Fundamentals of Mathematics, 2008a

607
10.7.3 Division of Signed Numbers
To determine the signs in a division problem, recall that
12
3
= 4 since 12 = 3 · 4
This suggests that
(+)
(+) = (+)
(+)
(+)
= (+) since (+) = (+) (+)
What is 12
−3 ?
−12 = (−3) (−4) suggests that 12
−3
= −4. That is,
(+)
(−) = (−)
(+) = (−) (−) suggests that (+)
(−) = (−)
What is −12
3 ?
−12 = (3) (−4) suggests that −12
3
= −4. That is,
(−)
(+) = (−)
(−) = (+) (−) suggests that (−)
(+) = (−)
What is −12
−3 ?
−12 = (−3) (4) suggests that −12
−3
(−)
(−) = (+)
(−) = (−) (+) suggests that (−)
(−) = (+)
= 4. That is,
We have the following rules for dividing signed numbers.
Rules for Dividing Signed Numbers
Dividing signed numbers:
1. To divide two real numbers that have the same sign, divide their absolute values. The quotient is
positive.
(+) (−)
(+)
= (+)
(−) = (+)
2. To divide two real numbers that have opposite signs, divide their absolute values. The quotient is
negative.
(−)
(+)
= (−)
(+)
(−) = (−)
10.7.3.1 Sample Set B
Find the following quotients.
Example 10.39
−10
2
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