1. Section 1.1 Properties of Real Numbers

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

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

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

5. Graphing on a Number Line: 1. 2. 3. 4. 5. 024-2-4 Rational, Real Irrational, Real Natural, Whole, Integer, Rational, Real Integer, Rational, Real Irrational, Real White Boards

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

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

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

9. Absolute Value Absolute value of a real number is the distance from zero on the number line. 1. 2. 3. = 4 = – 18 = 1.5

10. page 9 79. 81. White Boards