Page 1 of 5
Dividing Integers
BEFORE
Now
WHY?
You multiplied integers.
You’ll divide integers.
So you can find a squirrel’s body
temperature, as in Example 3.
You can evaluate a division equation by solving the
related multiplication equation.
Word Watch
Review Words
mean, p. 101
1 Copy and complete the table.
Division Equation
18 9 _?_
15 5 _?_
14 7 _?_
10 (2) _?_
12 (4) _?_
Related Multiplication
Equation
_?_ p 9 18
?
?
?
?
Quotient
2
?
?
?
?
Copy and complete the statement using positive or negative.
2 A negative integer divided by a positive integer is _?_.
3 A negative integer divided by a negative integer is _?_.
In the activity, you saw that the rules for dividing integers are similar to
the rules for multiplying integers.
Dividing Integers
tch Out!
Wa
You cannot divide
a number by 0. Any number
divided by 0 is undefined.
For example, 8 0 _?_
can be rewritten as
_?_ p 0 8. No number
times 0 will result in a
nonzero product.
278
Chapter 6
Integers
Words
Numbers
Same Sign The quotient of
two integers with the same
sign is positive.
10 2 5
Different Signs The quotient
of two integers with different
signs is negative.
Zero The quotient of 0 and
any nonzero integer is 0.
24
8
3
15 (3) 5
18
3
6
0 17 0
0
0
9
Page 2 of 5
EXAMPLE
1
Dividing Integers
The quotient of two integers with different
signs is negative.
a. 28 (4) 7
60
5
b. 12
The quotient of two integers with the same
sign is positive.
c. 0 (13) 0
The quotient of 0 and any nonzero integer is 0.
Your turn now
1. 24 6
Geography
EXAMPLE
2
Find the quotient.
39
3. 13
0
2. 2
4. 19 (1)
Finding the Mean
Bangor, Maine The table shows
the high temperatures for four days in
January in Bangor, Maine. Find the
mean of the temperatures.
Solution
Day
Monday
Tuesday
Wednesday
Thursday
Temperature
7C
4C
7C
2C
1 Find the sum of the temperatures.
7 (4) (7) (2) 20
2 Divide the sum by the number of temperatures, 4.
20 4 5
■
Bangor, Maine
Bangor, Maine, is home to
the statue of mythical
lumberman Paul Bunyan.
Standing 31 feet tall and
weighing 3700 pounds,
the statue greets visitors
entering Bangor. What is
the statue’s mean weight
per foot of height?
ANSWER The mean high temperature for the four days was 5C.
Your turn now
Solve the following problem.
5. A submarine’s elevations over several hours are 284 ft, 245 ft,
372 ft, 356 ft, and343 ft. Find the mean of the elevations.
Temperature Conversions Operations with positive and negative numbers
are needed to convert temperatures between degrees Celsius C and degrees
Fahrenheit F.
9
• To convert Celsius to Fahrenheit, use the formula F C 32.
5
5
• To convert Fahrenheit to Celsius, use the formula C (F 32).
9
Lesson 6.5
Dividing Integers
279
Page 3 of 5
EXAMPLE
3
Converting a Temperature
Biology During hibernation, an Arctic ground squirrel can decrease its
body temperature to 30C. Convert this temperature to degrees
Fahrenheit.
Solution
9
5
Write formula for degrees Fahrenheit.
9
5
Substitute 30 for C.
F C 32
(30) 32
6
9 p (30)
5p1
32
1
Use rule for multiplying fractions.
Divide out common factor.
54 32
Multiply.
22
Add.
ANSWER The temperature 30C is equal to 22F.
Your turn now
Convert the temperature from degrees Fahrenheit to
degrees Celsius or from degrees Celsius to degrees Fahrenheit.
6. 0C
7. 4F
8. 45C
9. 77F
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 710
Getting Ready to Practice
Vocabulary Tell whether the statement is true or false. Explain.
1. The quotient of a negative integer and a positive integer is positive.
with
Review
Need help with finding the
mean? See p. 101.
2. The mean of 10, 2, and 7 is 5.
5
3. The expressions and 0 (5) are both equal to 0.
0
Find the quotient.
