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# Multiplying fractions word problem: bike

Video transcript

You can ride your bike
1/5 of a mile per minute. If it takes you
3 and 1/3 minutes to get to your friend's
house, how many miles away does your friend live? And this here is pictures
of these guys on bicycles. It's pretty clear they're
not riding to work, or some of these guys aren't
even riding a bicycle. But let's focus on the question. So you can ride your bike
1/5 of a mile per minute. And you're going to
do this for 3 and 1/3 minutes-- times 3 and 1/3. So we really have
to figure out, how do we multiply 1/5
times 3 and 1/3? So there's a couple of
ways to think about it. You could literally view a 3 and
1/3 as this is the same thing as 1/5 times 3 plus 1/3. That's exactly
what 3 and 1/3 is. And then we can just apply
the distributive property. This would be 1/5
times 3-- I'm going to keep the colors the
same-- plus 1/5 times 1/3. And this is going to
be equal to-- well, we could rewrite 1/5
times 3 as 1/5 times 3/1. That's what 3 really is if
we wrote it as a fraction. And then, of course, we're going
to have plus 1/5 times 1/3. And let's just think about
what each of these evaluate to. Here you multiplied
the numerators, and you multiplied
the denominators. So this is going to be equal
to 1 times 3 over 5 times 1. And this business
right over here is going to be-- and
remember, order of operations. We want to do our
multiplication first. So this is going to be 1
times 1 over 5 times 3. And so that's going to be
equal to 3/5 plus 1/15. And now we have different
denominators here. But lucky for us,
3/5, if we multiplied the numerator and
the denominator by 3, we're going to get
a denominator of 15. And so that's equal to 9/15
plus 1/15, which equals 10/15. And if you divide the numerator
and the denominator both by 5, you're going to get 2/3. So your friend lives 2/3
miles away from your house. Well, that's kind
of interesting. And this was kind of
a long way to do it. Let's think about if there's
a simpler way to do it. So this is the same
thing as 1/5 times-- and I'm just going to write
3 and 1/3 as a mixed number. So it's 1/5 times 3 and 1/3 can
be rewritten as 9/3-- sorry, I'm going to rewrite 3 and
1/3 as an improper fraction. So this is the
same thing as 9/3-- that's 3-- plus 1/3, which is
the same thing as 1/5-- well, I switched colors
arbitrarily-- which is the same thing-- I'm still
on the same color-- as 1/5 times 9/3 plus 1/3 is 10/3. And now we can just
multiply the numerator and multiply the denominator--
or multiply the numerators. So this is 1 times
10-- I'm trying to stay good with the
color coding-- over 5 times 3, which is exactly equal
to what we just got. 1 times 10 is equal to 10. 5 times 3 is 15. 10/15, we already established,
is the same thing as 2/3. So your friend lives 2/3
of a mile away from you.