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Prealgebra

Chapter 3

PrealgebraChapter 3

Chapter 3

Try It

3.3
  1. ⓐ >
  2. ⓑ <
  3. ⓒ >
  4. ⓓ >
3.4
  1. ⓐ <
  2. ⓑ >
  3. ⓒ <
  4. ⓓ >
3.5
  1. ⓐ −4
  2. ⓑ 3
3.6
  1. ⓐ −8
  2. ⓑ 5
3.7

1

3.8

5

3.9
  1. ⓐ −4
  2. ⓑ 4
3.10
  1. ⓐ −11
  2. ⓑ 11
3.11
  1. ⓐ 12
  2. ⓑ −28
3.12
  1. ⓐ 9
  2. ⓑ −37
3.13
  1. ⓐ 17
  2. ⓑ 39
  3. ⓒ −22
  4. ⓓ −11
3.14
  1. ⓐ 23
  2. ⓑ 21
  3. ⓒ −37
  4. ⓓ −49
3.15
  1. ⓐ >
  2. ⓑ >
  3. ⓒ <
  4. ⓓ =
3.16
  1. ⓐ>
  2. ⓑ =
  3. ⓒ >
  4. ⓓ <
3.17
  1. ⓐ 3
  2. ⓑ 18
3.18
  1. ⓐ 11
  2. ⓑ 63
3.19

2

3.20

3

3.21

16

3.22

9

3.23
  1. ⓐ −9
  2. ⓑ 15
  3. ⓒ −20
  4. ⓓ 11−(−4)
3.24
  1. ⓐ 19
  2. ⓑ −22
  3. ⓒ −9
  4. ⓓ −8−(−5)
3.25

5 yards

3.26

−30 feet

3.27



6

3.28



7

3.29



−6

3.30



−7

3.31



−2

3.32



−3

3.33



2

3.34



3

3.35
  1. ⓐ
  2. ⓑ

  3. ⓒ

  4. ⓓ
3.36
  1. ⓐ

  2. ⓑ

  3. ⓒ

  4. ⓓ
3.37
  1. ⓐ −17
  2. ⓑ 57
3.38
  1. ⓐ −46
  2. ⓑ 26
3.39

−50

3.40

−70

3.41

13

3.42

0

3.43
  1. ⓐ 2
  2. ⓑ −12
3.44
  1. ⓐ 2
  2. ⓑ −1
3.45
  1. ⓐ −6
  2. ⓑ 10
3.46
  1. ⓐ −1
  2. ⓑ 17
3.47

9

3.48

13

3.49

196

3.50

8

3.51

−7 + 4 = −3

3.52

−8 + (−6) = −14

3.53

[9 + (−16)] + 4 = −3

3.54

[−8 + (−12)] + 7 = −13

3.55

4 degrees Celsius

3.56

−33 feet

3.57

14-yard line

3.58

37-yard line

3.59



2

3.60



3

3.61



−2

3.62



−3

3.63



−10

3.64



−11

3.65



10

3.66



11

3.67

ⓐ


ⓑ


ⓒ


ⓓ

3.68

ⓐ


ⓑ


ⓒ


ⓓ

3.69

ⓐ


−2
ⓑ


4

3.70

ⓐ


−3
 ⓑ


3

3.71
  1. ⓐ 8, 8
  2. ⓑ −18, −18
3.72
  1. ⓐ 8, 8
  2. ⓑ −22, −22
3.73
  1. ⓐ 19, 19
  2. ⓑ −4, −4
3.74
  1. ⓐ 23, 23
  2. ⓑ 3, 3
3.75

−29

3.76

−26

3.77

3

3.78

13

3.79

−69

3.80

−47

3.81
  1. ⓐ −2
  2. ⓑ −15
3.82
  1. ⓐ −2
  2. ⓑ −7
3.83
  1. ⓐ −2
  2. ⓑ 36
3.84
  1. ⓐ −19
  2. ⓑ 9
3.85
  1. ⓐ −14 − (−23) = 37
  2. ⓑ −17 − 21 = −38
3.86
  1. ⓐ 11 − (−19) = 30
  2. ⓑ −11 − 18 = −29
3.87

