Properties of operations
Commutative Property
Numbers can be added or multiplied in any order without changing the answer. Commutative Property of Addition a + b = b + a or 3 + 2 = 2 + 3 Commutative Property of Multiplication a • b = b • a or 3(2) = 2(3) Associative Property Regrouping the numbers does not change the answer. The order of the numbers stays the same. Associative Property of Addition (a + b) + c = a + (b + c) or (2 + 3) + 4 = 2 + (3 + 4) Associative Property of Multiplication (a • b) • c = a • (b • c) or (2 • 3) • 4 = 2 • ( 3 • 4) Additive Identity When you add 0 to a number, you will get that number back as your answer. a + 0 = a or 6 + 0 = 6 Multiplicative Identity When you multiply any number by 1, you will get that number back as your answer. a(1) = a or 9 · 1 = 9 Multiplicative Property of Zero When you multiply any number by 0, the answer will always be zero. a(0) = 0 or 2 · 0 = 0 Additive Inverse When you add a number and its opposite, you will always get 0. a + –a = 0 or 8 + –8 = 0 Multiplicative Inverse When you multiply a number and its inverse (or opposite) you will always get 1. a * 1/a = 1 or 7 * 1/7 = 1 Distributive Property The Distributive Property shows you how to multiply a single term by two or more terms inside a set of parentheses. a(b + c) = ab + ac or 2(3 + 4) = 2(3) + 2(4) = 6 + 8 (b + c)a = ba + ca or (6 + 7)8 = (6)8 + (7)8 = 48 + 56 a(b – c) = ab – ac or 9(15 – 3) = 9(15) – 9(3) = 135 – 27 (b – c)a = ba - ca or (9 – 7)6 = (9)6 – (7)6 = 54 – 42 |
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