Properties of Real Numbers Students will be able to recognize properties of real numbers and use them to solve problems.

Identity Properties Additive Identity: The additive identity is 0, because when you add 0 to a number you get the identical number. Example: = 4 Definition: n + 0 = n Multiplicative Identity: The multiplicative identity is 1, because when you multiply any number by 1 you get the identical number. Example: -12 · 1 = -12 Definition: n · 1 = n

Inverse Properties Additive Inverse: The sum of a number and its additive inverse (or opposite) is 0. Example: 8 + (-8) = 0 Definition: n + (-n) = 0 Multiplicative Inverse: The product of a number and its multiplicative inverse is 1. Example: Definition:

Commutative Properties Commutative Property of Addition: The order does not change the sum Example: = Definition: a + b = b + a Commutative Property of Multiplication: The order does not change the product. Example: Definition: a · b = b · a

Associative Properties Associative Property of Addition: The grouping does not change the sum. Example: (2 + 5) + 9 = 2 + (5 + 9) Definition: (a + b) + c = a + (b + c) Associative Property of Multiplication: The grouping does not change the product. Example: (3 · 7)4 = 3(7 · 4) Definition: (ab)c = a(bc)

Distributive Property Example: -2(4 + 7) = -2(4) + (-2)(7) Definition: a(b + c) = ab + ac

Examples: Find the additive inverse and the multiplicative inverse of each of the following: ¾ Inverses AdditiveMultiplicative 5 - -¾ ½

Examples: Identify the property demonstrated by each equation: = (¼) = 1 7.3(4 + 2) = 3(4) + 3(2) 8.(2 · 3) · 6 = 2 · (3 · 6) = 2.3 Commutative Prop. of + Multiplicative Inverse Distributive Prop. Assoc. Prop. of mult. Additive Identity