Multiplication and division of fractions cheat sheet

Before we get started.

You have to know how to reduce fractions to multiply and divide fractions. The good news is that you do not have to have like denominators like you did with addition and subtraction of fractions, but YOU MUST BE ABLE TO REDUCE FRACTIONS. YOU CAN REDUCE VERTICALLY AND CROSSWAYS ONLY!!!

To reduce fractions

You have to find what is known as the GCF (greatest common factor) and divide all of your numbers by the GCF.

4 1

16 = 4 I know how to reduce because the GCF of 4 & 16 is 4. In other words, the biggest number that will divide into both 4 & 16 is 4. When I divide 4 & 16 by 4, I get the fraction ¼.

When can you reduce fractions?

You can reduce fractions vertically (up and down) like I did above, or you can reduce fractions cross ways like below.

3 ÷ 3 8 ÷ 4 My original problem is 3 8 Once reduced it is 1 2

4 ÷ 4 X 15 ÷ 3 4 X 15 1 X 5

In the red, the GCF for 3 & 15 is 3, so I divided both numbers by 3 to get my new fraction.

In the blue, the GCF for 4 & 8 is 4, so I divide both numbers by 4 to get my new fraction.

Explained another way, it looks like this.

To multiply a fraction

You will always multiply straight across the problem, in perfect rows. You do not multiply cross ways like we did above when reducing. It will look something like this.

5 7 35 I just multiplied 5 times 7

6 X 8 = 48 I just multiplied 6 times 8

When you get your answer, you will have to do the GCF test to make sure that your fraction is in lowest terms. Finding the GCF looks like this.

To find the GCF of 15, 70, and 100

I have to list all of the factors (numbers that divide into) 15, 70, 100

15--- (1, 3, 5, 15)

70---(1, 2, 5, 7, 10, 14, 35, 70)

100--(1, 2, 4, 5, 10, 20, 25, 50, 100)

I can see that 5 is the largest number in all three sets of the factors. 5 must be the GCF.

To divide fractions

I have to multiply by what is called the reciprocal or multiplicative inverse. This is just a fancy way of saying that I need to flip the second fraction over.

The two steps to dividing fractions are always the same.

1. Change the division sign to multiplication

2. Flip the second fraction over

7 6

12 ÷ 13

Step 1: 7 6

12 X 13

Step 2: 7 13 Then I multiply the fractions straight across to get 91

12 X 6 72