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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ?
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how would i solve a y=kx equation if y=5x ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ?
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how do you figure out if an equation is a direct variation or not ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon .
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if y=4 when x=5 , how do i find y when x=10 ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 .
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what is 9 plus ten ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we do n't know what the rate is . k tells us the rate . if x goes down , y will be down .
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can someone explain to me how to tell if this equation is a direct variation or not : 4x + y = 3 and what is k in this equation if it is a direct variation ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there .
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what exactly is direct equation ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon .
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what is the equation for direct variation ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x .
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does y - 5 = 2x show direct variation ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs .
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what is the equation for the direct variation when y = 1 and x = 5 ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon .
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what is the equation of the function that is graphed as line b ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon .
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do the variation equation that might model the situation is c=kf ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost .
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could the situation still be modeled by a direct variation equation ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x .
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how long does it take the elevator to travel 250 feet ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x .
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what is another good real-life situation about direct variation ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs .
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what is | 2x + 1 | > 5 graphed on a line ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we do n't know what the rate is . k tells us the rate . if x goes down , y will be down .
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why do you use k what does k mean ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit .
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but could n't you just divide 18 by 2.25 and get 8 instead of using all of these fractions and variables ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 .
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i do n't understand how -2x=3y is a direct variation and 5y-x=4 and 5x-2y+3=0 are not ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x .
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is direct variation the same as direct linear variation ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x .
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how would you do direct variation if your y needs to become smaller ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost .
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how many kg of water are in a person with a mass of 50kg ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we do n't know what the rate is . k tells us the rate . if x goes down , y will be down .
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what is the volume if the temperature increases to 420 degrees k ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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ok so i have a problem that is 8+2y=0 how do you know what is x ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 .
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how would you find the direct variation in an equation like -4x + 3y = 3 ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate .
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how do you know what the x and y are ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon .
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if you doubled x would the corresponding y double in the direct variation ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x .
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what does varies directy mean ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there .
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example : x=1|2|3| y=10|20|30 that would be a direct variation right ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is .
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could direct variation be like y=-2.25x , or can y only go up as x goes up and y go down as x goes down ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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but 8 gallons is $ 18.05 would n't it be 7 gallons pluse you would have to add tax ?
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x . so that means that y is equal to some constant , we 'll just call that k , times x . this is what it means to vary directly . if x goes up , y will go up . we do n't know what the rate is . k tells us the rate . if x goes down , y will be down . now , they give us more information , and this will help us figure out what k is . if a gallon of gas costs $ 2.25 , how many gallons could you purchase for $ 18 ? so if x is equal to 1 -- this statement up here , a gallon of gas -- that tells us if we get 1 gallon , if x is equal to 1 , then y is $ 2.25 , right ? y is what it costs . they tell us 1 gallon costs $ 2.25 , so you could write it right here , $ 2.25 is equal to k times x , times 1 . well , i did n't even have to write the times 1 there . it 's essentially telling us exactly what the rate is , what k is . we do n't even have to write that 1 there . k is equal to 2.25 . that 's what this told us right there . so the equation , how y varies with x , is y is equal to 2.25x , where x is the number of gallons we purchase . y is the cost of that purchase , so it 's $ 2.25 a gallon . and then they ask us , how many gallons could you purchase for $ 18 ? so $ 18 is going to be our total cost . it is y cost of filling the car . so 18 is going to be equal to 2.25x . now if we want to solve for x , we can divide both sides by 2.25 , so let 's do that . you divide 18 by 2.25 , divide 2.25x by 2.25 , and what do we get ? let me scroll down a little bit . the right-hand side , the 2.25 's cancel out , you get x . and then what is 18 divided by 2.25 ? so let me write this down . so first of all , i just like to think of it as a fraction . 2.25 is the same thing -- let me write over here -- 2.25 is equal to 2 and 1/4 , which is the same thing as 9 over 4 . so 18 divided by 2.25 is equal to 18 divided by 9 over 4 , which is equal to 18 times 4 over 9 , or 18 over 1 times 4 over 9 . and let 's see , 18 divided by 9 is 2 , 9 divided by 9 is 1 . that simplifies pretty nicely into 8 . so 18 divided by 2.25 is 8 , so we can buy 8 gallons for $ 18 .
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we 're told that the total cost of filling up your car with gas varies directly with the number of gallons of gasoline you are purchasing . so this first statement tells us that if x is equal to the number of gallons purchased , and y is equal to the cost of filling up the car , this first statement tells us that y varies directly with the number of gallons , with x .
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how long will the food last if all the soldiers leave ?
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last video , we got a little bit of practice adding decimals that involved tenths . now let 's do slightly more complicated examples . so let 's say we wan na add four to 5.7 , or we could read the second number as five and 7/10 . pause this video , and see if you can do this . the way that my brain tries to tackle this is , i try to separate the whole numbers from the tenths , so you can view this as being the same thing as four plus five plus 7/10 . all i did here is i broke up the five and 7/10 into five plus 7/10 , and the reason why my brain likes to do that is because i can then say okay four plus five , that 's just going to be equal to nine , and then i just have to add the 7/10 . so it 's gon na be nine and 7/10 which i can rewrite , this is going to be equal to nine and 7/10 . nine and 7/10 i could write as 9.7 . even though in future videos we 're going to learn other ways of adding decimals , especially larger , more complicated decimals , this is still how my brain adds four plus 5.7 . especially if i need to do it in my head . i say okay , four plus five is nine , and then i have that 7/10 , so it 's going to be nine and 7/10 or 9.7 . now let 's do another example where both numbers involve a decimal . let 's say i want to add 6.3 to 7.4 . so 6.3 plus 7.4 . once again , pause this video and try to work through it on your own . well my brain does it the same way . i break up the whole numbers and the decimals . once again , there 's many different ways of adding decimals , but this is just one way that seems to work . especially for decimals like this . so we could view this as six and 3/10 , so i 'm breaking up the 6.3 , the six and 3/10 , into six plus 3/10 plus seven and 4/10 . seven plus 4/10 , and then this you can view as , so you could view this as six plus seven , six plus seven , plus , plus 3/10 , plus 3/10 plus 4/10 , plus 4/10 . if you add the ones here , you have six ones and seven ones , that 's going to be equal to 13 , and then 3/10 and 4/10 . if you have three of something and then you add four of that , that 's going to be 7/10 , and we would write 7/10 as 0.7 . seven in the tenths place . then what 's 13 plus 7/10 ? well that is going to be 13 . this is going to be equal to 13.7 . 13.7 , and we are done . let me do one more example that will get a little bit , a little bit more involved . so let me delete all of these . let 's say i wanted to add 6.3 to , and i 'm gon na add that to 2 point , 2.9 . pause the video and see if you can figure this out . let 's do the same thing . this is going to be six and 3/10 , so six plus 3/10 , plus two , plus 9/10 , or you could view this as six plus two , so i 'll put all my ones together . six plus two , and then i 'll put my tenths together , plus 3/10 , plus 3/10 . plus 9/10 , plus 9/10 . and so the six plus two is pretty straightforward . that is going to be equal to eight . now what 's 3/10 plus 9/10 ? this is gon na get a little bit interesting . 3/10 plus 9/10 , and i could write it out . i could say this is three tenths , this is nine tenths . well 3/10 plus 9/10 is equal to 12/10 . this is going to be 12/10 , but how do we write 12/10 as a number ? well 12/10 is the same thing as 10/10 plus 2/10 . the reason why i broke it up this way is 10/10 is one whole , so this is going to be equal to one . when you add these two together , it 's 12/10 which is the same thing as one and 2/10 . so one plus 2/10 or , well let me just write it that way . this i can rewrite as plus one plus 2/10 , and then i think you see where this is going . i could add the eight and the one , and i get nine and 2/10 . so nine and 2/10 . so it 's going to be 9.2 . the reason why this one was a little bit more interesting is i added the ones , i got six plus two is eight , but then when i added the tenths , i got something that was more than a whole . i got 12/10 which is one and 2/10 , and so i added one more whole to the eight to get nine , and then i had those 2/10 leftover . this is really good to understand because in the future when you 're adding decimals , you 'll be doing stuff like carrying from one place to another , and this is essentially what we did . when we added the 3/10 plus the 9/10 , we got 12/10 , and so we added an extra whole , and then we had the leftover 2/10 . hopefully , that makes some sense .
