- Multiply and Divide Fractions
- Home
- Product of a Unit Fraction and a Whole Number
- Product of a Fraction and a Whole Number: Problem Type 1
- Introduction to Fraction Multiplication
- Fraction Multiplication
- Product of a Fraction and a Whole Number Problem Type 2
- Determining if a Quantity is Increased or Decreased When Multiplied by a Fraction
- Modeling Multiplication of Proper Fractions
- Multiplication of 3 Fractions
- Word Problem Involving Fractions and Multiplication
- The Reciprocal of a Number
- Division Involving a Whole Number and a Fraction
- Fraction Division
- Fact Families for Multiplication and Division of Fractions
- Modeling Division of a Whole Number by a Fraction
- Word Problem Involving Fractions and Division

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# 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 = $\frac{28}{(4 × 7)}$