Drill #2 Evaluate each expression if a = 6, b = ½, and c =

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

Properties of Real Numbers* For any real numbers a, b, and c AdditionMultiplication Commutativea + b = b + aa(b) = b(a) Associative(a + b)+c =a+(b + c)(ab)c = a(bc) Identitya + 0 = a = 0 + aa(1) = a = 1(a) Inversea + (-a) = 0 = -a + aa(1/a) =1= (1/a)a Distributivea(b + c)= ab + ac & a(b - c)= ac – ac

Example 1: Name the property** a.(3 + 4a) 2 = 2 (3 + 4a) b.62 + ( ) = ( ) + 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.