n't have this memorized or you have n't already mastered this . | why is 1+1 a basic classic ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | and now i 'm going to introduce you to another way of thinking about this . it 's called the number line . and actually , i think this is how i do it in my head when i forget -- if i do n't have it memorized . | why did you use a number line ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | where does the addition sign originate from ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | what is 90 + 79 + 63 ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | how do you speed up mastery challenges ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | why is the addition sign a shape of a cross ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . | what is 5000 times 10000000 ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | but if we look at the number line you start at 8 and you add 1 . 8 plus 1 is equal to 9 . let 's do some harder problems . | if the selling price of 8 pens is equal to the cost of 10 pens , what is the profit percent ? |
welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . hopefully by the end of this presentation or in a couple of weeks it will seem basic . so let 's get started with , i guess we could say , some problems . well let 's say i s... | welcome to the presentation on basic addition . i know what you 're thinking , sal , addition does n't seem so basic to me . well , i apologize . | why is sal so good at explaining things ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and then i have minus 4xy right over here . then let 's go to the x squared terms . i have negative 2 times x squared , or minus 2x squared . so let 's look at this . | why ca n't you simplify -y+x squared +2x+y squared ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | then let 's go to the x squared terms . i have negative 2 times x squared , or minus 2x squared . so let 's look at this . | would n't -2x squared be -4x ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so this right over here simplifies to 1x squared . or i could literally just write x squared . 1x squared is the same thing as x squared . so plus x squared , and then these there 's nothing really left to simplify . | and would n't you add the squared x 's and the normal x 's ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and then let 's see , i have an x term right over here , and that actually looks like the only x term . so that 's plus 2x . and then i only have one y squared term -- i 'll circle that in orange -- so plus y squared . | so then you 'd have -4x + 9x + 2x= 7x ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | think about it they were numbers . if y was 3 and an x was a 2 , then a y would be a 3 while an xy would have been a 6 . and a y is very different than a y squared . | would n't an xy be a 5 ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | or you could say add the coefficients , 4 plus negative 4 , gives you 0 xy 's . either way , these two cancel out . if i have 4 of something and i take away those 4 of that something , i 'm left with none of them . | in the similar way when we cancel out coefficients along with variables ( -4x+4y ) , do we cancel out variables also ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and we 're done . and obviously you might have gotten an answer in some other order , but the order in which i write these terms do n't matter . it just matters that you were able to simplify it to these four terms . | when mr. khan rearranges the terms , why does it not affect the order of operations and final outcome of the equation ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | can terms like 4xy combine with 4xa to create 16x^2ya ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | once again , if the why it took on the value 3 , then the y squared would be the value 9 . so even though you see the same letter here , they are n't the same -- i guess you can not add these two or subtract these two terms . a y is different than a y squared , is different than an xy . | what does the letter after the number stand for ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so those simplify to this right over here . now let 's look at the xy terms . if i have 4 of this , 4 xy 's and i were to take away 4 xy 's , how many xy 's am i left with ? well , i 'm left with no xy 's . | what if xy have same numbers ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and then i have right over here -- i could have written 0xy , but that seems unnecessary -- then right over here i have my x squared terms . negative 2 plus 3 is 1 . or another way of saying it , if i have 3x squared and i were to take away 2 of those x squared , so i 'm left with the 1x squared . | how do you know if its negative 2 or minus 2 ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and we 're done . and obviously you might have gotten an answer in some other order , but the order in which i write these terms do n't matter . it just matters that you were able to simplify it to these four terms . | is there a specific order for the terms once you finish the equation ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | where does the y^2 go ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . | why not include that in the final output ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so plus 3x squared . and then let 's see , i have an x term right over here , and that actually looks like the only x term . so that 's plus 2x . | 2 , how is it possible to have a term like 4xy ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | how do you combine like terms ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | in terms ( no pun intended ... ) of exponents ... why can we add exponents when multiplying like terms ... but we ca n't add exponents when adding like terms ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . so those simplify to this right over here . | can anyone please explain combining negative coefficients and distribution ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . so those simplify to this right over here . | for instance if i have to simplify 2b - ( -1 + -4 ) - 6b how do i keep track of what 's supposed to be negative ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . | how do i figure out which sign is supposed to flip ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | now let 's look at the xy terms . if i have 4 of this , 4 xy 's and i were to take away 4 xy 's , how many xy 's am i left with ? well , i 'm left with no xy 's . | is 4xy the same as 4*x*y or is xy a separate variable ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | what is the difference between x^2 and xy and y^2 ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | what are `` like terms '' ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so first , let 's think about the y terms . so you have a negative 3y there . do we have any more y term ? | how am i suppose to know that moving the 4xy from the -3y wo n't make the equation go wrong ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so plus x squared , and then these there 's nothing really left to simplify . so plus 2x plus y squared . and we 're done . | where did you get the plus sign from ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | think about it they were numbers . if y was 3 and an x was a 2 , then a y would be a 3 while an xy would have been a 6 . and a y is very different than a y squared . | would n't you put a subtraction sign there ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | wait could n't you simplify the term -y + x^2 + 2x + y^2 more ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . so those simplify to this right over here . now let 's look at the xy terms . | can you simplify the exponent variables further ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | i have this 3x squared right over there . so plus 3x squared . and then let 's see , i have an x term right over here , and that actually looks like the only x term . | for example , -1x to the power of 2 = -1x * -1x , or 3x to the power of 4 = 3x * 3x * 3x * 3x ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | think about it they were numbers . if y was 3 and an x was a 2 , then a y would be a 3 while an xy would have been a 6 . and a y is very different than a y squared . | when you have an xy do you always have to add say x= 2 and y=3 would that = 23 ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | why would you subtract eventhough there is a + sign ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and we 're done . and obviously you might have gotten an answer in some other order , but the order in which i write these terms do n't matter . it just matters that you were able to simplify it to these four terms . | when sal said the order does n't matter our teacher said the exact opposite , who is right ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | then let 's go to the x squared terms . i have negative 2 times x squared , or minus 2x squared . so let 's look at this . | say there 's a equation 5x+6y-x-5y would 5y be negative because there is a minus sign or would it be positive ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so i have minus 2x squared . do i have any other x squared ? yes , i do . | why does algebra have so many x 's y 's and z 's , what do they stand for ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . | what is the difference between linear and quadratic equations ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . so those simplify to this right over here . | how do you know if you 're subtracting 2 terms or multiplying with a negative number ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | can i not combine `` unlike '' terms ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | when you simplify all of the terms to the lowest possible , do you have to put the plus sign in between all of the terms ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | why r there 2 many colors ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | how are 2 variables able to combine ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | how do you combine like terms ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | once again , if the why it took on the value 3 , then the y squared would be the value 9 . so even though you see the same letter here , they are n't the same -- i guess you can not add these two or subtract these two terms . a y is different than a y squared , is different than an xy . | when simplifying the equations , how do we know when to add and subtract ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and then i have minus 4xy right over here . then let 's go to the x squared terms . i have negative 2 times x squared , or minus 2x squared . so let 's look at this . | would n't 2x be x squared ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so i 'll just write it out -- i 'll just reorder it . so we have negative 3y plus 2y . now , let 's think about -- and i 'm just going in an arbitrary order , but since our next term is an xy term -- let 's think about all of the xy terms . | why is the y2 considered separate from the -3y and +2y ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and we 're done . and obviously you might have gotten an answer in some other order , but the order in which i write these terms do n't matter . it just matters that you were able to simplify it to these four terms . | i know this might sound dumb or tricky but , are you allowed to make decimals when simplifying ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | : ( one of the sample questions is 4a^2b^-2/ba^4 - 12a^2ba/ba^2 i do n't know how to work it ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and then i have right over here -- i could have written 0xy , but that seems unnecessary -- then right over here i have my x squared terms . negative 2 plus 3 is 1 . or another way of saying it , if i have 3x squared and i were to take away 2 of those x squared , so i 'm left with the 1x squared . | why are there 2 letters not 1 ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | if i have 4 of this , 4 xy 's and i were to take away 4 xy 's , how many xy 's am i left with ? well , i 'm left with no xy 's . or you could say add the coefficients , 4 plus negative 4 , gives you 0 xy 's . either way , these two cancel out . | is n't xy a 5 not a 6 ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | example : -2+ ( -5y ) -3y+5 because i 'm getting confused as to what must be done with the brackets ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so i have minus 2x squared . do i have any other x squared ? yes , i do . | why do the people who created or thought about the letters use x and y the most instead of the other letters of the alphabet ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | what 's the coefficient here ? it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . | ca n't you simplify -y and y to the power of 2 ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . so those simplify to this right over here . | what happens if y equals a negative then what happens ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and we 're done . and obviously you might have gotten an answer in some other order , but