Main content

## Arithmetic (all content)

### Unit 5: Lesson 22

Multiplying mixed numbers# Multiplying mixed numbers

CCSS.Math:

Multiplying mixed numbers is similar to multiplying whole numbers, except that you have to account for the fractional parts as well. By converting mixed numbers into improper fractions, you can multiply the two numbers together in a straightforward way. Once you have the product as an improper fraction, you can convert it back into a mixed number. Created by Sal Khan and Monterey Institute for Technology and Education.

## Video transcript

Multiply 1 and 3/4
times 7 and 1/5. Simplify your answer and write
it as a mixed fraction. So the first thing we want to
do is rewrite each of these mixed numbers as improper
fractions. It's very difficult, or at least
it's not easy for me, to directly multiply
mixed numbers. One can do it, but it's much
easier if you just make them improper fractions. So let's convert each of them. So 1 and 3/4 is equal to-- it's
still going to be over 4, so you're still going to have
the same denominator, but your numerator as an improper
fraction is going to be 4 times 1 plus 3. And the reason why this makes
sense is 1 is 4/4, or 1 is 4 times 1 fourths, right? 1 is the same thing as 4/4, and
then you have three more fourths, so 4/4 plus 3/4
will give you 7/4. So that's the same thing
as 1 and 3/4. Now, let's do 7 and 1/5. Same exact process. We're going to still be talking
in terms of fifths. That's going to be
the denominator. You take 5 times 7, because
think about it. 7 is the same thing as 35/5. So you take 5 times 7 plus this
numerator right here. So 7 is 35/5, then you have
one more fifth, so you're going to have 35 plus 1,
which is equal to 36/5. So this product is the exact
same thing as taking the product of 7/4 times 36/5. And we could multiply
it out right now. Take the 7 times 36 as our new
numerator, 4 times 5 as our new denominator, but that'll
give us large numbers. I can't multiply 7 and
36 in my head, or I can't do it too easily. So let's see if we can
simplify this first. Both our numerator and our
denominator have numbers that are divisible by 4, so let's
divide both the numerator and the denominator by 4. So in the numerator, we can
divide the 36 by 4 and get 9. If you divide something in the
numerator by 4, you need to divide something in the
denominator by 4, and the 4 is the obvious guy, so 4
divided by 4 is 1. So now this becomes 7 times 9,
and what's the 7 times 9? It's 63, over 1 times 5. So now we have our answer as an
improper fraction, but they want it as a mixed number
or as a mixed fraction. So what are 63/5? So to figure that out-- let me
pick a nice color here-- we take 5 into 63. 5 goes into 6 one time. 1 times 5 is 5. You subtract. 6 minus 5 is 1. Bring down the 3. 5 goes into 13 two times. And you could have immediately
said 5 goes into 63 twelve times, but this way, at
least to me, it's a little bit more obvious. And then 2 times 5 is 12,
and then we have sorry! 2 times 5 is 10. That tells you not to
switch gears in the middle of a math problem. 2 times 5 is 10, and then you
subtract, and you have a remainder of 3. So 63/5 is the same thing as 12
wholes and 3 left over, or 3/5 left over. And if you wanted to go back
from this to that, just think: 12 is the same thing as
60 fifths, or 60/5. 60/5 plus 3/5 is 63/5,
so these two things are the same thing. These two things
are equivalent. This is as an improper
fraction. This is as a mixed number
or a mixed fraction. But this is our answer right
there: 12 and 3/5.