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## 5th grade (Eureka Math/EngageNY)

### Unit 4: Lesson 5

Topic E: Multiplication of a fraction by a fraction- Multiplying 2 fractions: fraction model
- Multiplying 2 fractions: number line
- Represent fraction multiplication with visuals
- Multiplying fractions with visuals
- Multiplying 2 fractions: 5/6 x 2/3
- Multiplying fractions
- Multiplying mixed numbers
- Multiply mixed numbers
- Multiplying fractions word problem: laundry
- Multiplying fractions word problem: muffins
- Multiplying fractions word problem: bike
- Multiply fractions word problems

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# Multiplying fractions word problem: bike

CCSS.Math:

Sal solves a word problem by multiplying a fraction by a mixed number. Created by Sal Khan.

## Want to join the conversation?

- isn't 3 1/3's improper fraction supposed to be 10/3(1 vote)
- Yes because 3 x 3 + 1 get us 10 the we put it over are denominater that is 3 so we times both fractions(2 votes)

- Is there a quicker way and easier way ?(7 votes)
- If I'm being honest the way he explains things is very confusing. I couldn't understand the lesson.(4 votes)
- not gonna lie I din't understand most of that(2 votes)
- Isn't 3 times 3 plus 1 10/3? Why'd he right 9/3 + 1/3?(2 votes)
- There is a much easier way and less complicated way. You don’t have to do all the complex steps that sal has shown. He is just showing different ways to do it so hopefully you might get it. Start with 1/5 x 3 1/3. 3 1/3 can be changed to 10/3 * 1/5 =10/15. Then you can simplify to 2/3 which gives you the answer. Hope this helps!(2 votes)
- How do u guys know all of these stuff without making mistakes in the video?(0 votes)
- umm, why did he not simplify the 10 and the 5 before multiplying them? that would have make things much easier(0 votes)
- He could but maybe it would be easier for some people if he does the other way.(4 votes)

- 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.(1 vote)
- Can I find one with a whole number. I've only been getting the single fraction?(1 vote)

## 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.