# Fact Families for Multiplication and Division of Fractions

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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 = $\frac{28}{(4 × 7)}$