2. Properties Objective: To use the properties of numbers. Do Now 1.) 6 + 5 = 3.) ( 2  1 )  4 = 2.) 5 + 6 =4.) 2  ( 1  4 ) = 11 8 8

3. Properties Commutative Property: A change in the order. This only works for addition and multiplication. Examples: 1.) 3 + 7 = 7 + 3 3.) a + b = 2.) 2 6 = 6 2 b + a 4.) ab =ba Important note

4. Properties Associative Property: A change in the grouping. Important note This only works for addition and multiplication. Examples: 1. ( 5 + 3) + 2 = 5 + ( 3 + 2)2. 4 (1 3) = (4 1) 3 3. a + ( b + c ) =( a + b) + c4. (ab) c = a (bc)

5. Identity Properties 1.) Identity Property of Addition When zero is added to a number, the number does not change. Examples: 1. 4 + 0 = 42. a + 0 = a Zero is the identity element for Addition.

6. Identity Properties 2.) Identity Property of Multiplication When a number is multiplied by one, the number does not change. Examples: 1. 8  1 = 82. 1 a = a One is the identity element for Multiplication.

7. Properties Practice Problems A. True or False 2.) 27 + 0 = 27 This demonstrates the identity property of multiplication. F The identity property of addition B.Complete the example 1.) The identity property of multiplication 14 = _________ 1.) 3 + (8 + 4) = (3 + 8) + 4 This demonstrates the associative property. T 14 1

8. Properties Distributive Property: Deals with two operations Multiplication with addition Examples: 1. 2(3 + 4) = 2(3) + 2(4) 2. a(b + c) = ab + ac 1. 2(3 – 4) = 2(3) – 2(4) 2. a(b – c) = ab – ac Multiplication with subtraction Examples: