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

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 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 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-3 Multiplication and Division of Real Numbers

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-4 Sign of the Product Rule The product of two numbers with like signs is a positive number. The product of two numbers with unlike signs is a negative number. Example: a.) 4( – 5) = – 20 b.) ( – 6)(7) = -42 c.) ( – 9)(-3) = 27

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-5 Helpful Hint At this point some students begin confusing problems like -2 – 3 with (-2)(-3) and problems like 2-3 and (-2)(-3). Make sure you understand the difference between these problems. Subtraction Problems – 2 – 3 = – = – 1 Multiplication Problems (-2) ( – 3) = 6 (2)(-3)= – 6

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-6 Divide Numbers 1. The quotient of two numbers with like signs is a positive number. 2. The quotient of two numbers with unlike signs is a negative number. Example: a.)b.)c.) The Sign of the Quotient of Two Real Numbers

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-7 Helpful Hint (+)(+) = + (–)(–) = + (+)(–) = – (–)(+) = – Like signs give positive products and quotients. Unlike signs give negative products and quotients. For multiplication and division of two real numbers:

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-8 Remove Negative Signs from Denominators If a and b represent any real numbers, b  0, then We generally do not write fractions with a negative sign in the denominator. When a negative sign appears in a denominator, we can move it to the numerator or place it in front of the fraction. The fraction would be written as or.

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-9 Real Number Operations

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-10 Evaluate Divisions Involving Zero If a represents any real number except 0, then 0  a = = 0 Division by 0 is undefined.