2.5 Dividing Integers 177EXAMPLE (^1) Divide and check the result:
a. b. c. d.
StrategyWe will use the rule for dividing two integers that have different
(unlike) signs.
WHYEach division involves a positive and a negative integer.
Solution
a.Find the absolute values: and.
To check, we multiply the quotient, , and the divisor,7. We should get the
dividend,.
Check: The result checks.
b.Find the absolute values: and.
Check: The result checks.
c.Find the absolute values: and.
Check: The result checks.
d.Recall from Section 1.5, that if a divisor has ending zeros, we can simplify the
division by removing the same number of ending zeros in the divisor and
dividend.
There are two zeros in the divisor.
Remove two zeros from the dividend
and the divisor, and divide.
Check: 40(600)24,000 Use the original divisor and dividend in the check.
Divide the absolute values, 240 by 6,
to get 40.
Then make the final answer negative.
24,000 600 240 6 40
16(11) 176
Divide the absolute values, 176 by 11, to get 16.
Then make the final answer negative.176
11
16
01760 176 0 110 11
6(5) 30
Divide the absolute values, 30 by 5, to get 6.
Then make the final answer negative.30 (5) 6
0300 30 0 50 5
2(7) 14
14
2
Divide the absolute values, 14 by 7, to get 2.
Then make the final answer negative.14
7
2
0 140 14 070 7
24,000 600
176
11
30 (5)
14
7
Self Check 1
Divide and check the result:a.b.c.d.
Now TryProblems 13, 15, 21, and 2718,000 300
336
14
28 (4)
45
5
EXAMPLE (^2) Divide and check the result:
a. b. c. d.
StrategyWe will use the rule for dividing two integers that have the same (like)
signs.
WHYIn each case, we are asked to find the quotient of two negative integers.
Solution
a.Find the absolute values: and.
Check: 4(3) 12 The result checks.
Divide the absolute values, 12 by 3, to get 4.
The final answer is positive.
12
3
4
0 120 12 0 30 3
200 (40)
315
9
48 (6)
12
3
Self Check 2
Divide and check the result:a.b.c.d.
Now TryProblems 33, 37, 41, and 43400 (20)
301
7
24 (4)
27
3
16
11 176
11
66
66
0F F
F