Properties COMMUTATIVE ASSOCIATIVE AND IDENTITY Commutative Property The

Properties: COMMUTATIVE, ASSOCIATIVE, AND IDENTITY

Commutative Property The order in which two numbers are added or multiplied does not change their sum. 7+9=9+7 A+B=B+A 4 • 6=6 • 4 a • b=b • a

Associative Property The way in which three numbers are grouped when they are added or multiplied does not change their sum or product. 3 + (9 + 4) = (3 + 9) + 4 A + (B + C) = (A + B) + C 8 • (5 • 7) = (8 • 5) • 7 a • (b • c) = (a • b) • c

Identity Property The sum of an addend and 0 is the addend. The product of a factor and 1 is the factor. 13 + 0 = 13 7 • 1=7 A+0=A a • 1=a

Practice: Identify the Property. . . 1. 7 • 1 = 7 2. 5 + (4 + 3) = (5 + 4) + 3 3. 6 + 7 = 7 + 6

More Identifying Practice. . . 1. 8 + (7 + 6) = (8 + 7) + 6 2. 5 + 0 = 5 3. 9 • (4 • 6) = (9 • 4) • 6

Are These Expressions Equivalent? 1. 8 ÷ 4 = 4 ÷ 8 2. 9 + (7 • 6) = (9 + 7) • 6 3. 9 – 7 = 7 – 9

Rewrite each expression as an expression that does not use parentheses 1. 2 + (x + 4) = ____ 2. 2 • (n • 7) = _____ 3. 20 • (6 • y) = _____

More Rewriting Practice. . . 1. (y + 14) + 25 = _____ 2. (6 + m) + 9 = _____ 3. 4 • (8 • m) = ______

Properties Reminder. . . 1. Commutative Property: 8 + 5 = 5 + 8 or 8 • 5 = 5 • 8 2. Associative Property: 7 + (3 + 4) = (7 + 3) + 4 or 7 • (3 • 4) = (7 • 3) • 4 3. Identity Property: 7 + 0 = 7 or 7 • 1 = 7