Drill #3 Evaluate each expression if a = 6, b = ½, and c = 2. 1. 2. 3. 4.

Drill #4 Evaluate each expression if a = -3, b = ½, c = 1. Name ALL sets of numbers to which each number belongs:

Drill #5 Name the property illustrated by each statement 1. (3 + 4a) 2 = 6 + 8a 2. ¼ - ¼ = 0 3. 1(10x) = 10x 5(6*7) = (5*6)7 State the Additive and Mult. Inverse of each 5. -6.2 6. 3 ½

1-2 Properties of Real Numbers Objective: To determine sets of numbers to which a given number belongs and to use the properties of real numbers to simplify expressions.

Rational and Irrational numbers* Rational numbers: a number that can be expressed as m/n, where m and n are integers and n is not zero. All terminating or repeating decimals and all fractions are rational numbers. Examples: Irrational Numbers: Any number that is not rational. (all non-terminating, non-repeating decimals)

Rational Numbers (Q)* The following are all subsets of the set of rational numbers: Integers (Z): {…-4, -3, -2, -1, 0, 1, 2, 3, 4, …} Whole (W): {0, 1, 2, 3, 4, 5, …} Natural (N): { 1, 2, 3, 4, 5, …}

Venn Diagram for Real Numbers * Reals, R I = irrationals Q = rationals Z = integers W = wholes N = naturals Q I Z W N

Find the value of each expression and name the sets of numbers to which each value belongs: I, R Q, R W, Z, Q, R Z, Q, R

Find the value of each expression and name the sets of numbers to which each value belongs:

Properties of Real Numbers** For any real numbers a, b, and c Addition Multiplication Commutative a + b = b + a a(b) = b(a) Associative (a + b)+c =a+(b + c) (ab)c = a(bc) Identity a + 0 = a = 0 + a a(1) = a = 1(a) Inverse a + (-a) = 0 = -a + a a(1/a) =1= (1/a)a Distributive a(b + c)= ab + ac & a(b - c)= ac – ac

Name the property: Examples* (3 + 4a) 2 = 2 (3 + 4a) 62 + (38 + 75) = (62 + 38) + 75 5 – 2(x + 2) = 5 – 2 ( 2 + x)

Simplify An Expression: Examples Simplify each expression: #1: 3( 2q + r) + 5(4q – 7r) #2: 3(4x – 2y) – 2(3x + y) #3: 9x +3y + 12y -0.9x

Multiplicative and Additive Inverses: Examples #1. ¾ #2. – 2.5 #3. 0 #4.

Inverses And the Identity* The inverse of a number for a given operation is the number that evaluates to the identity when the operation is applied. Additive Identity = 0 Multiplicative Identity = 1