Number & Operations for Teachers 

Copyright David & Cynthia Thomas, 2009

Properties of Fraction Operations

When considering fact families for fraction operations, one must first recognize that, while addition of fractions is commutative, subtraction is not. Both addition and subtraction, however, are closed on the set of rational numbers (fractions). Table 4.1 summarizes this fact.

	Fractions
Addition	closed commutative
Subtraction	closed not commutative

Table 4.1: Properties of Fraction Operations – Addition & Subtraction

As with whole numbers and integers, fact families for the addition and subtraction of fractions may be represented as a set of four operations.

Example 4.4

Write a fact family for 1/2 + 1/3 = 5/6

Solution 4.4

1/2 + 1/3 = 5/6

5/6 – 1/3 = 1/2

1/3 + 1/2 = 5/6

5/6 – 1/2 = 1/3

Example 4.5

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

Solution 4.5

1/2 – 1/3 = 1/6

1/3 + 1/6 = 1/2

1/2 – 1/6 = 1/3

1/6 + 1/3 = 1/2