1. 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.

2. 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 = 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)

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 = 0
Multiplication Property of - 1: ∙ a= - a ∙ 3 = -3

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 = 0
Multiplication Property of - 1: ∙ a= - a ∙ 3 = -3

5. We must be able to identify and use the properties of real numbers such as:
Ex: Name the properties that each statement illustrates: ) = ) 9 ∙ (-1 ∙ x)=9 ∙ (-x)
Answers: ) Commutative Property of Additions ) 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 t Solution.

6. 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 ( ). This is not true.

7. Class Work:
Pages: Problems : 7 through 45
(2n + 1)