4. 6 (2)
5. 6 2
6. 6 (2)
7. 36 (12)
8. 26 13
9. 42 (7)
10. Boiling Point The boiling point of water is 100C. What is this
temperature in degrees Fahrenheit?
280
Chapter 6
Integers
Page 4 of 5
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
11–22
23–28, 33
29–32, 34–35
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Find the quotient.
11. 44 11
12. 64 32
13. 70 (10)
14. 34 (17)
15. 76 (19) 16. 84 (7)
17. 63 (9)
18. 52 13
19. 24 8
21. 0 (121)
22. 96 (12)
20. 72 (9)
Find the mean of the integers.
23. 10, 6, 3, 9
24. 46, 33, 0, 11
25. 10, 27, 4, 9
26. 8, 11, 18, 8
27. 7, 9, 9, 7, 0
28. 17, 4, 5, 21, 30
Convert the temperature from degrees Fahrenheit to degrees
Celsius or from degrees Celsius to degrees Fahrenheit.
29. 50°C
30. 32°F
31. 13°F
32. 1°C
33. Bowling Alley A bowling alley’s gains and losses over 5 months are
$450, $675, $1230, $776, and $95. Find the mean of the monthly
gains and losses for the bowling alley.
34. Bathing Monkeys During the winter in Japan, macaque monkeys find
warmth in a hot spring that is fed by the Shirane Volcano. The water
temperature is typically around 39C, while the air temperature can
reach 5C. Convert these temperatures to degrees Fahrenheit.
35. Cooking A recipe says to preheat your oven to 160C. Your oven has
temperature settings in degrees Fahrenheit. At what temperature should
you set your oven?
Algebra Evaluate the expression when s 16 and t 5.
36. t (1)
37. s (8)
38. 64 s
39. 45 t
40. 0 s
41. s (4) 2
42. 25 t 7
43. 10 t s
44. Critical Thinking What can you tell about two integers when their
quotient is positive? negative? zero?
45. Estimate Explain why the expression 2C 30 can be used to estimate
the value of a Celsius temperature in degrees Fahrenheit. Then use the
expression to estimate the value of 15C in degrees Fahrenheit.
Copy and complete the statement using <, >, or .
46. 4 (2) 1 _?_ 4 2 1
47. 46 (23) _?_ 46 23
48. 0 4 9 _?_ 0 7 9
49. 25 (5) (1) _?_ 5
Lesson 6.5
Dividing Integers
281
Page 5 of 5
50. Astronomy Find the mean of the following average temperatures of
four of Saturn’s moons: 328F, 330F, 289F, 305F.
Use the number line to complete
the statement using <, >, or .
a b
c
0
d
e
51. a c _?_ 0
52. d c _?_ 0
53. e d _?_ a
54. 0 a _?_ 0 e
55. e a _?_ e d
56. c d _?_ a b
57. Challenge The mean of four integers is 0. Three of the integers
are 9, 7, and 3. What is the fourth integer?
Mixed Review
Find the quotient. (Lesson 5.4)
9
59. 7 10
3
58. 5 4
7
49
60. 12
60
8
11
61. 13
26
64. 41(52)
65. 67(80)
Find the product. (Lesson 6.4)
62. 13(5)
63. 29(6)
Basic Skills Write a fraction to represent the shaded part of
the set or region.
66.
67.
68.
69.
Test-Taking Practice
INTERNET
70. Extended Response The temperature was 5°C at 6:15 A.M., 49°F at
State Test Practice
noon, and 5°C at 6:15 P.M. Make a line graph of the temperature data in
degrees Fahrenheit. What was the change in temperature, in degrees
Fahrenheit, between 6:15 A.M. and noon? What was the change in
temperature, in degrees Fahrenheit, between noon and 6:15 P.M.?
CLASSZONE.COM
Same Numbers, Different Answers
Copy and complete each statement using the numbers
3, 2, 4, and 5. Use all four numbers in each statement.
_?_ p _?_ p _?_ _?_ 26
282
Chapter 6
Integers
_?_ _?_ _?_ _?_ 6