1. Find opposites of numbers EXAMPLE 4 a. If a = – 2.5, then – a = – ( – 2.5 ) = 2.5. b. If a =, then – a = –. 3 4 3 4

2. Find absolute values of numbers EXAMPLE 5 2 3 2 3 a. If a = –, then | a | = |– | = – (– ) = 2 3 2 3 b. If a = 3.2, then |a| = |3.2| = 3.2.

3. EXAMPLE 6 Analyze a conditional statement Identify the hypothesis and the conclusion of the statement “If a number is a rational number, then the number is an integer.” Tell whether the statement is true or false. If it is false, give a counterexample. Hypothesis: a number is a rational number Conclusion: the number is an integer The statement is false. The number 0.5 is a counterexample, because 0.5 is a rational number but not an integer. SOLUTION

4. GUIDED PRACTICE for Example 4, 5 and 6 For the given value of a, find –a and |a|. 8. a = 5.3 – 5.3, 5.3 ANSWER

5. GUIDED PRACTICE for Example 4, 5 and 6 9. a = – 7 10. a = 4 9 – 7, 7 ANSWER 4 9 4 9,

6. GUIDED PRACTICE for Example 4, 5 and 6 Identify the hypothesis and the conclusion of the statement. Tell whether the statement is true or false. If it is the false, give a counterexample. 11. If a number is a rational number, then the number is positive Conclusion: the number is positive – false The number –1 is a counterexample, because –1 is a rational number but not positive. Hypothesis: a number is a rational number ANSWER

7. GUIDED PRACTICE for Example 4, 5 and 6 Conclusion: the number is positive – false The number –2 is a counterexample, because the absolute value of –2 is 2, but –2 is negative. If the absolute value of a number is a positive, then the number is positive. 12. Hypothesis: the absolute value of a number is positive ANSWER