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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 5

Lesson 21: Multiplying fractions- Intro to multiplying 2 fractions
- Multiplying 2 fractions: fraction model
- Multiplying 2 fractions: number line
- Multiplying fractions with visuals
- Multiplying 2 fractions: 5/6 x 2/3
- Multiplying fractions
- Finding area with fractional sides 1
- Finding area with fractional sides 2
- Area of rectangles with fraction side lengths
- Multiplying fractions review

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# Intro to multiplying 2 fractions

Sal introduces multiplying 2 fractions. Created by Sal Khan.

## Want to join the conversation?

- Is there another way to put answers in simplest form another way then the ones shown in the video?(19 votes)
- I personally think it is easier to simplify a fraction by dividing the numerator and the denominator by their lowest common factor, eg.

4/8

LCM = 4

4 divide 4 = 1

8 divide 4 = 2

= 1/2

Or...

6/8

LCM = 2

6 divide 2 = 3

8 divide 2 = 4

= 3/4

Hope that helps.(21 votes)

- 1/20 x 2 11/20=(7 votes)
- 0.1275 would be the answer(2 votes)

- Hello!

I don't really understand why we are splitting 2/3 into 4/5th. I thought splitting things is considered division?

Thank-you!

- Andy An(5 votes)- Fractions can be confusing.That step is division, but the equation is not.When you multiply with whole numbers, you take one number and make it grow, but since fractions are less than one,they have strange properties that basically switch the function of multiplication and division.If you didn't understand this and/or this didn't help you, rewatch the video and pay close attention.(7 votes)

- So 5/8 x 4/10 would be 1/4(3 votes)
- Yes.

5/8 and 4/10 would be 5 * 4 or 20 in the numerator, and 8*10 or 80 in the denominator. 20/80 can be reduced to 2/8 and then 1/4.(9 votes)

- Aren't we supposed to multiply both the denominators till they have an equivalent value? Or is it supposed to be until they have a common denominator?(3 votes)
- We only need a common denominator to add/subtract fractions. We do not use a common denominator to mulitply/divide fractions.(7 votes)

- I understand how you do it and I can follow the instructions to get the desired result.

However, can someone explain why when we multiply the 2 fractions together we are 'taking 2/3 of 4/5'? I've never thought of multiplication in this way before.

2/3 x 4/5 = 8/15

but

2/3 & 4/5, when changed using the LCM, would be 10/15 & 12/15. Larger fractions than the 8/15. I always thought that multiplication would increase our final result, but this is not the case?

So in terms of multiplication with fractions, I should view it as taking a portion? Example - 2/3 OF 4/5?

Thanks to anyone that answers me :)(5 votes)- Yes, we are taking a portion due to the fact that we are multiplying fractions, which are less than one.For more information, see my reply to Andy's post.(0 votes)

- how do you simifly farctions(2 votes)
- It has a few spelling errors. But other than that, good question!(4 votes)

- When we multiplying fractions, why do we multiply the numerators and the denominator?(3 votes)
- Do you always need to simplify?(2 votes)
- It's not necessary, but it is really helpful for when you need a reduced fraction.(2 votes)

- When you make the statement, "If you have 12 of something and want to take 2/3 of it, you are going to take 8," you have done two WRONG things. First, you stop looking at the problem from the visual viewpoint. Second, you throw out a mathematical statement with no evidence, no explanation of how you got to the fact of that statement. I am left totally clueless from either perspective. I cannot do these types of problems. Where do you explain any of it from the beginning and consistently?(2 votes)
- So, let's say that you have twelve of something, right?

Part 1:

If you want to take 2/3's of 12,

we should find 1/3 of 12 first so that we can multiply 1/3 of 12 and 2 which will get us 2/3's of 12,

because 2/3 is 1/3 times 2.

It works the same way for other fractions:

2/7 times 2 is 4/7

3/8 times two is 6/8

To find 1/3 of 12, simply multiply 12 by the numerator of 1/3(which is 1), and divide 12 by the denominator(which is 3).

Part 2:

Doing the operations I stated in the last sentence:

Multiply 12 by the numerator(which is 1): 1 times 12 = 12

Divide the number we got by the denominator(which is 3): 12 / 3 = 4

4 is 1/3 of 12. So, to find 2/3 of 12, we multiply 4 by 2

Part 3:

4 * 2 = 8

8 is 2/3 of 12!(2 votes)

## Video transcript

Let's think about what it
means to multiply 2 over 3, or 2/3, times 4/5. In a previous
video, we've already seen how we can
actually compute this. This is going to be equal
to-- in the numerator, we just multiply the numerators. So it's going to be 2 times 4. And in the denominator, we
just multiply the denominator. So it's going to be 3 times 5. And so the numerator
is going to be 8, and the denominator
is going to be 15. And this is about as
simple as we can make it. 8 and 15 don't have any factors
common to each other, than 1, so this is what it is. It's 8/15. But how, why does that
actually makes sense? And to think about
it, we'll think of two ways of visualizing it. So let's draw 2/3. I'll draw it relatively big. So I'm going to draw 2/3, and
I'm going to take 4/5 of it. So 2/3, and I'm going
to make it pretty big. Just like this. So this is 1/3. And then this would be 2/3. Which I could do a little bit
better job making those equal, or at least closer
to looking equal. So there you go. I have thirds. Let me do it one more time. So here I have drawn thirds. 2/3 represents 2 of them. It represents 2 of them. One way to think about
this is 2/3 times 4/5 is 4/5 of this 2/3. So how do we divide
this 2/3 into fifths? Well, what if we divided each
of these sections into 5. So let's do that. So let's divide each into 5. 1, 2, 3, 4, 5. 1, 2, 3, 4, 5. And I could even divide
this into 5 if I want. 1, 2, 3, 4, 5. And we want to take 4/5
of this section here. So how many fifths
do we have here? We have 1, 2, 3, 4,
5, 6, 7, 8, 9, 10. And we've got to be careful. These really aren't fifths. These are actually
15ths, because the whole is this thing over here. So I should really say
how many 15ths do we have? And that's where we
get this number from. But you see if 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Where did that come from? I had 3, I had thirds. And then I took each
of those thirds, and I split them into fifths. So then I have five
times as many sections. 3 times 5 is 15. But now we want 4/5 of
this right over here. This is 10/15 right over here. Notice it's the
same thing as 2/3. Now if we want to
take 4/5 of that, if you have 10 of something,
that's going to be 8 of them. So we're going to
take 8 of them. So 1, 2, 3, 4, 5, 6, 7, 8. We took 8 of the
15, so that is 8/15. You could have thought about
it the other way around. You could have
started with fifths. So let me draw it that way. So let me draw a whole. So this is a whole. Let me cut it into
five equal pieces, or as close as I can
draw five equal pieces. 1, 2, 3, 4, 5. 4/5, we're going to
shade in 4 of them. 4 of the 5 equal pieces. 3, 4. And now we want to
take 2/3 of that. Well, how can we do that? Well, let's split each
of these 5 into 3 pieces. So now we have
essentially 15ths again. So 1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13, 14, 15. We want to take 2/3
of this yellow area. We're not taking 2/3
of the whole section. We're taking 2/3 of the 4/5. So how many 15ths
do we have here? We have 1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12. So if you have 12 of
something, and you want to take 2/3 of that, you're
going to be taking 8 of it. So you're going to be taking
1, 2, 3, 4, 5, 6, 7, 8 or 8 of the fifteenths now. So either way, you get
to the same result. One way, you're thinking
of taking 4/5 of 2/3. Another way you could think of
it as you're taking 2/3 of 4/5.