Chapter 1-4: Properties Commutative Property: the order in which you add or multiply numbers does not change the sum or product Ex = * 8 = 8 * 6 Associate Property: the way in which you group numbers when they are added or multiplied doesn’t effect the sum or product Ex. (5 + 8) + 2 = 5 + (8 + 2) (4 * 6) * 3 = 4 * (6 * 3) Additive Identity: When 0 is added to any number the sum is always that number Multiplicative Identity: When any number is multiplied by 1, the product is that number Multiplicative Property of Zero: When any number is multiplied by 0, the product is always 0

Counterexample: an example that shows a conjecture is not true Simplify: writing algebraic expression in simpler form Deductive Reasoning: the process of using facts, properties, or rules to justify reasoning or reach valid conclusions Example 1 Identify Properties Name the property shown by each statement. a. 5 ⋅ 7 ⋅ 2 = 7 ⋅ 5 ⋅ 2 b. (1 + 8) + 4 = 1 + (8 + 4)c = 100

Example 2 Find a Counterexample State whether the following conjecture is true or false. If false, provide a counterexample. a. Subtraction of whole numbers is commutative. Example 4 Simplify Algebraic Expressions Simplify each expression. a. (c ⋅ 4) ⋅ 7 b. (m + 6) + 2