1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objectives Compare real numbers. Simplify expressions involving opposites and absolute value. 2.1 The Real Numbers and Absolute Value

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms absolute value integers irrational numbers natural numbers negative numbers opposites positive numbers rational numbers real numbers 2.1 The Real Numbers and Absolute Value whole numbers

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Sets of Numbers 2.1 The Real Numbers and Absolute Value Natural or counting numbers: N = 1, 2, 3, 4,... Whole numbers: W = 0, 1, 2, 3, 4,... Integers: I =... –3, –2, –1, 0, 1, 2, 3,...

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties 2.1 The Real Numbers and Absolute Value Definition of Absolute Value: The absolute value of a real number x is the distance from x to 0 on a number line. The symbol |x| means the absolute value of x. Definition of Rational Number: Any number that can be expressed in the form, where a and b are integers and b  0, is a rational number. a b

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills 2.1 The Real Numbers and Absolute Value a.5 –12b.9 17 a.5 is to the right of –12 on a number line, so 5 > –12. b.9 is to the left of 17 on a number line, so 9 < 17. Insert an ordering symbol to make each statement true. Compare values of real numbers.

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills 2.1 The Real Numbers and Absolute Value |–11| = 11 To find the absolute value of –11, find the distance from –11 to 0 on a number line. Find the absolute value of a number. TOC