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well my brain does it the same way . i break up the whole numbers and the decimals . once again , there 's many different ways of adding decimals , but this is just one way that seems to work .
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what happens if the numbers get larger and have more decimals ?
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last video , we got a little bit of practice adding decimals that involved tenths . now let 's do slightly more complicated examples . so let 's say we wan na add four to 5.7 , or we could read the second number as five and 7/10 . pause this video , and see if you can do this . the way that my brain tries to tackle this is , i try to separate the whole numbers from the tenths , so you can view this as being the same thing as four plus five plus 7/10 . all i did here is i broke up the five and 7/10 into five plus 7/10 , and the reason why my brain likes to do that is because i can then say okay four plus five , that 's just going to be equal to nine , and then i just have to add the 7/10 . so it 's gon na be nine and 7/10 which i can rewrite , this is going to be equal to nine and 7/10 . nine and 7/10 i could write as 9.7 . even though in future videos we 're going to learn other ways of adding decimals , especially larger , more complicated decimals , this is still how my brain adds four plus 5.7 . especially if i need to do it in my head . i say okay , four plus five is nine , and then i have that 7/10 , so it 's going to be nine and 7/10 or 9.7 . now let 's do another example where both numbers involve a decimal . let 's say i want to add 6.3 to 7.4 . so 6.3 plus 7.4 . once again , pause this video and try to work through it on your own . well my brain does it the same way . i break up the whole numbers and the decimals . once again , there 's many different ways of adding decimals , but this is just one way that seems to work . especially for decimals like this . so we could view this as six and 3/10 , so i 'm breaking up the 6.3 , the six and 3/10 , into six plus 3/10 plus seven and 4/10 . seven plus 4/10 , and then this you can view as , so you could view this as six plus seven , six plus seven , plus , plus 3/10 , plus 3/10 plus 4/10 , plus 4/10 . if you add the ones here , you have six ones and seven ones , that 's going to be equal to 13 , and then 3/10 and 4/10 . if you have three of something and then you add four of that , that 's going to be 7/10 , and we would write 7/10 as 0.7 . seven in the tenths place . then what 's 13 plus 7/10 ? well that is going to be 13 . this is going to be equal to 13.7 . 13.7 , and we are done . let me do one more example that will get a little bit , a little bit more involved . so let me delete all of these . let 's say i wanted to add 6.3 to , and i 'm gon na add that to 2 point , 2.9 . pause the video and see if you can figure this out . let 's do the same thing . this is going to be six and 3/10 , so six plus 3/10 , plus two , plus 9/10 , or you could view this as six plus two , so i 'll put all my ones together . six plus two , and then i 'll put my tenths together , plus 3/10 , plus 3/10 . plus 9/10 , plus 9/10 . and so the six plus two is pretty straightforward . that is going to be equal to eight . now what 's 3/10 plus 9/10 ? this is gon na get a little bit interesting . 3/10 plus 9/10 , and i could write it out . i could say this is three tenths , this is nine tenths . well 3/10 plus 9/10 is equal to 12/10 . this is going to be 12/10 , but how do we write 12/10 as a number ? well 12/10 is the same thing as 10/10 plus 2/10 . the reason why i broke it up this way is 10/10 is one whole , so this is going to be equal to one . when you add these two together , it 's 12/10 which is the same thing as one and 2/10 . so one plus 2/10 or , well let me just write it that way . this i can rewrite as plus one plus 2/10 , and then i think you see where this is going . i could add the eight and the one , and i get nine and 2/10 . so nine and 2/10 . so it 's going to be 9.2 . the reason why this one was a little bit more interesting is i added the ones , i got six plus two is eight , but then when i added the tenths , i got something that was more than a whole . i got 12/10 which is one and 2/10 , and so i added one more whole to the eight to get nine , and then i had those 2/10 leftover . this is really good to understand because in the future when you 're adding decimals , you 'll be doing stuff like carrying from one place to another , and this is essentially what we did . when we added the 3/10 plus the 9/10 , we got 12/10 , and so we added an extra whole , and then we had the leftover 2/10 . hopefully , that makes some sense .
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once again , there 's many different ways of adding decimals , but this is just one way that seems to work . especially for decimals like this . so we could view this as six and 3/10 , so i 'm breaking up the 6.3 , the six and 3/10 , into six plus 3/10 plus seven and 4/10 .
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how do you add two digit numbers to decimals like 1.9 + 2 or 80+ 7.1 ?
