Properties of Real Numbers Section 1.2 Properties of Real Numbers

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

Real Numbers Ex: ½ , 0.3, 1, 2, 2, , , -1.07 Irrational Numbers Integers Ex: …, -2, -1, 0, 1, 2, … Whole Numbers Ex: 0, 1, 2, 3 … Natural Numbers Ex: 1, 2, 3 …

Natural Numbers: 1, 2, 3, … Whole Numbers: 0, 1, 2, 3, … Textbook: Page 5 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, … 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: 2 4 -2 -4 Rational, Real 1. 2. 3. 4. 5. Irrational, Real Natural, Whole, Integer, Rational, Real White Boards 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

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

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

Absolute Value Absolute value of a real number is the distance from zero on the number line. = 4 = – 18 = 1.5

page 9 White Boards 79. 81.