Section 1 2 Properties of Real Numbers R

Section 1. 2 Properties of Real Numbers

R Real Numbers Living Things = Rational Animals I Integers Mammals W Whole Dogs N Natural Border Collies Irrational Plants IRR

Real Numbers Rational Numbers Ex: ½ , 0. 3, 1, 2, 2, , Integers Ex: …, -2, -1, 0, 1, 2, … Whole Numbers Ex: 0, 1, 2, 3 … Natural Numbers Ex: 1, 2, 3 … , -1. 07 Irrational Numbers Ex: - , ,

Natural Numbers: 1, 2, 3, … • Numbers used for counting Whole Numbers: 0, 1, 2, 3, … • Natural Numbers and 0 Integers: …, -2, -1, 0, 1, 2, … Textbook: Page 5 • Natural Numbers, 0, and their opposites Rational Numbers: • Repeating or terminating decimal Irrational Numbers: cannot be written as a ratio of integers; non-repeating or non-terminating decimals

Graphing on a Number Line: -4 0 2 4 Rational, Real 1. Irrational, Real 2. 3. -2 Natural, Whole, Integer, Rational, Real White Boards 4. 5. Integer, Rational, Real Irrational, Real

The opposite (additive inverse) of any number a is –a When you add together, = 0 The Identity Element! The reciprocal (multiplicative inverse) of any nonzero number a is When you multiply together, = 1

Mixed Number: Improper Fraction: White Boards Opp. Rec.

Properties of Real Numbers Property Addition Multiplication Closure Words a + b is a real number. ab = ba Commutative Order a + b = b + a (ab)c = a(bc) Associative Group (a + b) + c = a + (b + c) a 1 = a, 1 a = a Identity Mirror a + 0 = a, 0 + a = a a + (-a) = 0 a = 1, a ≠ 0 Inverse Undo Distributive 1 st x 1 st + 1 st x 2 nd a(b + c) = ab + ac Identifying Properties of Real Numbers: White Boards 1. (-7)(2 5) = (-7)(5 2) Commutative Property of Multiplication 2. 3 ( 8 + 0) = 3 8 Identity Property of Addition 3. - 5 + [2 + (-3)] = (-5 + 2) + (-3) Associative Property of Addition

Absolute Value • Absolute value of a real number is the distance from zero on the number line. 1. 2. 3. =4 = – 18 = 1. 5

page 9 White Boards 79. 81.