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last video , we got a little bit of practice adding decimals that involved tenths . now let 's do slightly more complicated examples . so let 's say we wan na add four to 5.7 , or we could read the second number as five and 7/10 . pause this video , and see if you can do this . the way that my brain tries to tackle this is , i try to separate the whole numbers from the tenths , so you can view this as being the same thing as four plus five plus 7/10 . all i did here is i broke up the five and 7/10 into five plus 7/10 , and the reason why my brain likes to do that is because i can then say okay four plus five , that 's just going to be equal to nine , and then i just have to add the 7/10 . so it 's gon na be nine and 7/10 which i can rewrite , this is going to be equal to nine and 7/10 . nine and 7/10 i could write as 9.7 . even though in future videos we 're going to learn other ways of adding decimals , especially larger , more complicated decimals , this is still how my brain adds four plus 5.7 . especially if i need to do it in my head . i say okay , four plus five is nine , and then i have that 7/10 , so it 's going to be nine and 7/10 or 9.7 . now let 's do another example where both numbers involve a decimal . let 's say i want to add 6.3 to 7.4 . so 6.3 plus 7.4 . once again , pause this video and try to work through it on your own . well my brain does it the same way . i break up the whole numbers and the decimals . once again , there 's many different ways of adding decimals , but this is just one way that seems to work . especially for decimals like this . so we could view this as six and 3/10 , so i 'm breaking up the 6.3 , the six and 3/10 , into six plus 3/10 plus seven and 4/10 . seven plus 4/10 , and then this you can view as , so you could view this as six plus seven , six plus seven , plus , plus 3/10 , plus 3/10 plus 4/10 , plus 4/10 . if you add the ones here , you have six ones and seven ones , that 's going to be equal to 13 , and then 3/10 and 4/10 . if you have three of something and then you add four of that , that 's going to be 7/10 , and we would write 7/10 as 0.7 . seven in the tenths place . then what 's 13 plus 7/10 ? well that is going to be 13 . this is going to be equal to 13.7 . 13.7 , and we are done . let me do one more example that will get a little bit , a little bit more involved . so let me delete all of these . let 's say i wanted to add 6.3 to , and i 'm gon na add that to 2 point , 2.9 . pause the video and see if you can figure this out . let 's do the same thing . this is going to be six and 3/10 , so six plus 3/10 , plus two , plus 9/10 , or you could view this as six plus two , so i 'll put all my ones together . six plus two , and then i 'll put my tenths together , plus 3/10 , plus 3/10 . plus 9/10 , plus 9/10 . and so the six plus two is pretty straightforward . that is going to be equal to eight . now what 's 3/10 plus 9/10 ? this is gon na get a little bit interesting . 3/10 plus 9/10 , and i could write it out . i could say this is three tenths , this is nine tenths . well 3/10 plus 9/10 is equal to 12/10 . this is going to be 12/10 , but how do we write 12/10 as a number ? well 12/10 is the same thing as 10/10 plus 2/10 . the reason why i broke it up this way is 10/10 is one whole , so this is going to be equal to one . when you add these two together , it 's 12/10 which is the same thing as one and 2/10 . so one plus 2/10 or , well let me just write it that way . this i can rewrite as plus one plus 2/10 , and then i think you see where this is going . i could add the eight and the one , and i get nine and 2/10 . so nine and 2/10 . so it 's going to be 9.2 . the reason why this one was a little bit more interesting is i added the ones , i got six plus two is eight , but then when i added the tenths , i got something that was more than a whole . i got 12/10 which is one and 2/10 , and so i added one more whole to the eight to get nine , and then i had those 2/10 leftover . this is really good to understand because in the future when you 're adding decimals , you 'll be doing stuff like carrying from one place to another , and this is essentially what we did . when we added the 3/10 plus the 9/10 , we got 12/10 , and so we added an extra whole , and then we had the leftover 2/10 . hopefully , that makes some sense .
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nine and 7/10 i could write as 9.7 . even though in future videos we 're going to learn other ways of adding decimals , especially larger , more complicated decimals , this is still how my brain adds four plus 5.7 . especially if i need to do it in my head .
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what does sal mean by larger decimals ?
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akira receives a prize at a science fair for having the most informative project . her trophy is in the shape of a square pyramid and is covered in shiny gold foil . so this is what her trophy looks like . how much gold foil did it take to cover the trophy , including the bottom ? and so they give us some dimensions and we want how much gold foil and it 's in inches squared so it 's really going to be an area . so pause this video and see if you can figure that out . how much gold foil did it take to cover the trophy ? alright now let 's work through this together . and so essentially what they 're asking is what is the surface area of this square pyramid . and we 're doing to include the base 'cause the surface area is how much , it 's the area of the gold foil that is needed . now , sometimes , some of you might be able to think about this just by looking at this figure , but just to make sure we do n't miss any area , i 'm gon na open up this square pyramid and think about it in two dimensions . so what we 're gon na do is imagine if i were to unleash or if i were to cut the top and , let me do this in red , if i were to cut this edge , if i were to cut this edge , if i were to cut that edge , and that edge . so the edges that connect the triangular sides and if i were to just open it all up , what would this look like ? so if i were to open it all up ? well at the bottom you would have your square base . let me color that in . so you have your square base . so let me draw that . you have your square base , this is gon na be a rough drawing . and what are the dimensions there ? it 's three by three . we know this is a square pyramid so the base , all the sides are the same . they give us one side , but then this is three inches then this is gon na be three inches , as well . let me color that same color just so we recognize that we 're talking about this same base . and now if we open up the triangular faces , what 's it going to look like ? well this is going to look like this . this is a rough hand drawing , hopefully it makes sense . this is going to look like this . each of these triangular faces , they all have the exact same area . and the reason why i know that , they all have the same base , three , and they all have the same height , six inches . i 'll draw that in a second . so they all look something like this . just hand drawing it . and all of their heights , all of their height are six inches . so this right over here is six inches . this over here is six inches . this over here is six inches , and this over here is six inches . so to figure out how much gold foil we need we 're trying to figure out this surface area , which is really just gon na be the combined area of these figures . well the area of this central square is pretty easy to figure out . it 's three inches by three inches so it would be nine inches squared . now what are the area of the triangles ? well we could figure out the area of one of the triangles and then multiply by four , since there are four triangles . so the area of this triangle right over here , it 's going to be 1/2 times our base , which is three , times three , times our height , which is six . let 's see , one half times three times six , that 's one half times 18 which is equal to nine . nine square inches , or nine inches squared . so what 's gon na be our total area ? well you have the area of your square base plus you have the four sides , which each have an area of nine . so i could write it out , i could write four times nine or i could write nine -- do that black color . or i would write nine plus nine plus nine plus nine . and just to remind ourselves , that right over there is the area of one triangular face . triangular , triangular face . so this is all of the triangular faces . triangular faces . and of course we have to add that to the area of our square base . so this is nine plus nine times four , you could do this as nine times five , which is going to be 45 square inches . nine plus nine plus nine plus nine plus nine .
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so pause this video and see if you can figure that out . how much gold foil did it take to cover the trophy ? alright now let 's work through this together .
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what would the shape of the gold foil have to be to exactly cover all of the trophy ?
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akira receives a prize at a science fair for having the most informative project . her trophy is in the shape of a square pyramid and is covered in shiny gold foil . so this is what her trophy looks like . how much gold foil did it take to cover the trophy , including the bottom ? and so they give us some dimensions and we want how much gold foil and it 's in inches squared so it 's really going to be an area . so pause this video and see if you can figure that out . how much gold foil did it take to cover the trophy ? alright now let 's work through this together . and so essentially what they 're asking is what is the surface area of this square pyramid . and we 're doing to include the base 'cause the surface area is how much , it 's the area of the gold foil that is needed . now , sometimes , some of you might be able to think about this just by looking at this figure , but just to make sure we do n't miss any area , i 'm gon na open up this square pyramid and think about it in two dimensions . so what we 're gon na do is imagine if i were to unleash or if i were to cut the top and , let me do this in red , if i were to cut this edge , if i were to cut this edge , if i were to cut that edge , and that edge . so the edges that connect the triangular sides and if i were to just open it all up , what would this look like ? so if i were to open it all up ? well at the bottom you would have your square base . let me color that in . so you have your square base . so let me draw that . you have your square base , this is gon na be a rough drawing . and what are the dimensions there ? it 's three by three . we know this is a square pyramid so the base , all the sides are the same . they give us one side , but then this is three inches then this is gon na be three inches , as well . let me color that same color just so we recognize that we 're talking about this same base . and now if we open up the triangular faces , what 's it going to look like ? well this is going to look like this . this is a rough hand drawing , hopefully it makes sense . this is going to look like this . each of these triangular faces , they all have the exact same area . and the reason why i know that , they all have the same base , three , and they all have the same height , six inches . i 'll draw that in a second . so they all look something like this . just hand drawing it . and all of their heights , all of their height are six inches . so this right over here is six inches . this over here is six inches . this over here is six inches , and this over here is six inches . so to figure out how much gold foil we need we 're trying to figure out this surface area , which is really just gon na be the combined area of these figures . well the area of this central square is pretty easy to figure out . it 's three inches by three inches so it would be nine inches squared . now what are the area of the triangles ? well we could figure out the area of one of the triangles and then multiply by four , since there are four triangles . so the area of this triangle right over here , it 's going to be 1/2 times our base , which is three , times three , times our height , which is six . let 's see , one half times three times six , that 's one half times 18 which is equal to nine . nine square inches , or nine inches squared . so what 's gon na be our total area ? well you have the area of your square base plus you have the four sides , which each have an area of nine . so i could write it out , i could write four times nine or i could write nine -- do that black color . or i would write nine plus nine plus nine plus nine . and just to remind ourselves , that right over there is the area of one triangular face . triangular , triangular face . so this is all of the triangular faces . triangular faces . and of course we have to add that to the area of our square base . so this is nine plus nine times four , you could do this as nine times five , which is going to be 45 square inches . nine plus nine plus nine plus nine plus nine .
