Number & Operations for Teachers

Properties of Fraction Operations

When considering fact families for fraction operations, one must first recognize that, while multiplication of fractions is commutative, division is not. Both multiplication and division, however, are closed on the set of rational numbers (fractions). Table 5.1 summarizes this fact.

Fractions

Multiplication

closed

commutative

Division

closed

not commutative

Table 5.1: Properties of Fraction Operations – Multiplication & Division

As with whole numbers and integers, where a x b = c, fact families for the multiplication and division of fractions may be represented as a set of four operations: a x b = c, c ÷ b = a, b x a = c, and c ÷ a = b.

Example 5.3

Write a fact family for 1/2 x 1/3 = 1/6

Solution 5.3

1/2 x 1/3 = 1/6

1/6 ÷ 1/3 = 1/2

1/3 x 1/2 = 1/6

1/6 ÷1/2 = 1/3

Example 5.4

Write a fact family for 1/2 ÷ 1/3 = 3/2

Solution 5.4

1/2 ÷ 1/3 = 3/2

1/3 x 3/2 = 1/2

1/2 ÷ 3/2 = 1/3

3/2 x 1/3 = 1/2