# how do you multiply fractions?

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**In case of Proper and improper fractions **

We multiply** **the numerators and the denominators of the fractions separately.

We should always express any fraction in its lowest terms. So, after getting the result fraction we should reduce it i.e. cancel the common factor between the numerator and denominator.

This can also be done before multiplying the numerators and the denominators.

Let us work out an example

`(5/12) * (4/15) = 20/180 = 1/9` (by cancellation)

or cancel the common factor of 5 and 15 & 4 and 12 (before multiplying)

It gives `(1/3) * (1/3) = 1/9`

**In case of mixed fractions**

Convert them into improper fractions and continue the same steps as mentioned above.

Let us work out with another example

`3 1/3 * 2 1/5 = (10/3) * (12/5) = 120/15 = 8/1 =8`

`(10/3) * (12/5) = (2/1) * (4/1) = 8` (by cancelling 10 & 5 and 3 & 12)

Step1: Change all the numbers into fractions.

Step 2: Cancel numbers from the top and bottom. Remember, cancelling at this point keeps the numbers smaller...but if you don't do it your answer can still be correct.

Step 3: Multiply all the top numbers and put the answer on the top Multiply all the bottom numbers and put the answer on the bottom.

Step 4: Reduce your answer and put it into the desired format

Example: `3 1/2 *` `` ```4 2/5`

Step 1: `3 1/2 = 7/2` and `4 2/5 = 22/5`

Step 2: `` 2 on the bottom can cancel with 22 on the top as below

At this point, I like rewriting the problem so I can draw lines through numbers that match on the top and bottom.

7 x (2 x 11)

------------------

2X 5

7 x 11

---------

5

Step 3: 7 x 11 = 77 and 5 = 5 so the answer will be `77/5`

Step 4: 77/5 does not reduce, meaning I cannot fine a common multiple of the top and bottom numbers to simplify this fraction. I can change it to a mixed number if that helps understand the number better (like for answering the question how many hole pies are needed to serve this much to a group of guests?)

`77/5= 15 2/5`

**Sources:**

To multiply fractions, we have to multiply the top numbers and multiply the bottom numbers. And, cancel the common factor to simplify it.

For example:

`4/9 xx 6/7`

Multiply the numerators and multiply the denominators.

`= (4 xx6)/(9xx7)`

Cancel the common factor between the numerator and denominator. The common factor is 3. Cancelling it, the fraction becomes:

`= (4xx2)/(3xx7)`

The simplified form is:

`=8/21`

**Therefore, `4/9xx9/7=8/21` .**