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and we 're doing to include the base 'cause the surface area is how much , it 's the area of the gold foil that is needed . now , sometimes , some of you might be able to think about this just by looking at this figure , but just to make sure we do n't miss any area , i 'm gon na open up this square pyramid and think about it in two dimensions . so what we 're gon na do is imagine if i were to unleash or if i were to cut the top and , let me do this in red , if i were to cut this edge , if i were to cut this edge , if i were to cut that edge , and that edge .
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and desktop computers do n't have touchscreen and sal is using a desktop computer & a mac so how is it touch screened ?
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we 've already seen and you 're probably getting tired of me pointing it out repeatedly , that this yellow area right over here , this area under the curve y is equal to f of x and above the positive x-axis or i guess i can say just above the x-axis between x equals a and x equals b , that we can denote this area right over here as the definite integral of from a to b of f of x dx . now what i want to explore in this video and it 'll come up with kind of an answer that you probably could have guessed on your own , but at least get an intuition for it , is that i want to start thinking about the area under the curve that 's a scaled version of f of x . let 's say it 's y is equal to c times f of x. y is equal to some number times f of x , so it 's scaling f of x . and so i want this to be kind of some arbitrary number , but just to help me visualize , you know i have to draw something so i 'm just gon na kind of in my head let 's just pretend the c is a three for visualization purposes . so it 's going to be three times , so instead of one , instead of this far right over here it 's going to be about this far . for right over here , instead of this far right over here it 's going to be that and another right over there . and then instead of it 's going to be about there . and then instead of it being like that it 's going to be one , two and then three , right around there . so i 'm starting to get a sense of what this curve is going to look like , a scaled version of f of x . and at least what i 'm drawing is pretty close to three times f of x , but just to give you an idea is going to look something like , and let 's see over here if this distance , do a second one , a third one , is gon na be up here . it 's gon na look something like this . it 's gon na look something like that . so this is a scaled version and the scale i did right here i assumed a positive c greater than zero , but this is just for visualization purposes . now what do we think the area under this curve is going to be between a and b ? so what do we think this area right over here is going to be ? now we already know how we can denote it . that area right over there is equal to the definite integral from a to b of the function we 're integrating is c f of x dx . i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again . well let 's say the vertical dimension is alpha and the horizontal dimension is beta . we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height . now obviously that changes as our x changes , but when you think back to the reimann sums the f of x was what gave us the height of our rectangles . we 're now scaling up the height or scaling i should say because we might be scaling down depending on the c. we 're scaling it , we 're scaling one dimension by c. if you scale one dimension by c you 're gon na scale the area by c. so this right over here , the integral , let me just rewrite it . the integral from a to b of c f of x dx , that 's just going to be the scaled , we 're just going to take the area of f of x , so let me do that in the same color . we 're going to take the area under the curve f of x from a to b f of x dx and we 're just going to scale it up by this c. so you might say , `` okay maybe i could have felt `` that was , you know , if i have a c inside the integral `` now i can take the c out of the integral '' , and once again this is not a rigorous proof based on the definition of the definite integral , but it hopefully gives you a little bit of intuition why you can do this . if you scale up the function , you 're essentially scaling up the vertical dimension , so the area under this is going to just be a scaled up version of the area under the original function f of x . and once again really , really , really useful property of definite integrals that 's going to help us solve a bunch of definite integrals . and kind of clarify what we 're even doing with them .
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how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again . well let 's say the vertical dimension is alpha and the horizontal dimension is beta .
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but should n't it be `` greater than one '' since this is a vertical stretch ( not a compression , from the way it was drawn ) ?
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we 've already seen and you 're probably getting tired of me pointing it out repeatedly , that this yellow area right over here , this area under the curve y is equal to f of x and above the positive x-axis or i guess i can say just above the x-axis between x equals a and x equals b , that we can denote this area right over here as the definite integral of from a to b of f of x dx . now what i want to explore in this video and it 'll come up with kind of an answer that you probably could have guessed on your own , but at least get an intuition for it , is that i want to start thinking about the area under the curve that 's a scaled version of f of x . let 's say it 's y is equal to c times f of x. y is equal to some number times f of x , so it 's scaling f of x . and so i want this to be kind of some arbitrary number , but just to help me visualize , you know i have to draw something so i 'm just gon na kind of in my head let 's just pretend the c is a three for visualization purposes . so it 's going to be three times , so instead of one , instead of this far right over here it 's going to be about this far . for right over here , instead of this far right over here it 's going to be that and another right over there . and then instead of it 's going to be about there . and then instead of it being like that it 's going to be one , two and then three , right around there . so i 'm starting to get a sense of what this curve is going to look like , a scaled version of f of x . and at least what i 'm drawing is pretty close to three times f of x , but just to give you an idea is going to look something like , and let 's see over here if this distance , do a second one , a third one , is gon na be up here . it 's gon na look something like this . it 's gon na look something like that . so this is a scaled version and the scale i did right here i assumed a positive c greater than zero , but this is just for visualization purposes . now what do we think the area under this curve is going to be between a and b ? so what do we think this area right over here is going to be ? now we already know how we can denote it . that area right over there is equal to the definite integral from a to b of the function we 're integrating is c f of x dx . i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again . well let 's say the vertical dimension is alpha and the horizontal dimension is beta . we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height . now obviously that changes as our x changes , but when you think back to the reimann sums the f of x was what gave us the height of our rectangles . we 're now scaling up the height or scaling i should say because we might be scaling down depending on the c. we 're scaling it , we 're scaling one dimension by c. if you scale one dimension by c you 're gon na scale the area by c. so this right over here , the integral , let me just rewrite it . the integral from a to b of c f of x dx , that 's just going to be the scaled , we 're just going to take the area of f of x , so let me do that in the same color . we 're going to take the area under the curve f of x from a to b f of x dx and we 're just going to scale it up by this c. so you might say , `` okay maybe i could have felt `` that was , you know , if i have a c inside the integral `` now i can take the c out of the integral '' , and once again this is not a rigorous proof based on the definition of the definite integral , but it hopefully gives you a little bit of intuition why you can do this . if you scale up the function , you 're essentially scaling up the vertical dimension , so the area under this is going to just be a scaled up version of the area under the original function f of x . and once again really , really , really useful property of definite integrals that 's going to help us solve a bunch of definite integrals . and kind of clarify what we 're even doing with them .
