Real Numbers Chapter 1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-1

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Study Skills for Success in Mathematics 1.2 – Problem Solving 1.3 – Fractions 1.4 – The Real Number System 1.5 – Inequalities and Absolute Value 1.6 – Addition of Real Numbers 1.7 – Subtraction of Real Numbers 1.8 – Multiplication and Division of Real Numbers 1.9 – Exponents, Parentheses and Order of Operations 1.10 – Properties of the Real Number System Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-3 Properties of the Real Number System

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-4 Commutative Property Commutative Property of Addition If a and b represent any two real numbers, then a + b = b + a = Commutative Property of Multiplication If a and b represent any real numbers, then a · b = b · a 6 · 3 = 3 · 6 Commutative (commute) changes the order. *Note that the commutative property does not hold for subtraction and division 7 = 7 18 = 18

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-5 Associative Property Associative Property of Addition If a, b, and c represent three real numbers, then (a + b) + c = a + (b + c) (3 + 4) + 5 = 3 + (4 + 5) Associative Property of Multiplication If a, b, and c represent any three real numbers, then (a · b) · c = a ·(b · c) (6 · 2) · 4 = 6 · (2 · 4) Associative (associate) changes the grouping. *Note that the associative property does not hold for subtraction and division = = · 4 = 6 · 8 48 = 48

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-6 Distributive Property If a, b, and c represent three real numbers, then a(b + c) = ab + ac Distributive involves two operations (usually multiplication and division). 2(3 + 4) = 2(3) + 2(4) 2(7) = = 14

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-7 Identity Properties If a represents any real number, then a + 0 = a and 0 + a = a a · 1 = a and 1 · a = a Identity Property of Addition Identity Property of Multiplication = = 4 13 · 1 = 13 1 · 13 = 13

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-8 Inverse Properties If a represents any real number, then a + (-a)= 0 and (-a) + a = 0 Inverse Property of Addition Inverse Property of Multiplication a · = 1 and · a = a (a  0) 7 + (-7) = 0 (-7) + 7 = 0 12 · = 1 · 12 = 1