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# 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 7 of them in
total and each of them has eaten 2/5 of a pie. Ken said you can
solve this problem by multiplying 2/5 times 7. And that makes sense. Each of them ate 2/5,
and there are 7 folks. I would multiply 2/5 times 7. So he multiplied and got 14/35. Now this is a little
bit suspicious. And here's 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 14/35 cannot
be correct because 14/35 is less than one whole pie. So this is definitely
true, that 14/35 is less than one whole pie. Which of the following best
explains this situation? So 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 14/35. And 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 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 7/7, which is equivalent to 2/5 times 1, which
is equivalent to 2/5. 14/35 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 seven 2/5. It literally could
mean, so 2/5 times 7, literally means one 2/5, plus
another 2/5, plus another 2/5. So we do this seven times. So that's four 2/5. That's five 2/5. That's six 2/5. And that's seven 2/5. Sorry, my brain isn't working. And that's seven 2/5. And if you were to
add all of these together, how many
fifths do you have? How many fifths do you have? Well, you have 2 plus
2 plus 2 plus 2 plus 2. Let's see, that's five. Plus 2, plus 2. You have 2, seven times, fifths. Or this is another way of saying
you have 7 times-- let me write it this way-- you
have 2 times 7 fifths. Or another way of saying it
is this is equal to 14/5. This is well over more than 1. 5 goes into 14 two times, and
you have a remainder of 4. So it's 2 and 4/5 pie. So this is what he
should have done. But you might be saying, well,
how would I just multiply this if I didn't even have
to think it through, adding all these 2/5 together? Well, one way to
think about it is that 7 is the same thing as 7/1. So he could have just
said 2/5 times 7/1. 7/1 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 would get
the same answer. So now let's actually go back
and select the right choice. I forgot that we actually
had to say 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 seven times. This is exactly right. This is exactly what
we just went through. The correct answer
is 14/5 or 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, Ken multiplied
correctly but forgot to cancel out the
7's in the fractions. Since 7/7 is equal
to 1, 2/5 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 C, since Ken
must add up all the pie for 7 of them, he should
have added 7 and 2/5 instead of multiplying. No, that makes no sense. He should be multiplying. Ken is correct. His friends just didn't
each that much pie. No, that doesn't
make sense either. It's explanation A.