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now what i want to explore in this video and it 'll come up with kind of an answer that you probably could have guessed on your own , but at least get an intuition for it , is that i want to start thinking about the area under the curve that 's a scaled version of f of x . let 's say it 's y is equal to c times f of x. y is equal to some number times f of x , so it 's scaling f of x . and so i want this to be kind of some arbitrary number , but just to help me visualize , you know i have to draw something so i 'm just gon na kind of in my head let 's just pretend the c is a three for visualization purposes .
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why does y=f ( x ) graph and y=c*f ( x ) look different in shape ?
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we 've already seen and you 're probably getting tired of me pointing it out repeatedly , that this yellow area right over here , this area under the curve y is equal to f of x and above the positive x-axis or i guess i can say just above the x-axis between x equals a and x equals b , that we can denote this area right over here as the definite integral of from a to b of f of x dx . now what i want to explore in this video and it 'll come up with kind of an answer that you probably could have guessed on your own , but at least get an intuition for it , is that i want to start thinking about the area under the curve that 's a scaled version of f of x . let 's say it 's y is equal to c times f of x. y is equal to some number times f of x , so it 's scaling f of x . and so i want this to be kind of some arbitrary number , but just to help me visualize , you know i have to draw something so i 'm just gon na kind of in my head let 's just pretend the c is a three for visualization purposes . so it 's going to be three times , so instead of one , instead of this far right over here it 's going to be about this far . for right over here , instead of this far right over here it 's going to be that and another right over there . and then instead of it 's going to be about there . and then instead of it being like that it 's going to be one , two and then three , right around there . so i 'm starting to get a sense of what this curve is going to look like , a scaled version of f of x . and at least what i 'm drawing is pretty close to three times f of x , but just to give you an idea is going to look something like , and let 's see over here if this distance , do a second one , a third one , is gon na be up here . it 's gon na look something like this . it 's gon na look something like that . so this is a scaled version and the scale i did right here i assumed a positive c greater than zero , but this is just for visualization purposes . now what do we think the area under this curve is going to be between a and b ? so what do we think this area right over here is going to be ? now we already know how we can denote it . that area right over there is equal to the definite integral from a to b of the function we 're integrating is c f of x dx . i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again . well let 's say the vertical dimension is alpha and the horizontal dimension is beta . we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height . now obviously that changes as our x changes , but when you think back to the reimann sums the f of x was what gave us the height of our rectangles . we 're now scaling up the height or scaling i should say because we might be scaling down depending on the c. we 're scaling it , we 're scaling one dimension by c. if you scale one dimension by c you 're gon na scale the area by c. so this right over here , the integral , let me just rewrite it . the integral from a to b of c f of x dx , that 's just going to be the scaled , we 're just going to take the area of f of x , so let me do that in the same color . we 're going to take the area under the curve f of x from a to b f of x dx and we 're just going to scale it up by this c. so you might say , `` okay maybe i could have felt `` that was , you know , if i have a c inside the integral `` now i can take the c out of the integral '' , and once again this is not a rigorous proof based on the definition of the definite integral , but it hopefully gives you a little bit of intuition why you can do this . if you scale up the function , you 're essentially scaling up the vertical dimension , so the area under this is going to just be a scaled up version of the area under the original function f of x . and once again really , really , really useful property of definite integrals that 's going to help us solve a bunch of definite integrals . and kind of clarify what we 're even doing with them .
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and at least what i 'm drawing is pretty close to three times f of x , but just to give you an idea is going to look something like , and let 's see over here if this distance , do a second one , a third one , is gon na be up here . it 's gon na look something like this . it 's gon na look something like that . so this is a scaled version and the scale i did right here i assumed a positive c greater than zero , but this is just for visualization purposes .
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is there a reason or is it suppose to look the same but sal simply made a small drawing error ?
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we 've already seen and you 're probably getting tired of me pointing it out repeatedly , that this yellow area right over here , this area under the curve y is equal to f of x and above the positive x-axis or i guess i can say just above the x-axis between x equals a and x equals b , that we can denote this area right over here as the definite integral of from a to b of f of x dx . now what i want to explore in this video and it 'll come up with kind of an answer that you probably could have guessed on your own , but at least get an intuition for it , is that i want to start thinking about the area under the curve that 's a scaled version of f of x . let 's say it 's y is equal to c times f of x. y is equal to some number times f of x , so it 's scaling f of x . and so i want this to be kind of some arbitrary number , but just to help me visualize , you know i have to draw something so i 'm just gon na kind of in my head let 's just pretend the c is a three for visualization purposes . so it 's going to be three times , so instead of one , instead of this far right over here it 's going to be about this far . for right over here , instead of this far right over here it 's going to be that and another right over there . and then instead of it 's going to be about there . and then instead of it being like that it 's going to be one , two and then three , right around there . so i 'm starting to get a sense of what this curve is going to look like , a scaled version of f of x . and at least what i 'm drawing is pretty close to three times f of x , but just to give you an idea is going to look something like , and let 's see over here if this distance , do a second one , a third one , is gon na be up here . it 's gon na look something like this . it 's gon na look something like that . so this is a scaled version and the scale i did right here i assumed a positive c greater than zero , but this is just for visualization purposes . now what do we think the area under this curve is going to be between a and b ? so what do we think this area right over here is going to be ? now we already know how we can denote it . that area right over there is equal to the definite integral from a to b of the function we 're integrating is c f of x dx . i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again . well let 's say the vertical dimension is alpha and the horizontal dimension is beta . we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height . now obviously that changes as our x changes , but when you think back to the reimann sums the f of x was what gave us the height of our rectangles . we 're now scaling up the height or scaling i should say because we might be scaling down depending on the c. we 're scaling it , we 're scaling one dimension by c. if you scale one dimension by c you 're gon na scale the area by c. so this right over here , the integral , let me just rewrite it . the integral from a to b of c f of x dx , that 's just going to be the scaled , we 're just going to take the area of f of x , so let me do that in the same color . we 're going to take the area under the curve f of x from a to b f of x dx and we 're just going to scale it up by this c. so you might say , `` okay maybe i could have felt `` that was , you know , if i have a c inside the integral `` now i can take the c out of the integral '' , and once again this is not a rigorous proof based on the definition of the definite integral , but it hopefully gives you a little bit of intuition why you can do this . if you scale up the function , you 're essentially scaling up the vertical dimension , so the area under this is going to just be a scaled up version of the area under the original function f of x . and once again really , really , really useful property of definite integrals that 's going to help us solve a bunch of definite integrals . and kind of clarify what we 're even doing with them .
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i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again .
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if integration gives the area under a curve , will it be always positive ?