the order in which i write these terms do n't matter . it just matters that you were able to simplify it to these four terms . | why do n't you use the equal sign ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | if i have 4 of this , 4 xy 's and i were to take away 4 xy 's , how many xy 's am i left with ? well , i 'm left with no xy 's . or you could say add the coefficients , 4 plus negative 4 , gives you 0 xy 's . either way , these two cancel out . | could you use the distributive property to distribute out the xy ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | why can the terms be reordered ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so even though you see the same letter here , they are n't the same -- i guess you can not add these two or subtract these two terms . a y is different than a y squared , is different than an xy . now with that said , let 's see if there is anything that we can simplify . | how is y different than y squared ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and we 're done . and obviously you might have gotten an answer in some other order , but the order in which i write these terms do n't matter . it just matters that you were able to simplify it to these four terms . | does the order really matter ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | and we 're done . and obviously you might have gotten an answer in some other order , but the order in which i write these terms do n't matter . it just matters that you were able to simplify it to these four terms . | can you combine like terms when the variables are in a different order ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | it 's 2 . where obviously both are dealing -- they 're both y terms , not xy terms , not y squared terms , just y . and so negative 3 plus 2 is negative 1 , or negative 1y is the same thing as negative y . | are 3xy and 2yx considered like terms ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | or i could literally just write x squared . 1x squared is the same thing as x squared . so plus x squared , and then these there 's nothing really left to simplify . | what app or website is that drawing thing sal khan uses ? |
now we have a very , very , very hairy expression . and once again , i 'm going to see if you can simplify this . and i 'll give you little time to do it . so this one is even crazier than the last few we 've looked at . we 've got y 's and xy 's , and x squared and x 's , well more just xy 's and y squared and on and ... | so i have minus 2x squared . do i have any other x squared ? yes , i do . | why ca n't i just add an x^4 with an x , so it would become x^5 ? |
( music ) ( `` in the sky with diamonds '' by scalding lucy ) juliana : this portrait that we 're looking at is by august sander , german photographer . this portrait is titled `` secretary at a radio station , cologne '' and it 's from about 1931 . steven : let 's see if i can remember this because it 's been a long t... | he 's almost sort of paused in the middle of something that it also looks posed . sander is definitely posing him . he 's got light set up in a certain way that 's really contrasty , it brings out the white of his jacket and then there 's sort of silver and there 's sort of the gleam of the bowl . | was sander trying to convey a message by posing this wounded soldier in a wheel chair in front of a stair case ? |
( music ) ( `` in the sky with diamonds '' by scalding lucy ) juliana : this portrait that we 're looking at is by august sander , german photographer . this portrait is titled `` secretary at a radio station , cologne '' and it 's from about 1931 . steven : let 's see if i can remember this because it 's been a long t... | because there 's a long history in photography going back to mundy of men photographing women and looking at different types of women , especially shadowsizing working class women . steven : actually it goes before photography . ( crosstalk ) steven : [ unintelligible ] dega . | did any painters of their day create paintings in black in white as a response to or inspired by photography ? |
( music ) ( `` in the sky with diamonds '' by scalding lucy ) juliana : this portrait that we 're looking at is by august sander , german photographer . this portrait is titled `` secretary at a radio station , cologne '' and it 's from about 1931 . steven : let 's see if i can remember this because it 's been a long t... | sander is definitely posing him . he 's got light set up in a certain way that 's really contrasty , it brings out the white of his jacket and then there 's sort of silver and there 's sort of the gleam of the bowl . beth : and it 's also so carefully composed ; these lines of bins or whatever they are that sort of com... | how were gelatin silver prints made ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | can an absolute value be a negative number instead of a positive one ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . | why is n't there a number line ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . | what effect does the absolute value bring into an equation ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | so what 's this going to be equal to ? 3 times 3 is 9 . so it 's the absolute value of 9 minus 9 , which is the absolute value of 0 , which is , indeed , 0 . so it does , indeed , equal 0 , and we are done . | can you explain to me why , for example |3x-9|=0 , that the -9 does not change to positive even though it has the absolute value bars ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | what do the absolute value signs mean ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | do you multiply the variables by whatever are outside the absolute value signs ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | if i told you that the absolute value of x is equal to 0 , you know that x has to be equal to 0 . that 's the only value whose absolute value is 0 . so if i told you that the absolute value of 3x minus 9 is 0 , than we know that 3x minus 9 has to be equal to 0 , and that 's kind of unique about the 0 is that , it 's th... | what real-world applications are there for absolute value ? |
we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . so we 're told that the absolute value of the something -- in this case the something is ... | we 're told , solve the absolute value of 3x minus 9 is equal to 0 , and graph the solution on a number line . so let 's just rewrite the absolute value equation . they told us that the absolute value of 3x minus 9 is equal to 0 . | what happens when there are absolute value bars on both sides of the equation ? |
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