88 Chapter 2 Integers and Algebraic Expressions Absolute Value The absolute value of a number a is denoted 0a 0 . The value of 0a 0 is the distance between a and 0 on the number line. From the number line, we see that and . 04 0 4 04 0 4 Finding Absolute Value Example 4 Determine the absolute value. a. 05 0 b. 03 0 c. 00 0 Solution: a. The number 5 is 5 units from 0 on the number line. 5 5 5 4 3 2 1 0 1 2 3 4 5 05 0 5 b. The number 3 is 3 units from 0 on the number line. 3 3 5 4 3 2 1 0 1 2 3 4 5 03 0 3 c. The number 0 is 0 units from 0 on the number line. 0 0 5 4 3 2 1 0 1 2 3 4 5 00 0 0 3. Opposite Two numbers that are the same distance from zero on the number line, but on opposite sides of zero, are called opposites. For example, the numbers 2 and 2 are opposites (see Figure 2-6). Same distance 4 3 2 1 0 Figure 2-6 1 2 3 4 The opposite of a number, a, is denoted 1a2. The opposite of a negative number is a positive number. That is, for a positive number, a, the value of a is negative and 1a2 a. 08 0 TIP: The absolute value of a nonzero number is always positive. The absolute value of zero is 0. Answers 10. 8 11. 1 12. 16 Original number Opposite Simplified a (a) Form 5 152 5 7 172 7 f The opposite of a negative number is a positive number. f The opposite of a positive number is a negative number. Skill Practice Determine the absolute value. 10. 11. 0 1 0 12. 016 0
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