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we 've already seen and you 're probably getting tired of me pointing it out repeatedly , that this yellow area right over here , this area under the curve y is equal to f of x and above the positive x-axis or i guess i can say just above the x-axis between x equals a and x equals b , that we can denote this area right over here as the definite integral of from a to b of f of x dx . now what i want to explore in this video and it 'll come up with kind of an answer that you probably could have guessed on your own , but at least get an intuition for it , is that i want to start thinking about the area under the curve that 's a scaled version of f of x . let 's say it 's y is equal to c times f of x. y is equal to some number times f of x , so it 's scaling f of x . and so i want this to be kind of some arbitrary number , but just to help me visualize , you know i have to draw something so i 'm just gon na kind of in my head let 's just pretend the c is a three for visualization purposes . so it 's going to be three times , so instead of one , instead of this far right over here it 's going to be about this far . for right over here , instead of this far right over here it 's going to be that and another right over there . and then instead of it 's going to be about there . and then instead of it being like that it 's going to be one , two and then three , right around there . so i 'm starting to get a sense of what this curve is going to look like , a scaled version of f of x . and at least what i 'm drawing is pretty close to three times f of x , but just to give you an idea is going to look something like , and let 's see over here if this distance , do a second one , a third one , is gon na be up here . it 's gon na look something like this . it 's gon na look something like that . so this is a scaled version and the scale i did right here i assumed a positive c greater than zero , but this is just for visualization purposes . now what do we think the area under this curve is going to be between a and b ? so what do we think this area right over here is going to be ? now we already know how we can denote it . that area right over there is equal to the definite integral from a to b of the function we 're integrating is c f of x dx . i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again . well let 's say the vertical dimension is alpha and the horizontal dimension is beta . we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height . now obviously that changes as our x changes , but when you think back to the reimann sums the f of x was what gave us the height of our rectangles . we 're now scaling up the height or scaling i should say because we might be scaling down depending on the c. we 're scaling it , we 're scaling one dimension by c. if you scale one dimension by c you 're gon na scale the area by c. so this right over here , the integral , let me just rewrite it . the integral from a to b of c f of x dx , that 's just going to be the scaled , we 're just going to take the area of f of x , so let me do that in the same color . we 're going to take the area under the curve f of x from a to b f of x dx and we 're just going to scale it up by this c. so you might say , `` okay maybe i could have felt `` that was , you know , if i have a c inside the integral `` now i can take the c out of the integral '' , and once again this is not a rigorous proof based on the definition of the definite integral , but it hopefully gives you a little bit of intuition why you can do this . if you scale up the function , you 're essentially scaling up the vertical dimension , so the area under this is going to just be a scaled up version of the area under the original function f of x . and once again really , really , really useful property of definite integrals that 's going to help us solve a bunch of definite integrals . and kind of clarify what we 're even doing with them .
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we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height . now obviously that changes as our x changes , but when you think back to the reimann sums the f of x was what gave us the height of our rectangles .
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what about negative c , can the area be negative ?
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we 've already seen and you 're probably getting tired of me pointing it out repeatedly , that this yellow area right over here , this area under the curve y is equal to f of x and above the positive x-axis or i guess i can say just above the x-axis between x equals a and x equals b , that we can denote this area right over here as the definite integral of from a to b of f of x dx . now what i want to explore in this video and it 'll come up with kind of an answer that you probably could have guessed on your own , but at least get an intuition for it , is that i want to start thinking about the area under the curve that 's a scaled version of f of x . let 's say it 's y is equal to c times f of x. y is equal to some number times f of x , so it 's scaling f of x . and so i want this to be kind of some arbitrary number , but just to help me visualize , you know i have to draw something so i 'm just gon na kind of in my head let 's just pretend the c is a three for visualization purposes . so it 's going to be three times , so instead of one , instead of this far right over here it 's going to be about this far . for right over here , instead of this far right over here it 's going to be that and another right over there . and then instead of it 's going to be about there . and then instead of it being like that it 's going to be one , two and then three , right around there . so i 'm starting to get a sense of what this curve is going to look like , a scaled version of f of x . and at least what i 'm drawing is pretty close to three times f of x , but just to give you an idea is going to look something like , and let 's see over here if this distance , do a second one , a third one , is gon na be up here . it 's gon na look something like this . it 's gon na look something like that . so this is a scaled version and the scale i did right here i assumed a positive c greater than zero , but this is just for visualization purposes . now what do we think the area under this curve is going to be between a and b ? so what do we think this area right over here is going to be ? now we already know how we can denote it . that area right over there is equal to the definite integral from a to b of the function we 're integrating is c f of x dx . i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again . well let 's say the vertical dimension is alpha and the horizontal dimension is beta . we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height . now obviously that changes as our x changes , but when you think back to the reimann sums the f of x was what gave us the height of our rectangles . we 're now scaling up the height or scaling i should say because we might be scaling down depending on the c. we 're scaling it , we 're scaling one dimension by c. if you scale one dimension by c you 're gon na scale the area by c. so this right over here , the integral , let me just rewrite it . the integral from a to b of c f of x dx , that 's just going to be the scaled , we 're just going to take the area of f of x , so let me do that in the same color . we 're going to take the area under the curve f of x from a to b f of x dx and we 're just going to scale it up by this c. so you might say , `` okay maybe i could have felt `` that was , you know , if i have a c inside the integral `` now i can take the c out of the integral '' , and once again this is not a rigorous proof based on the definition of the definite integral , but it hopefully gives you a little bit of intuition why you can do this . if you scale up the function , you 're essentially scaling up the vertical dimension , so the area under this is going to just be a scaled up version of the area under the original function f of x . and once again really , really , really useful property of definite integrals that 's going to help us solve a bunch of definite integrals . and kind of clarify what we 're even doing with them .
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i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again .
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but how do we take the slope of an area ?
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we 've already seen and you 're probably getting tired of me pointing it out repeatedly , that this yellow area right over here , this area under the curve y is equal to f of x and above the positive x-axis or i guess i can say just above the x-axis between x equals a and x equals b , that we can denote this area right over here as the definite integral of from a to b of f of x dx . now what i want to explore in this video and it 'll come up with kind of an answer that you probably could have guessed on your own , but at least get an intuition for it , is that i want to start thinking about the area under the curve that 's a scaled version of f of x . let 's say it 's y is equal to c times f of x. y is equal to some number times f of x , so it 's scaling f of x . and so i want this to be kind of some arbitrary number , but just to help me visualize , you know i have to draw something so i 'm just gon na kind of in my head let 's just pretend the c is a three for visualization purposes . so it 's going to be three times , so instead of one , instead of this far right over here it 's going to be about this far . for right over here , instead of this far right over here it 's going to be that and another right over there . and then instead of it 's going to be about there . and then instead of it being like that it 's going to be one , two and then three , right around there . so i 'm starting to get a sense of what this curve is going to look like , a scaled version of f of x . and at least what i 'm drawing is pretty close to three times f of x , but just to give you an idea is going to look something like , and let 's see over here if this distance , do a second one , a third one , is gon na be up here . it 's gon na look something like this . it 's gon na look something like that . so this is a scaled version and the scale i did right here i assumed a positive c greater than zero , but this is just for visualization purposes . now what do we think the area under this curve is going to be between a and b ? so what do we think this area right over here is going to be ? now we already know how we can denote it . that area right over there is equal to the definite integral from a to b of the function we 're integrating is c f of x dx . i guess to make the question a little bit clearer , how does this relate to this ? how does this green area relate to this yellow area ? well one way to think about it is we just scaled the vertical dimension up by c , so one way that you could reason it is if i 'm finding the area of something , if i have the area of a rectangle and i have the vertical dimension is let 's say i do n't want to use those same letters over and over again . well let 's say the vertical dimension is alpha and the horizontal dimension is beta . we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height . now obviously that changes as our x changes , but when you think back to the reimann sums the f of x was what gave us the height of our rectangles . we 're now scaling up the height or scaling i should say because we might be scaling down depending on the c. we 're scaling it , we 're scaling one dimension by c. if you scale one dimension by c you 're gon na scale the area by c. so this right over here , the integral , let me just rewrite it . the integral from a to b of c f of x dx , that 's just going to be the scaled , we 're just going to take the area of f of x , so let me do that in the same color . we 're going to take the area under the curve f of x from a to b f of x dx and we 're just going to scale it up by this c. so you might say , `` okay maybe i could have felt `` that was , you know , if i have a c inside the integral `` now i can take the c out of the integral '' , and once again this is not a rigorous proof based on the definition of the definite integral , but it hopefully gives you a little bit of intuition why you can do this . if you scale up the function , you 're essentially scaling up the vertical dimension , so the area under this is going to just be a scaled up version of the area under the original function f of x . and once again really , really , really useful property of definite integrals that 's going to help us solve a bunch of definite integrals . and kind of clarify what we 're even doing with them .
