Chapter 1-4: PropertiesCommutative Property: the order in which you add or multiply numbers does not change the sum or product

Ex. 4 + 5 = 5 + 4 6 * 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 numberMultiplicative Identity: When any number is multiplied by 1, the product is that numberMultiplicative 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 conclusionsExample 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 + 0 = 100

Example 2 Find a CounterexampleState whether the following conjecture is true or false. If false, provide acounterexample.

a. Subtraction of whole numbers is commutative.

Example 4 Simplify Algebraic ExpressionsSimplify each expression.

a. (c ⋅ 4) ⋅ 7 b. (m + 6) + 2