Section 2.1 Integers, Absolute Value, and Opposite 87 Answers 4–6 5 4 3 2 1 0 1 2 3 4 5 7. 8. 9. Locating Integers on the Number Line Locate each number on the number line. a. 4 b. 7 c. 0 d. 2 Solution: On the number line, negative numbers lie to the left of 0, and positive numbers lie to the right of 0. 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 As with whole numbers, the order between two integers can be determined using the number line. • A number a is less than b (denoted a b) if a lies to the left of b on the number line (Figure 2-3). • A number a is greater than b (denoted a b) if a lies to the right of b on the number line (Figure 2-4). Figure 2-3 Figure 2-4 Determining Order Between Two Integers Use the number line from Example 2 to fill in the blank with or to make a true statement. a. 7 4 b. 0 4 c. 2 7 Solution: a. 7 4 7 lies to the left of 4 on the number line. Therefore, 7 4. b. 0 4 0 lies to the right of 4 on the number line. Therefore, 0 4. c. 2 7 2 lies to the right of 7 on the number line. Therefore, 2 7. 2. Absolute Value On the number line, pairs of numbers like 4 and 4 are the same distance from zero (Figure 2-5). The distance between a number and zero on the number line is called its absolute value. Distance is 4 units. 4 3 2 1 0 1 2 3 4 5 Figure 2-5 Distance is 4 units. 5 Example 3 b a a is greater than b. a b a b a is less than b. a b Example 2 Skill Practice Locate each number on the number line. 4. 5 5. 1 6. 4 5 4 3 2 1 0 1 2 3 4 5 Skill Practice Fill in the blank with or . 7. 3 8 8. 3 8 9. 0 11
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