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we know that the area is going to be alpha times beta . now if i scale up the vertical dimension by c , so instead of alpha this is c times alpha and this is , the width is beta , if i scale up the vertical dimension by c so this is now c times alpha , what 's the area going to be ? well it 's going to be c alpha times beta , or another way to think of it , when i scale one of the dimensions by c i take my old area and i scale up my old area up by c. and that 's what we 're doing , we 're scaling up the vertical dimension by c. when you multiply c times f of x , f of x is giving us the vertical height .
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what if we scale the horizontal axis instead of the vertical axis , by c ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie .
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what is the diffrence between fractions and decimals ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie .
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what is the line that separates the numerator from the denominator ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 .
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can we ever put the denominator on top of the numerator and still get a improper fraction ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first .
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what is the mersadie 's emblem ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices .
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ann has how much more than carol ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices .
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why is pizza also called pie ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these .
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how were there instantly 8 pieces ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie .
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how you convert the denominator ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie .
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have you watched the star wars the force awakens ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 .
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what fraction of the population remained in single damily homes ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ?
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tiffany ate 1 slice of cake.omar ate 2 slices.if tiffany ate 1/5 of the cake and all the slices are the same size , what fraction of the cake was eaten in total ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these .
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could n't you just add the amount of pie eaten by brandon and gabriela together ( 5 + 3 ) to arrive at ( 5+3 ) /9 or 8/9 ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ?
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why does sal only make the vidios ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten .
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what is 2/5 = to ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see .
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is there a easier way to multiply fractions ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie .
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if jose makes four flower arrangements , how many daisy flowers do you need ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices .
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why is pie a `` slang '' term for pizza , in the annotation ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see .
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why is the bottom number is called the denominator ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie .
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why are fractions so important ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ?
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how many yards did alicia use to make the tablecloth ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices .
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in the video , why does the slices have to be equal slices , will the amount be different ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it .
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do you need to know fractions , or lets say division to get a good job ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices .
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how many total pieces were there ?
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brandon ate 5 slices of apple -- of pie . i 'm just assuming it 's apple pie . they did n't tell me that . gabriela ate 3 slices . if there were originally 9 slices , what fraction of the pie was eaten ? so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best . so let 's see how good i am at drawing a pie . so i 'll just draw it from the top view as a circle . and there 're 9 slices . i think it 's a reasonable assumption to say that they 're 9 equal slices . so we have 9 equal slices of pie . and i 'll just make sure they 're initially 9 equal slices . what fraction of the pie was eaten ? so let 's first divide this into 9 sections . so one way i could do that , i could divide it into 3 sections first , so it looks like a peace symbol . it actually looks more like the mercedes emblem . so i 'll draw it into 3 sections first . then i 'll do each of those into 3 sections , and i 'll have 9 . so let 's see , i 'll draw like that and like that . keep in mind , i 'm trying to make these as equal as possible . so bear with me if they do n't look 100 % equal , but i 'm trying . i am trying my best . so 9 equal slices -- so that looks pretty respectable . so here 's our pie that initially had 9 equal slices . now , they tell us that brandon ate 5 slices of pie . so brandon eats -- he seems like a hungry young man -- so he eats 1 , 2 , 3 , 4 , 5 . you could say that he ate 5/9 of the pie . but that 's not it . that 's not what they 're asking . it 's saying total , not just how much did brandon eat , but how much was eaten total between brandon and gabriela . and they tell us gabriela ate 3 slices . so she ate 1 -- sounds like they did n't really eat dinner -- 1 , 2 , 3 . so now let 's answer their question . what fraction of the pie was eaten ? well , we know that there was a total of 9 equal slices of pie . what fraction was eaten ? well , as we see , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 . 8/9 of the pie was eaten . so let 's actually type that in . and then we will do it right over here . we 'd say 8 , and we use that little slash symbol on your computer like this . 8 over 9 or 8 divided by 9 or 8/9 of the pie was eaten . let 's do a couple more of these . ishaan ate 2 slices of pizza . omar ate 3 slices . if there were originally 8 slices , what fraction of the pie is remaining ? so this is interesting . actually , let me copy and paste this so that i can do it on my little notepad right over here . so let 's do it right over -- trying to find some space . there you go . let me put that in here . so the same thing , we have -- well , this is a pizza now , not a pie . and so pizza i will draw in brown . it has 8 , and we can assume it 's initially 8 equal slices . so it 's actually a little bit easier to draw 8 equal slices , since 8 is an even number . so let 's see . that is my best attempt at drawing a circle . and let 's see , first i can divide the pizza into 2 slices , then i can divide it into 4 slices . and i 'm going to try to make them look as equal as possible . and now i 'm going to -- with two more cuts , i should be able to get 8 so -- and one more just like this . so there you have it , a pizza that has 8 equal slices . now , they tell us ishaan ate 2 slices of pizza . so he eats 1 , 2 slices of pizza . omar ate 3 slices . omar ate 3 . so he eats 1 , 2 , 1 , 2 , 3 slices of pizza . now , you might immediately say , oh , ok , the answer to this must be 1 , 2 , 3 , 4 , 5 . it must be that they ate 5 slices of pizza over a total of 8 slices of pizza . so they ate 5/8 of the pizza . you would be right in saying that they ate 5/8 of the pizza , because they ate 1 , 2 , 3 , 4 , 5 out of a total of 8 pieces . but that 's not what this question is asking . they are asking , what fraction of the pizza is remaining ? so what 's left over after ishaan and omar had their go at the pizza ? well , what 's remaining is 1 , 2 , 3 slices . so what 's remaining is 3 out of the original 8 equal parts or 3/8 of the pizza is remaining . so let 's input that . so we could go right here . and we would say 3 over 8 , 3/8 , is remaining . so let 's check our answer , and we got it right .
