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EXAMPLE 4
a.
Find opposites of numbers
If a = – 2.5, then – a = –(– 2.5) = 2.5.
b. If a = 3 , then – a = – 3 .
4
4
EXAMPLE 5
a.
Find absolute values of numbers
2
2
2
2
If a = – , then | a | = |– | = – (– ) =
3
3
3
3
b. If a = 3.2, then |a| = |3.2| = 3.2.
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.
SOLUTION
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.
GUIDED PRACTICE
for Example 4, 5 and 6
For the given value of a, find –a and |a|.
8.
a = 5.3
ANSWER
– 5.3, 5.3
GUIDED PRACTICE
9.
a=–7
ANSWER
7, 7
10.
a= – 4
9
ANSWER
4 ,4
9 9
for Example 4, 5 and 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
ANSWER
Hypothesis: a number is a rational number
Conclusion: the number is positive – false
The number –1 is a counterexample, because –1 is a
rational number but not positive.
GUIDED PRACTICE
for Example 4, 5 and 6
12. If the absolute value of a number is a
positive, then the number is positive.
ANSWER
Hypothesis: the absolute value of a number is positive
Conclusion: the number is positive – false
The number –2 is a counterexample, because the
absolute value of –2 is 2, but –2 is negative.