# Fact Families for Multiplication and Division of Fractions

The multiplication and division facts of fractions can be written from the multiplication and division facts of the numbers involved.

For example, the multiplication and division facts for 4, 5 and 20 are:

4 × 5 = 20

5 × 4 = 20

20 ÷ 5 = 4

20 ÷ 4 = 5

From above facts, the multiplication and division facts for fractions involving these numbers are derived as:

4 = $\frac{20}{5}$

5 = $\frac{20}{4}$

1 = $\frac{20}{(4×5)}$

Find the fact families for multiplication and division of fractions for

3, 8, 24

### Solution

Step 1:

The multiplication and division facts for 3, 8 and 24 are:

3 × 8 = 24

8 × 3 = 24

24 ÷ 8 = 3

24 ÷ 3 = 8

Step 2:

The fraction fact families for multiplication and division of 3, 8, and 24 are: ;

3 = $\frac{24}{8}$

8 = $\frac{24}{3}$

1 = $\frac{24}{(3 × 8)}$

Find the fact families for multiplication and division of fractions for

4, 7, 28

### Solution

Step 1:

The multiplication and division facts for 4, 7 and 28 are:

4 × 7 = 28

7 × 4 = 28

28 ÷ 7 = 4

28 ÷ 4 = 7

Step 2:

From above facts, the fraction fact families for multiplication and division for 4, 7, and 28 are:

4 = $\frac{28}{7}$

7 = $\frac{28}{4}$

1 = $\frac{28}{(4 × 7)}$