Algebra 1A Lesson 1-2 Practice 1A

Commutative & Associative Properties Primary objective: Students will be able to determine if an equation is commutative or associative.

Commutative Property: I like to think of the Commutative Property as the “commute” ative property. Let’s say you commute to work seven miles. When you come home it is still seven miles. Regardless of which direction you are going, it is the same distance. This is true for addition and multiplication. Changing the order, or direction, does not affect the sum (in addition) or the product (in multiplication). Study the following examples and notice that it is not applicable to subtraction or division, where order and direction are critical. Example 1:

5 + 7 = 12

7 + 5 = 12

12 = 12

Example 2:

5 * 7 = 35

7 * 5 = 35

35 = 35

Example 3:

7–5=2

5 – 7 = -2

2 ≠ -2

Example 4:

7 ÷ 5 = 7/5

5 ÷ 7 = 5/7

7/5 ≠ 5/7

Associative Property: I remember the associative property by thinking of whom I associate, or am grouped with. Study the following examples and notice how the grouping by parentheses affects the result. Example 5:

(3 + 5) + 7 8+7 15

3 + (5 + 7) 3 + 12 15

15 = 15

(4 * 5) * 6 20 * 6 120

4 * (5 * 6) 4 * 30 120

120 = 120

Example 7: (10 – 7) – 4 3–4 -1

10 – (7 – 4) 10 – 3 7

-1 ≠ 7

Example 8:

8 ÷ (4 ÷ 2) 8÷2 4

1≠4

Example 6:

(8 ÷ 4) ÷ 2 2÷2 1

As with the commutative property, the associative property is true for addition and multiplication, but not for subtraction or division.