45 degrees Fahrenheit

3.88

9 degrees Fahrenheit

3.89

10,103 feet

3.90

233 feet

3.91
  1. ⓐ $48
  2. ⓑ −$2
  3. ⓒ $18
3.92
  1. ⓐ −$54
  2. ⓑ No, −$5
3.93
  1. ⓐ −48
  2. ⓑ 28
  3. ⓒ −63
  4. ⓓ 60
3.94
  1. ⓐ −56
  2. ⓑ 54
  3. ⓒ −28
  4. ⓓ 39
3.95
  1. ⓐ −9
  2. ⓑ 17
3.96
  1. ⓐ −8
  2. ⓑ 16
3.97
  1. ⓐ −7
  2. ⓑ 39
3.98
  1. ⓐ −9
  2. ⓑ 23
3.99
  1. ⓐ −6
  2. ⓑ 36
3.100
  1. ⓐ −28
  2. ⓑ 52
3.101

−63

3.102

−84

3.103
  1. ⓐ 81
  2. ⓑ −81
3.104
  1. ⓐ 49
  2. ⓑ −49
3.105

29

3.106

52

3.109

21

3.111

39

3.112

13

3.113

−8

3.114

19

3.115

−5 (12) = −60

3.116

8 (−13) = −104

3.117

−63 ÷ −9 = 7

3.118

−72 ÷ −9 = 8

3.119
  1. ⓐ no
  2. ⓑ no
  3. ⓒ yes
3.120
  1. ⓐ no
  2. ⓑ no
  3. ⓒ yes
3.121

−4

3.122

−19

3.123

−6

3.124

−4

3.125

4x = 12; x = 3

3.126

3x = 6; x = 2

3.128

11

3.129

−12

3.130

−9

3.131

x + 7 = −2; x = −9

3.132

y + 11 = 2; y = −9

3.133

p − 2 = −4; p = −2

3.134

q − 7 = −3; q = 4

3.135

132 = −12y; y = −11

3.136

117 = −13z; z = −9

Section 3.1 Exercises

1.


3.


5.
  1. ⓐ >
  2. ⓑ <
  3. ⓒ <
  4. ⓓ >
7.
  1. ⓐ <
  2. ⓑ >
  3. ⓒ <
  4. ⓓ >
9.
  1. ⓐ −2
  2. ⓑ 6
11.
  1. ⓐ 8
  2. ⓑ −1
13.

4

15.

15

17.
  1. ⓐ −3
  2. ⓑ 3
19.
  1. ⓐ −12;
  2. ⓑ 12
21.
  1. ⓐ 7
  2. ⓑ 25
  3. ⓒ 0
23.
  1. ⓐ 32
  2. ⓑ 18
  3. ⓒ 16
25.
  1. ⓐ 28
  2. ⓑ 15
27.
  1. ⓐ −19
  2. ⓑ −33
29.
  1. ⓐ <
  2. ⓑ =
31.
  1. ⓐ >
  2. ⓑ >
33.

4

35.

56

37.

0

39.

8

41.

80

43.
  1. ⓐ −8
  2. ⓑ −(−6), or 6
  3. ⓒ −3
  4. ⓓ 4−(−3)
45.
  1. ⓐ −20
  2. ⓑ −(−5), or 5
  3. ⓒ −12
  4. ⓓ 18−(−7)
47.

−6 degrees

49.

−40 feet

51.

−12 yards

53.

$3

55.

+1

57.
  1. ⓐ 20,320 feet
  2. ⓑ −282 feet
59.
  1. ⓐ $540 million
  2. ⓑ −$27 billion
61.

Sample answer: I have experienced negative temperatures.

Section 3.2 Exercises

63.



11

65.



−9

67.



−2

69.



1

71.

−80

73.

32

75.

−135

77.

0

79.

−22

81.

108

83.

−4

85.

29

87.
  1. ⓐ −18
  2. ⓑ −87
89.
  1. ⓐ −47
  2. ⓑ 16
91.
  1. ⓐ −4
  2. ⓑ 10
93.
  1. ⓐ −13
  2. ⓑ 5
95.

−8

97.

10

99.

64

101.

121

103.

−14 + 5 = −9

105.

−2 + 8 = 6

107.

−15 + (−10) = −25

109.

[−1 + (−12)] + 6 = −7

111.

[10 + (−19)] + 4 = −5

113.

7°F

115.

−$118

117.

−8 pounds

119.

25-yard line

121.

20 calories

123.

−32

125.

Sample answer: In the first case, there are more negatives so the sum is negative. In the second case, there are more positives so the sum is positive.

Section 3.3 Exercises

127.



6

129.



−4

131.



−9

133.



12

135.
  1. ⓐ 9
  2. ⓑ 9
137.
  1. ⓐ 16
  2. ⓑ 16
139.
  1. ⓐ 17
  2. ⓑ 17
141.
  1. ⓐ 45
  2. ⓑ 45
143.

