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Lesson 2: Multiplying whole numbers and fractions

# 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?
• 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!
• I don't really get the whole number times the fraction part.
• 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.
• how would i multiply 1/4 by 96?
or 1/4 of 96
• 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 :).
• 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?
• 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.
• Need help. 3 wholes 4/5 times ten
• 3 4/5 x 10
= 19/5 x 10
= 38
• sal, how dose spliting up the numbers help
• he's just using it to explain how multiplying fraction by an integer works. You don't have to do it :)
• why does he needs 3 groups of 4 1/3s?
• can we do this in mixed fraction form too? and if we can how do we solve it?
• 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.
• Why did you use the method that you did?
• Just so you have somewhat of an understanding on how you can view equivalent fractions by using multiplication problems.
• what is 1 third plus 2 eigths
• 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