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so let me see if i can draw this thing out . so let me draw the pie . i will draw the pie in a yellowish color . so let me try my best .
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how do sal draw on a computer , with his mouse or with a drawing pad ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ?
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why there are two lines on s ( reminds me of ducktales ' sign ) , but on my keyboard , there is only one line crossing s ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas .
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how will you know which one is the base and the amount depending on the queston ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas .
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i 'm confused at the part when sal writes 0 , 0.7x = 12.60 how does that happen and why ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here .
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how much interest was phillip charged on his second bill ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off .
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what is 17 % of 400 ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ?
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what is the highest marked price that christopher can afford ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 .
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given a number , say 3000 that increases to 3150 after 6 months , how do i determine what precentage the number increased by ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas .
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by what percentage did gulnar 's bank account increase over the past day ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off .
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how do you find a percent when it decreases ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ?
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do you have to multiply if the sale is gone and you do n't know how to multiply , so what do you do ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 .
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a man saves rs 200 at the end of each year and lends the money at 5 % compound interest how much will it become at the end of 3 years ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off .
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a store has a total ot 15.000 available for its montly expensed the store budget sets aside 10 percent of is budget for electricity how much money does the store plan to spend on electricity each month ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number .
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how is 0.30x equivlant to 70 percent ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure .
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what does '' home school '' mean ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 .
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how does adding 20 percent the same as multiplying by 1.20 ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 .
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where did the 1,20 come from ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas .
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why not just 3x-3 ( 0.7 ) x=12.60 to shorten the problem ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 .
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if 50 liters were on hand , how much water should be added to reduce the sugar concentration to 3 % sugar ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off .
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how do you turn a fraction into a percent ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 .
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why would you put the variable x in front of the decimal 0.30 in the algabraic equation above ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas .
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and why is x =1 ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas .
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in class or somewhere else , how would you know to divide by x ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas .
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and how do we find how much is the original guava price ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas .
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i 'm not asking a question but u mostly confuse me when u did the math x-0.3x=12.60 this is what i came up with in my mind .3x to the second power =12.60 ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas .
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hi sal , how r u , i hav one doubt in this question , first u say that in 1st day 30 % off and in next day 30 % off closes so u hav to calculate without 30 % off on 2guavas ... .. but u calculated 30 % off on 2 guavas too ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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$ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ?
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so what is 30 % of the 6 guavas also what is the original price before sale ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 .
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would $ 5.46 be equivalent to $ 6 ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 .
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if 42 % of a number n is 8.4 , what is the value of n ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off .
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how to calculate a fraction ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off .
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how to calculate a percentage ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off .
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what is the survival rate of the seedling ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number .
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how did sal get 70 % in the math problem ?
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let 's say i go to the fruit store today and they have a sale on guavas . everything is 30 % off . this is for guavas . and it 's only today . only today . so i say , you know what , let me go buy a bunch of guavas . so i go and i buy 6 guavas . so i buy six guavas . and it ends up , when i go to the register , and we 're assuming no tax , it 's a grocery and i live in a state where they do n't tax groceries . so for the 6 guavas , they charge me , i get the 30 % off . they charge me $ 12.60 . $ 12.60 . so this is the 30 % off sale price on 6 guavas . i go home , and then my wife tells me , you know , sal , can you go get 2 more guavas tomorrow ? i say , sure . so the next day i go and i want to buy 2 more guavas . so , 2 guavas . but now the sale is off . there 's no more 30 % . that was only that first day that i bought the 6 . so how much are those two guavas going to cost me ? how much are those two guavas going to cost at full price ? at full price ? so , a good place to start is , to think about how much would those 6 guavas have cost us at full price ? this is the sale price , right here ? this is the sale price . how much would those have cost me at full price ? so let 's do a little bit of algebra here . pick a suitable color for the algebra . maybe this grey color . so , let 's say that x is equal to the cost of 6 guarvas . 6 guavas , at full price . so , essentially , if we take 30 % off of this , we should get $ 12.60 . so let 's do that . so if we have the full price of 6 guavas , we 're going to take 30 % off of that . so that 's the same thing as 0.30 . or i could just write 0.3 . i could ignore that zero if i like . actually , let me write it like this . my wife is always bugging me to write zeroes before decimals . so that 's the full price of 6 guavas minus 0.30 times the full price of guavas . some i 'm just taking 30 % off of the full price , off of the full price . this is how we figure out the sale price . this is going to be equal to that $ 12.60 right there . that 's going to be equal to $ 12.60 . i just took 30 % off of the full price . and now we just do algebra . we could imagine there 's a 1 in front -- you know , x is the same thing as 1x . so 1x minus 0.3x is going to be equal to 0.7x . so we get 0.7x , or we could say 0.70 if you like . same number . point , or 0.7x , is equal to 12.60 . and once you get used to these problems , you might just skip straight to this step right here . where you say , 70 % of the full price is equal to my sale price , right ? i took 30 % off . this is 70 % of the full price . you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals . so let 's do that . so we get 0.7 goes into 12.60 . let 's multiply both of these numbers by 10 , which is what we do when we move both of their decimals one to the right . so the 0.7 becomes a 7 . ignore that right there . the 12.60 becomes 126 , put the decimal right there . decimal right there . and we 're ready to just do straight up long division . so this is now a 7 , not a .7 . so 7 goes into 12 1 time . 1 times 7 is 7 . 12 minus 7 is 5 . bring down the 6 . 7 goes into 56 8 times . 8 times 7 is 56 . and then we have no remainder . so it 's 18 , and there 's nothing behind the decimal point . so it ; s 18 , in our case , $ 18 . so x is equal to $ 18 . remember what x was ? x was the full price of 6 guavas . x was the full price of 6. x is the full price of 6 guavas . now , the question is , how much will 2 guavas cost me at the full price ? well , this is full price of 6 . so you immediately could figure out what 's the full price of one guava . you divide 18 by 6 . so 18 divided by 6 is $ 3 . that 's $ 3 per guava at full price . and they 're asking us , we want 2 guavas . so 2 guavas is going to be 2 times $ 3 , so this is going to be $ 6 . $ 6 . another way you could have done it , you could have just said , hey , 6 at full price are going to cost me $ 18 . 2 is 1/3 of 6 . so 1/3 of $ 18 is $ 6 . so , just to give a quick review what we did . we said the sale price on six guavas , $ 12.60 . that 's 30 % off the full price . or you could say this is 70 % of the full price . 70 % of the full price . and so you could say , 30 % -- so if you say x is the full price of 6 guavas , you could say the full price of 6 guavas minus 30 % of the full price of 6 guavas is equal to 12.60 , and that 's equivalent to saying , 70 % of the full price is 12.60 . you divided -- then we just solved this algebraically . divide both sides by 0.7 , and then we got x , the full price of 6 guavas , is $ 18 , or that 's $ 3 per guava or $ 6 for 2 . anyway , hopefully you found that helpful .
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you might just skip to this step once you get used to these problems in a little bit . and now we just have to solve for x. divide both sides by 0.7 , so you get x is equal to 12.60 divided by 0.7 . we could use a calculator , but it 's always good to get a little bit of practice dividing decimals .
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what the heck does x-0.30x mean ?
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