Drill 2 Evaluate each expression if a 6

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

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) Examples:

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 Z N W Q I = irrationals Q = rationals Z = integers W = wholes N = naturals

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

Properties of Real Numbers* For any real numbers a, b, and c Addition Commutative a + b = b + a Multiplication a(b) = b(a) Associative (a + b)+c =a+(b + c) (ab)c = a(bc) Identity a+0=a=0+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 a(1) = a = 1(a)

Example 1: Name the property** a. (3 + 4 a) 2 = 2 (3 + 4 a) b. 62 + (38 + 75) = (62 + 38) + 75 c. 5 – 2(x + 2) = 5 – 2 ( 2 + x)

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

Example 2: Find the additive inverse and multiplicative inverse: a. ¾ b. – 2. 5 c. 0 d.