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### Course: Numbers & Operations - The Real & Complex Number Systems 211-217 > Unit 6

Lesson 6: Multiplying fractions word problems# Multiplying fractions word problem: bike

This video is all about understanding how to multiply fractions and mixed numbers. Watch as the steps are explained in a simple and fun way. Created by Sal Khan.

## Want to join the conversation?

- isn't 3 1/3's improper fraction supposed to be 10/3(27 votes)
- Hey, the answer is 10/3 but he just did 9/3 + 1/3 to simplify how to find ten thirds here(2 votes)

- I didn't get really why we should multiply! I do on paper though. But Sal understand that right way! Can someone explain that why should we multiply?(10 votes)
- As you learn word problems, you will find that there are a variety of formulas that occur and that you need to learn. This problem uses one of those formulas. Specifically, it used the formula: Distance = Rate (Time).

Sal knows this formula, so he knows he needs to multiply the speed/ rate (the 1/5 miles per minutes) times the time (the 3 1/3 minutes).

Hope this helps.(9 votes)

- umm, why did he not simplify the 10 and the 5 before multiplying them? that would have make things much easier(8 votes)
- He could but maybe it would be easier for some people if he does the other way.(7 votes)

- Isn't 3 times 3 plus 1 10/3? Why'd he right 9/3 + 1/3?(4 votes)
- what if we divide0:34what will we get ?(3 votes)
- at1:20to about1:45he multiplies 1/5X 3 + 3X like 1/3. How is this possible?(3 votes)
- Wait so I don't get it is this how u do it? for example 1/5 x 3/4 so first you multiply the numerator with the numerator which is 4 x 5= 20 and then you multiply the dinomerator's which is 1 x 3= 3 so then the answer would be 3/20? Is that right?(2 votes)
- Is it 9/3 or 10/3? I know the answer is 10/3, but did Sal mean to write 9/3? I mean, was 9/3 his answer, or was 10/3 his answer?(1 vote)
- I assume you are referring to the section at about3:00in the video. Sal is converting 3 1/3 into 10/3. He wrote it out in steps. 3 1/3 = (3*3)/3 + 1/3 = 9/3+1/3 = 10/3. He writes the result of 10/3 at about3:15in the video. The 9/3 is just an intermediate work result.

Hope this helps.(3 votes)

- Is there a faster way?

anybody(0 votes)- The second way shown in the video above is definitely faster; the first way definitely used a bit of algebra. You turn the mixed number (3 1/3) into an improper fraction (10/3), and then you multiply the numerators and denominators together. Then simplify your answer, also as shown above. It won't take you long after you do it several times.(6 votes)

- I am having problem with understanding the wording and the relationship with the numbers Comments following use the "plug and chug" method of D= R×T but which numbers go into where this is not as intuitive to me thats why I have always had problems with understanding maths and world application especially algebra eg. She has × apples and y oranges find y for how long it would take to bake an apple pie Vs making a glass of Orange juice ! ? the question given by Sal here are typical Of the reason for why I disliked maths my brain would instantly go foggy like the numbers and words were duelling it out with no winners but my patience losing out! please I need help there is something very wrong with my brain ! many have said (and I think that as many have thought) that i was retarded and/or dropped on my head! Perhaps....(1 vote)
- Don't worry... you're not the only one who feels this way about algebra :)

When your brain fogs up, I would suggest you take a cold drink of water or iced tea and maybe splash some cold water on your face? I would also suggest maybe taking a walk outside (of course, you can't do any of this in school). If you have money to spare you can buy a fidget toy to help concentrate: https://www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Daps&field-keywords=fidget+toys.

Hope I helped!! :)(2 votes)

## 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.