1.4 Properties of Real Numbers ( ) Vocabulary: Equivalent Expression: two expressions that have the same value for all values of the variable(s). Deductive Reasoning: The process of reasoning logically from given facts to a conclusion Counterexample: An example showing that a statement is false.

1.4 Properties of Real Numbers ( ) We must be able to identify and use the properties of real numbers such as: Commutative Property: of Addition: a + b = b + a 3 + 5 = 5 + 3 0f Multiplication: a ∙ b = b ∙ a 3 ∙ 5 = 5 ∙ 3 Associative Property: of Addition: (a+b)+c = a+(b+c) (3 + 5)+4 = 3+(5+4) 0f Multiplication: (a ∙ b)∙c = a∙(b∙ c) (3∙5)4 = 3∙(5∙4)

Identity Property: of Addition: a + 0= a 3 + 0 = 3 0f Multiplication: a ∙ 1 = a 3 ∙ 1 = 3 Zero Property of Multiplication: a ∙ 0 = 0 3 ∙ 0 = 0 Multiplication Property of - 1: - 1 ∙ a= - a - 1 ∙ 3 = -3

Identity Property: of Addition: a + 0= a 3 + 0 = 3 0f Multiplication: a ∙ 1 = a 3 ∙ 1 = 3 Zero Property of Multiplication: a ∙ 0 = 0 3 ∙ 0 = 0 Multiplication Property of - 1: - 1 ∙ a= - a - 1 ∙ 3 = -3

We must be able to identify and use the properties of real numbers such as: Ex: Name the properties that each statement illustrates: 1) 76 + 5 = 5 + 76 2) 9 ∙ (-1 ∙ x)=9 ∙ (-x) Answers: 1) Commutative Property of Additions 2) Multiplication Property of -1 Ex: Simplify and justify each step: 1) 8 + (9t + 4 ) Answers: (8 + 4) + 9t Associative Property (12) + 9t Addition of like terms 9t + 12 Solution.

We must also be able to see given information and make decisions using some common sense: Ex: For all real numbers r, s, and t, is (r ∙ s) ∙ t = t ∙ (s ∙ r) true or false? Answers: True, this is the commutative property of multiplication Ex: Your friend says that the associative property allows us to change the order in which we complete any two operations. Is this true? If false, provide a counterexample. Answers: False since Associative property only applies when both operations are adding or multiplying and not a combination of both. Counterexample: (8 ∙ 11) + 9 = 8 ( 11 + 9). This is not true.

Class Work: Pages: 26 - 28 Problems : 7 through 45 (2n + 1)