EXERCISES
For more exercises, see Extra Practice.
Practice and Problem Solving
A
Practice by Example
Examples 1 and 2
(pages 8 and 9)
Simplify each expression.
1. 3 + 6 3 4 27
2. 35 ⫼ 7 - 2 3
3. 8 - 2 ? 3 2
4. 6 - 6 ⫼ 3 4
5. 21 - 13 + 8 16
6. 6 ? 2 + 4 16
7. 12 - 8 ⫼ 2 + 3 11 8. 21 ⫼ 7 + 14 3 2
10. 4(4) - 2(5) 6
Example 3
(page 9)
B
Apply Your Skills
22.
e
9. 2 ? 2 + 0 ? 4 4
31
11. 2 + 3 ? 24 ⫼ 6 14 12. 4 ⫼ 4 ? 4 + 4 - 4 4
13. 7 + 3 ? (8 ⫼ 4) 13 14.
8 17 17.
16. 2(6) + 7 1
3
2 8
19. 6 + 6 1
20.
4
2(15 - 9) ? 9 108 15. [2 + (6 ? 8)] - 1 49
3(7 + 4) 33
18. 12 ⫼ (3 - 2) + 1 13
21 1 15 4
316
21. (21 + 3) ⫼ 4 ⫼ 2 3
22. Error Analysis A student found the value of the expression
30 ⫼ 6 - 1 to be 6. Explain the student’s error.
.
23.
Writing in Math Why do we need to agree on an order of
operations? We
Simplify each expression.
24. (56 - 5) ⫼ 17 3
25. 60 ⫼ 4 + 9 24
26. 2[8 + (5 - 3)] - 8
27. 12 ⫼ 3 3 4 16
28. 36 - 27 ⫼ 9 ⫼ 1
29. 6(4 + 1) - 5 25
30. 14 + 5 3 2 24
31. 440 ⫼ (2 + 18)
32. 16 ⫼ 8 3 2 4
33
22
12
Compare. Use S, R, or 5 to complete each statement.
33. 15 ? 3 - 2 ■ 15 ? (3 - 2) S
34. 18 - 6 ⫼ 3 ■ (18 - 6) ⫼ 3 S
35. 8 + 12 ⫼ 4 ■ (8 + 12) ⫼ 4 S
36. 22 - 7 ? 2 ■ (22 - 7) ? 2 R
37. 12 ⫼ 3 + 9 ? 4 ■ 12 ⫼ (3 + 9) ? 4 S
38. (19 - 15) ⫼ (3 + 1) ■ 19 - 15 ⫼ 3 + 1 R
Insert grouping symbols to make each number sentence true.
39. 7 + 4 ? 6 = 66
40. 7 ? 8 - 6 + 3 = 17
41. 3 + 8 - 2 ? 5 = 45
42. 6 ? 3 + 9 - 4 = 23
(7 ± 4) ? 6
66
(3 ± 8 – 2) ? 5
45
[7 ? (8 – 6)] ± 3
17
(6 ? 3) ± (9 – 4)
23
Write a numerical expression for each phrase. Then simplify.
43. five added to the product of four and nine 4 ? 9 ± 5; 41
44. twenty-one minus the sum of fifteen and five 21 – (15 ± 5); 1
45. seventeen minus the quotient of twenty-five and five
17 – (25 4 5); 12
1-2
The Order of Operations
11-12
46. On the Job A part-time employee worked 4 hours on Monday
GPS and 7 hours each day for the next 3 days. Write and simplify an
expression that shows the total number of hours worked.
C
Challenge
Write two expressions you could use to find the area of each shaded
figure. Find the area.
47.
2m
48.
6 in.
49.
4 ft
1 ft
2m
3 in.
5 in.
6m
2m
3 ft
5 ft
3 ft
2m
2 in.
1 ft
4 ft
6m
50. Open-Ended Write a word problem for the numerical expression
3(4 + 3) + 2. Then simplify the expression. See margin.
49.
51. Number Sense Use the digits 1–9 in order. Insert operation signs
and grouping symbols to get a value of 100.
Test Prep
Multiple Choice
A
3
4
5
A
A
B
B
E
D
E
D
C
B
E
D
C
B
E
D
C
B
A
2
C
B
A
1
C
C
52. Which expression has a value of 18? D
A. 3 ? 2 + 4
B. (18 - 10) ⫼ 4 + 15
C. 4 ? 2 + 3 - 2
D. 27 - 13 ? 2 + 17(6 - 5)
D
D
E
E
Test-Taking Tip
You should consider all
answer choices before
deciding on the
appropriate one.
Take It to the NET
Online lesson quiz at
www.PHSchool.com
53. Which expression gives the area of the garden? G
5 ft
F. 4(2 + 5) + 5 ? 5
2 ft
G. (2 + 5 + 2) ? (2 + 5 + 2) - 4(2 ? 2)
H. (2 + 5 + 2) - (2 ? 2)
I. 4(2 ? 2) + 4(5 ? 2) + 5 ? 5
2 ft
54. Which set of grouping symbols makes
the equation true? 2 ? 3 + 5 - 2 ? 2 = 12 D
A. (2 ? 3) + 5 - (2 ? 2)
B. 2 ? [3 + (5 - 2)] ? 2
C. 2 ? [3 + (5 - 2 ? 2)]
D. 2 ? (3 + 5) - 2 ? 2
55. What is the value of 8 ? 5 - 3(24 ⫼ 6)? F
F. 28
G. 64
H. 111
I. 148
Web Code: ada-0102
Mixed Review
Lesson 1-1
Write a variable expression for each word phrase.
k
20
56. the product of a number
n and 8 8n
57. k divided by 20
58. six less than a number h
59. the value, in cents, of d dimes
h–6
10d
60. A telephone call costs c cents per minute. Write a variable
expression for the cost of a 15-minute call. 15c
11-12
Chapter 1 Algebraic Expressions and Integers