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## Topic G: Repeated addition of fractions as multiplication

Current time:0:00Total duration:2:19

## Video transcript

If there are 6 people
in your family, and each person drinks 4/5 of
a gallon of milk each month, between what two whole numbers
is the number of gallons of milk your family
will drink each month? So let's think about
this a little bit. So I've got my milk gallon
here for inspiration. So there's 6 people
in my family, or in your family, whoever's
family we're talking about. And each of them drink
4/5 of a gallon per month. So we're going to go 6
times 4/5, or 4/5 times 6. Now, what is this
going to be equal to? Well, there are several ways
we could think about this. One, we can express
6 as a fraction. We could say that this is the
same thing as 6/1 times 4/5. And you multiply the numerators. You multiply the denominators. 6 times 4 is 24. And 1 times 5 is 5. So 24/5 gallons are going
to be drunk every month. And this is the same
thing-- let's see, 5 goes into 20 evenly
and has a remainder of 4. So we could write this
as 20/5 plus 4/5 5-- let me move over a little
bit so I don't run out of space, which
is the same thing. This is 4. So this is 4 and 4/5. So that's one way
to think about it. The other way, you could
think of this as 4/5 times 6, which is the same thing
as 4/5 plus 4/5 plus 4/5-- I think you get the idea--
plus 4/5 plus 4/5 plus 4/5. We took literally six 4/5's
and added them together. And what's this
going to be equal to? Well, this is going to
be 4 plus 4 plus 4 plus 4 plus 4 plus 4 over 5. This is how many 1/5's we have. Well, this is 6
times 4, or you could say 4 times 6, over 5,
which is equal to 24 over 5, which we've already
figured out is 4 and 4/5. So either way,
we're going to drink 4 and 4/5 gallons per month. Now let's try to answer
the actual question. Between what two whole numbers? Well, between 4 and
5 gallons a month. 4 and 4/5 is right
in between 4 and 5. We got it right.