Main content

### Course: Staging content lifeboat > Unit 14

Lesson 36: Multiplying fractions# Multiplying 2 fractions: fraction model

Visuals can be used to multiply fractions in a variety of ways, such as by using fraction models. By drawing rectangles and dividing them into equal parts, we can use an area model to multiply fractions. help to illustrate how the numerators and denominators of the two fractions interact to produce a product. Created by Sal Khan.

## Want to join the conversation?

- Ok. When you are simplifying or dividing, keep these in mind:

Any even number is divisible by 2, so if both the numerator and the denominator are even, then you can continue to simplify it by 2.

If the digits of a number add up to a multiple of 3, then it is divisible by 3. So when both the numerator and denominator are multiples of 3, then you can simplify it by 3.

Numbers ending in 5 or 0 are divisible by 5.

You can just continue to simplify fractions with the 2, 3, and/or 5; these usually should be sufficient. And when two or more fractions are getting multiplied, you can take the numerator of one fraction and use it to simplify another fractions denominator (which will make the final multiplication easier). For example, if you have (5/8)x(2/3), then first simplify it to (5/4)x(1/3)heres a tip(60 votes)- If the last two digits of a number are divisible by 4, then the number is divisible by 4.

If the number ends in 0, it is divisible by ten.

The three rule works for nine as well.(4 votes)

- Trade offer

Upvote for a cookie

Accept? Decline?(34 votes) - I have no idea what he is talking about and I've watched this video 3 times(23 votes)
- It is pretty easy all you have to do is multiply both numerator and denominator.(9 votes)

- I did not understand any of this I need more details.(15 votes)
- 1/2 *1/4 is simple and applies in all other.

2*4 = 8

1*1 = 1

therefore 1/2*1/4 = 1/8

if you wanted to do 2/3 * 5/7 it's the same.

multiply the denominator by the denominator and the numerator by the numerator.

2*5 = 10

3*7 = 21

therefore it is 10/21.

I hope you get it now.

numerator * numerator

denominator * denominator.

:)(6 votes)

- Thank you Khan, this was very very helpful for me(12 votes)
- When solving this type of simple math do we really need to understand it visually or conceptually?(8 votes)
- I think it helps to understand it both ways. For example if you can teach the math to someone else, then you really understand all of it, which is I guess the goal. Of course, while you don't technically "need" to understand both, especially with the simpler parts of math it is often very helpful seeing as the harder math usually includes many of the same concepts and if you don't understand all the aspects then that makes it harder to learn higher maths.(7 votes)

- it is easy without the models(10 votes)
- I keep getting stuck on the practice problems even though I have watched it at least 5 times.(5 votes)
- Same ;-; I keep having the same problem and the calculator has failed me.(10 votes)

- pupusas con queso y salsa(7 votes)
- The translate of that is (pupusas with cheese and sauce).

{lol} like btw this is not a question(5 votes)

- Is it possible to have a fraction as a numerator or denominator? Just curious.(6 votes)
- Yes, its possible. But it would be considered a complex fraction and would be simplified so the numerator & denominator became integers.(3 votes)

## Video transcript

Let's think a little
bit about what it means to multiply fractions. Say I want to multiply
1/2 times 1/4. Well, one way to
think about this is we could view
this as 1/2 of a 1/4. And what do I mean there? Well let me take a whole,
let me take a whole here, and let me divide
it into fourths. So let me divide
it into fourths, so I'll divided into
4 equal sections. And so 1/4 would be 1 of
these 4 equal sections. But we want to take 1/2 of that. So how do we take half of that? Well, we could divide this
into 2 equal sections, and then just take 1 of them. So divide it into
2 equal sections, and then take 1 of them. So we're taking this pink area,
this whole pink area is 1/4, and now we're going
to take 1/2 of it. We're now going
to take 1/2 of it. So that's this yellow
square right over here. But what fraction of the whole
does this yellow represent? Well, it now represents 1
out of 1, 2, 3, 4, 5, 6, 7, 8 equal sections. So this right over here, this
represents 1/8 of the whole. And so we see conceptually
that 1/2 times 1/4, it completely makes sense,
that 1/2 of 1/4 should be 1/8. And it hopefully makes
sense that you get this 8 by multiplying
the 2 times the 4. You started with
4 equal sections, but then you divided each
of those 4 equal sections into 2 equal sections. So then you have 8
total equal sections that you split your whole into. Let's do another
example, but now let's multiply two
fractions that don't have 1's in the numerator. So let's multiply, let's
multiply 2/3 times 4/5. And I encourage you
now to pause the video and do something very
similar to what I just did. Try to represent 4/5
of a whole and then try to represent 2/3 of that
4/5 and see what fraction of the whole you actually have. So pause now. So let's think about this. Let's represent 4/5. So if I have a
whole like this, let me try to divide it
into 5 equal sections. 5 equal sections, so let's say
that is 1 equal section, that is 2 equal sections, that is
3, 4, and 5-- I can do a better job than this. This is always the hard part. I'm trying my best to
make them look, at least, like equal sections--
2, 3, 4, and 5. I think you get the point here. I'm trying to make
them equal sections. And we want 4/5. So we want 4 of these
5 equal sections. So this would be 1 of the 5
equal sections, 2 of them, 3 of them, and then 4 of them. So that right over there is 4/5. Now we can view this
as 2/3 of the 4/5. So how can we think about that? Well, we could take this section
and divide it into thirds. So let's do that. Divide it into thirds. So we're going divide it
into 3 equal sections. So that's 1/3, and then 2/3. So we took each of
the 5 equal sections, and we divided them
into 3 equal sections. Now what's going to
be 2/3 of the 4/5? Well, that's going to be
this part right over here. So let me make this clear. This is 1/3 of the 4/5. And then this would
be 2/3 of the 4/5. So this right over here, would
be 2/3 of the 4/5, or 2/3 times 4/5. But what fraction of the
whole does that represent? Well, how many total, how many
total equal sections do we now have? Well, we have 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12, 13, 14, 15. So we have 15 equal sections. I'm using a new color. We have 15 equal sections,
and that make sense. We started with
5 equal sections, but then we divided each of
those into 3 equal sections. So now we have 5 times
3 total equal sections. And then how many of
those are now colored in? Well, we see it's 2 times 4. 1, 2, 3, 4, 5, 6, 7, 8. How many of them are in the
2/3 of the 4/5, I should say. And there's 8 of them, 8
of the 15 equals sections. And so there you have it. It should hopefully
now make visual sense, or it makes conceptual
sense, that 2/3 times 4/5-- you can obviously compute
it by just multiplying the numerators, 2 times 4 is 8. And then multiplying the
denominators, 3 times 5 is 15-- but hopefully this now makes
conceptual sense as 2/3 of 4/5.