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Current time:0:00Total duration:4:36

Multiplying fractions word problem: pumpkin pie

Video transcript

ken and Isaiah are eating pumpkin pie with their friends they want to figure out how much pie they have eaten so far there are seven of them in total and each of them has eaten two-fifths of a pie ken said you can solve this problem by multiplying 2/5 times 7 and that makes sense each of them a 2/5 and there's 7 folks I would multiply 2/5 times 7 so he multiplied and got 14 over 35 now this is a little bit suspicious and here is the work that he did he said 2/5 times 7 is equal to 2 times 7 over 5 times 7 which equals 14 35 so this is starting to smell real fishy right now Isaiah says that 14:30 fifths cannot be correct because 14 30 fifths is less than one whole pie so this is definitely true that 14 30 fifths is less than one whole pie which of the following best explains this situation so let's before even looking at the explanations let's see what's fishy about this so let me get my little notepad and write it out so he literally took 2/5 and he attempted to multiply it by 7 and he said that this is the same thing as taking the 2 times the 7 over the 5 times the 7 and that's how he got the 14 over 35 I encourage you to pause this and try to figure out why this doesn't make sense yourself now let's think about what actually went on here if you multiply 2/5 times or if you multiply 7 times you multiply the numerator times 7 and the denominator by 7 you're actually not changing the value of the fraction this is equivalent to saying 2/5 times 7 over 7 which is the equivalent to 2/5 times 1 which is equivalent to 2/5 14 over 35 is just another way it's an equivalent representation of 2/5 this is just how much pie only one person should have eaten so how should he have thought about this well there's a couple of ways you could think of it 2/5 times 7 could literally mean 7 2/5 it literally could mean so 2/5 times 7 literally means 1 2/5 plus another 2/5 plus another 2/5 so we do this 7 times so that's 4 2/5 that's 5 2/5 that's 6 2/5 and that's 7 two-fifths sorry my brain isn't working and that's seven two-fifths and if you were to add all of these together how many fifths do you have how many fists do you have well you have two plus two plus two plus two plus two let's see that's five plus two plus two you have to seven times fifths or this is another way of saying you have seven times let me write it this way you have two times seven fifths or another way of saying is this is equal to fourteen over fourteen over five and this is more than this is what well over more than one five goes into 14 two times and you have remainder of four so it's two and four fifths hi so this is what he should have done but you might be saying well you know this is well how would I just multiply this if I didn't even have to think it through all of these adding all these two fists together well one way to think about it is that seven is the same thing as 7 over one so he could have just said 2 over 5 times 7 over 1 7 over 1 is the exact same thing as 7 and that would be equal to 2 times 7 in the numerator which is 14 and the denominator would be 5 times 1 which is equal to 5 and you'd get the same answer so now let's actually go back and select the right choice I forgot that we actually had to see which which explanation is the right explanation so explanation 1 is that Ken didn't multiply correctly multiplying 2/5 times 7 is the same as adding 2/5 7 times this is exactly right this is exactly what we just went through the correct answer is 14 5th or 2 or 4 v 2 and 4/5 so explanation a seems to be the right one but we'll just read the other ones just to see if there's some flaws in them explanation B can multiplied correctly but forgot to cancel out the 7s in the fraction since 7/7 is equal to 1 - v times 7 is equal to 2/5 times 1 well obviously 2/5 times 7 is not the same thing as 2/5 times 1 so this is kind of nutty explanation see since ken must add up all the pie for 7 of them he should have added 7 and 2/5 instead of multiplied makes no sense he should be multiplying ken is correct this Francis should need that much pine oh that's that's that doesn't make sense either it's explanation a