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# Multiplying 2 fractions: number line

Learn the concept of multiplying fractions by fractions. Watch as the process is visually represented on a number line, helping to understand the 'why' behind the procedure. Created by Sal Khan.

## Want to join the conversation?

- At1:40, doesn't Sal mean the two halves?(64 votes)
- He's dividing the halves into fourths(73 votes)

- Why does he make this more confuseing than it needs to be?(14 votes)
- Then look at other video! He is trying his best!(32 votes)

- I do not understand this. Could you make more simpimler? Please?(11 votes)
- he is trying to(4 votes)

- The Number Line approach is interesting but its hard to do unless you have a notebook and pencil with you but in the case where you have to quickly solve a question like "If the tax refund (lets say 1200$) is being divided between 4 people, how large of a fraction is each person getting?", and you don't happen to have a pencil and notebook by your side, how could you more easily do a question like that in your head?(6 votes)
- If you're dividing 1 whole among 4 people, then each person gets 1/4 of whatever it is you're dividing.

Something tells me that's not what you meant, though. Because 1200 is a nice multiple of 100, we can simply drop the zeroes and add them back later on. The problem then changes from 1200/4 to 12/4. 12/4 can be simplified to 3 (4 + 4 + 4 = 12), and then tack the zeroes back on - we get a result of $300.(10 votes)

- is there a different way to do this ?(4 votes)
- Yes, there is. I actually answered a question just like this a couple of minutes ago... :D The way Mr. Khan likes to do it is by explaining it in a way that
*teaches*you the concept so you understand what you're doing. But the simpler way is actually, well.... a lot*simpler*. For example, if you're multiplying 1/8 by 2/5, first you multiply the numerators by each other (1 x 2) to get an answer of 2. Then you multiply the denominators by each other (8 x 5) to get 40. Finally, you put the 2 as your numerator and the 40 as your denominator to get a product of 2/40, but that isn't your final answer because each number can be simplified -- each divided by 2 -- to get a final product of 1/20. I hope this helped you!(11 votes)

- Why did you use a number line when you could do 2/3 x 4/5 which is easier then number line ?

Why do it the hardier way which is slower, when you could go the easier way which is way faster? You still get the write answer anyway so why not do it the faster way?(6 votes)- It's just to prove the concept that you are going 2/3 to 4/5 or 4/5 to 2/3, you can't just get that from looking at "2/3 x 4/5", you wouldn't know how you got the product from those numbers, yes you did multiplicate the fractions but why do you do that when they are not whole numbers?(6 votes)

- umm i don't understand how it become 1/8 2/8 3/83:06in number line ?(1 vote)
- On the number line, there is an increase (increment) of 1/8 each time. Each time a 1/8 is added, there will be that increase (e.g. after adding 1/8 to 0, the result is 1/8; after adding a 1/8 to the already present 1/8, the result is 2/8; adding another 1/8 to the 2 one-eighths gives a 3/8; adding yet another 1/8 to the 3 one-eighths gives a 4/8, etc.)(6 votes)

- how it feels to chew five gum... stimulate your senses.(3 votes)
- When i'm adding fractions do I need to add the numerator(3 votes)
- I will never get models. A little more help would be amazing!(2 votes)

## Video transcript

In a previous video, we saw
that we could view 2/3 times 6 as whatever number is
2/3 of the way to 6 on the number line,
which we saw is 4. Or another way to think about
it is that 4 is 2/3 of 6. 2/3 times 6 can be
viewed as-- well, how many do I have
if I take 2/3 of 6? Now, what we want to do now
is apply that same idea, but to multiply not a
fraction times a whole number, but a fraction times a fraction. So let's say that we wanted
to take 3/4 and multiply it by 1/2. And we know, of
course, the order that we multiply doesn't matter. This is the exact same
thing as 1/2 times 3/4. So to imagine
where this gets us, let's draw ourselves
a number line. And I'll do it pretty
large so that we have some space to work in. So that's 0. And then that is 1. And of course, our line
could keep on going. And let's first imagine 3/4
times 1/2 as 3/4 of the way to 1/2. So first let's plot
1/2 on our number line. Well, 1/2 is literally
halfway between 0 and 1. So that's 1/2 right over there. And how do we think about
3/4 of the way to 1/2? Well, what we could do is think
about well, what's 1/4 of 1/2? Well, we could divide this
part of the number line into 4 equal sections. So that's 2 equal sections. Now that's 4 equal sections. And while we're at it, let's
divide all of the halves into 4 equal sections. So let's divide all of the
halves into 4 equal sections. So that's 4 sections. And now let's do this one. I'm trying my best to
draw them equal sections. So I've taken each of
the halves and I've made them into 4 equal sections. So this point right
over here is 1/4 of 1/2. But that's not
what we care about. We want to get to 3/4 of 1/2. So we want to get
to 1, 2, 3/4 of 1/2. So this point right over here,
this is literally 3/4 times 1/2. And this is, of
course, 1/2 here. But what number is this? And let me do this
in a new color. We can now visualize
it on the number line. But what number
is this actually? Well, a big clue is
that, well, before we had the section
between 0 and 1 divided into 2 equal sections when
we only had to plot 1/2. But then we took each of
those 2 equal sections and then split them
into 4 more sections. By doing that, we
now essentially have divided the section between
0 and 1 into 8 equal sections. So each of these
is actually 1/8. So this point right
over here is 1/8. This is 2/8. And then this is 3/8. And that's in line
with what we've seen about multiplying
fractions before. This should be equal to
3 times 1 over 4 times 2, which is equal to 3/8. And everything that
we're talking about, so we don't get
confused, this is all referring to this point right
over here on the number line. But what if we thought about
it the other way around? What if we thought about it
as 1/2 of the way to 3/4? So we could divide the space
between 0 and 1 into fourths. So let's do that. So that is 1/4, 2/4, 3/4. So this right over
here is the number 3/4. And we want to go half
of the way to 3/4. Well, what is half
of the way to 3/4? Well, we split this section
into 2 equal sections. So we could split
right over there. And we want to go exactly
one of those sections. 1/2 of 3/4 gets us, once
again, right over here to this point-- 3/8. So either way you imagine it,
whether you're essentially taking 3/4 of 1/2, or saying
I'm going to go 3/4 of the way to 1/2, or you say I'm
going to go 1/2 of the way to 3/4, either way, hopefully
it now makes conceptual sense. You can visualize it, and
it makes numeric sense that this is going
to be equal to 3/8.