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

Lesson 19: Multiplying whole numbers and fractions- Multiplying fractions and whole numbers visually
- Equivalent fraction and whole number multiplication problems
- Multiply fractions and whole numbers
- Multiply fractions and whole numbers with fraction models
- Equivalent whole number and fraction multiplication expressions

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# Equivalent fraction and whole number multiplication problems

Sal relates mixed numbers to whole number/fraction multiplication problem. Created by Sal Khan.

## Want to join the conversation?

- can we do this in mixed fraction form too? and if we can how do we solve it?(28 votes)
- yes, we can. As you can see in the last part of the video, it showed 8/3. You can use the 3 and count up with 3, but do not go over 8. 6 so far, right? Now, you convert 6 into 2. (As in 2 wholes). Add the extra remainder.(The fraction of 2 that you did not count). Now, you get 2 2/3!(14 votes)

- I don't really get the whole number times the fraction part.(12 votes)
- Say you've got 15/12.

There are fifteen 12ths, or fifteen 1/12ths.

So 1/12 + 1/12 + 1/12... and you keep adding 1/12th onto each other 15 times until you get to 15/12.

Remember 1/12 is just 1 piece of 12 total pieces divided, imagine it as a cake or pizza you've divided into 12 pieces and you count each piece.

So you're only adding the Numerators (top numbers). the denominator (bottom number) never changes, so when you multiply a fraction by a whole number you're only multiplying the Numerator (top number).

You can do it that way... but really the number you're multiplying with is also still a fraction it's 2 wholes so you can write it as 2/1 which is just another way to represent that it's 2 wholes, when you do this multiplying 1 fraction then becomes the same as multiplying 2 fractions cos you've now got 2 fractions.(17 votes)

- how would i multiply 1/4 by 96?

or 1/4 of 96(11 votes)- You first make 96 into 96/1 then multiply strait across which makes 96/4.Now divide 96 and 4 which makes 14. 1/4x96=14 :).(11 votes)

- Why doesn't Khan ever say at the end something like " So it equals 8/3 which is also the same as 2 2/3"? Or in other word why doesn't he also mention the mixed number form of the answer?(8 votes)
- I think probably because he's trying to keep from confusing people who are learning this for the first time? I think it's just to keep it simple.(13 votes)

- Need help. 3 wholes 4/5 times ten(6 votes)
- 3 4/5 x 10

= 19/5 x 10

= 38(5 votes)

- sal, how dose spliting up the numbers help(8 votes)
- He's just using it to explain how multiplying fraction by an integer works. You don't have to do it :)(2 votes)

- why does he needs 3 groups of 4 1/3s?(8 votes)
- can we do this in mixed fraction form too? and if we can how do we solve it?(6 votes)
- Multiplying a mixed fraction by an integer:

Say the problem is 4 * (2 1/3). You can break 2 1/3 up into what it literally means, 2*wholes*and 1/3*part*, so 2 + 1/3.

4 * (2 + 1/3)

Here, the 4 distributes to the 2 and the 1/3, where 4 * (2 + 1/3) = 4*2 + 4*1/3. So let's do the separate multiplications before adding them:

4*2 = 8, 4 * 1/3 = 4/3

= 8 + 4/3 = 9 + (4-3)/3 = 9 1/3

You can apply this knowledge on the distributive property of multiplication a(b + c) = ab + ac to multiply mixed fractions by integers. Hope this helps, and take care.(4 votes)

- Why did you use the method that you did?(4 votes)
- Just so you have somewhat of an understanding on how you can view equivalent fractions by using multiplication problems.(6 votes)

- what is 1 third plus 2 eigths(5 votes)
- 1∕3 + 2∕8

Begin by simplifying the fractions.

1∕3 + 2∕8 = 1∕3 + (1 ∙ 2)∕(4 ∙ 2) = 1∕3 + 1∕4

Then write the fractions so that they have the same denominator.

1∕3 + 1∕4 = (1 ∙ 4)∕(3 ∙ 4) + (1 ∙ 3)∕(4 ∙ 3) = 4∕12 + 3∕12

Finally, add the numerators.

4∕12 + 3∕12 = (4 + 3)∕12 = 7∕12(3 votes)

## Video transcript

So we have here, it says 2 times
4/3 is equal to 8 times blank. And what I encourage you to do
is pause the video right now and try to think about what
should go in this blank. So I'm assuming
you've given your try. Now, let's think through this. So 2 times 4/3, we can literally
view that as the same thing as-- if we rewrite the 4/3, this
is the same thing as 2 times-- instead of writing
4/3 like this, I'm literally going to
write it as four 1/3's. And I know it sounds like I just
said the same thing over again. But I'm literally going to write
1/3 four times-- 1/3 plus 1/3 plus 1/3 plus 1/3. If you call each of
these 1/3, you literally have four of them. This is four 1/3's. 2 times 4/3 is the same thing as
2 times, literally, four 1/3's. Now, what would this be? Well, this is going to be equal
to-- let me just copy and paste this-- is going to
be this two times. So copy, and then
let me paste it. So that's one group of
those 1/3's, of those four 1/3's, or one group of
one of these four 1/3's. And then, we'll
have another one. And then, we'll
have another one. And we're going to
add them together. That's literally 2 times 4/3. So let's add these together. Now what do we have? Well, we have a bunch of 1/3's. And we need to count them up. We have one, two, three, four,
five, six , seven, eight 1/3's. This is literally
equal to-- and we could, just to make it
clear what I've just done, we could ignore the
parentheses and just add up all of these things together. So that might make it
a little bit clearer. So let me do that just to
make it clear that I literally take-- I've taken eight 1/3's
and I'm adding them together, which is the exact
same thing as 8/3. So let me clear that, and let me
clear that, let me clear that. And so this is literally, or
this is clearly, or hopefully clearly, equal to 8 times 1/3. I have 8 1/3's there. So going back to the
original question, what is this equal to? 2 times 4/3 is the same
thing as 8 times 1/3. And we've already seen
that 8 times 1/3, well, that's literally 8/3. So we could also write
it like this-- 8 over 3. Let me do that 3 in that
other color-- 8 over 3.