27

145.

29

147.

−39

149.

−48

151.

−42

153.

−59

155.

−51

157.

9

159.

−2

161.

−2

163.

22

165.

53

167.

−20

169.

0

171.

4

173.

6

175.

5.2

177.

−11

179.
  1. ⓐ −3
  2. ⓑ −9
181.
  1. ⓐ 3
  2. ⓑ 7
183.

−8

185.

−192

187.
  1. ⓐ −3 − (−10) = 13
  2. ⓑ 45 − (−20) = 65
189.
  1. ⓐ −6 − 9 = −15
  2. ⓑ −16 − (−12) = −4
191.
  1. ⓐ −17 − 8 = −25
  2. ⓑ −24 − 37 = −61
193.
  1. ⓐ 6 − 21 = −15
  2. ⓑ −19 − 31 = −50
195.

−10°

197.

96°

199.

21-yard line

201.

$65

203.

−$40

205.

$26

207.

13°

209.

Sample answer: On a number line, 9 is 15 units away from −6.

Section 3.4 Exercises

211.

−32

213.

−35

215.

36

217.

−63

219.

−6

221.

14

223.

−4

225.

−8

227.

13

229.

−12

231.

−49

233.

−47

235.

43

237.

−125

239.

64

241.

−16

243.

90

245.

−88

247.

9

249.

41

251.

−5

253.

−9

255.

−29

257.

5

259.
  1. ⓐ 1
  2. ⓑ 33
261.
  1. ⓐ −5
  2. ⓑ 25
263.

8

265.

21

267.

38

269.

−56

271.

−3·15 = −45

273.

−60 ÷ (−20) = 3

275.

−6 a + b −6 a + b

277.

−10 (p − q)

279.

−$3,600

281.

Sample answer: Multiplying two integers with the same sign results in a positive product. Multiplying two integers with different signs results in a negative product.

283.

Sample answer: In one expression the base is positive and then we take the opposite, but in the other the base is negative.

Section 3.5 Exercises

285.
  1. ⓐ no
  2. ⓑ no
  3. ⓒ yes
287.
  1. ⓐ no
  2. ⓑ no
  3. ⓒ yes
289.

−7

291.

−17

293.

−4

295.

6

297.

−16

299.

−14

301.

3x = 6; x = 2

303.

2x = 8; x = 4

305.

9

307.

−8

309.

3

311.

−12

313.

20

315.

0

317.

n + 4 = 1; n = −3

319.

8 + p = −3; p = −11

321.

a − 3 = −14; a = −11

323.

−42 = −7x; x = 6

325.

f(−15) = 75; f = 5

327.

−6 + c = 4; c = 10

329.

m − 9 = −4; m = 5

331.
  1. ⓐ 8
  2. ⓑ 5
333.
  1. ⓐ −9
  2. ⓑ 30
335.

20

337.

7

339.

−52

341.

−9

343.

5

345.

−42

347.

17 cookies

349.

Sample answer: It is helpful because it shows how the counters can be divided among the envelopes.

351.

Sample answer: The operation used in the equation is multiplication. The inverse of multiplication is division, not addition.

Review Exercises

353.


355.


357.


359.

<

361.

>

363.

>

365.

−6

367.

4

369.
  1. ⓐ −8
  2. ⓑ 8
371.
  1. ⓐ −32
  2. ⓑ 32
373.

21

375.

36

377.

0

379.

14

381.

−33

383.

<

385.

=

387.

55; −55

389.

7

391.

54

393.

−1

395.

−16

397.

−3

399.

−10°

401.

10

403.

1

405.

96

407.

−50

409.

−1

411.

21

413.
  1. ⓐ 3
  2. ⓑ −16
415.

−27

417.

−8 + 2 = −6

419.

10 + [−5 + (−6)] = −1

421.

16 degrees

423.



5

425.



7

427.

8

429.

−38

431.

−58

433.

−1

435.
  1. ⓐ −2
  2. ⓑ −11
437.

41

439.

−12 − 5 = −17

441.

−2 degrees

443.

−36

445.

121

447.

−7

449.

−8

451.

−45

453.

−9

455.

−81

457.

54

459.

4

461.

−66

463.

−58

465.

−12(6) = −72

467.
  1. ⓐ no
  2. ⓑ yes
  3. ⓒ no
469.

−12

470.

−6

471.

−7

472.

−32

473.

3x = 9; x = 3>

475.

9

477.

4

479.

−6y = −42; y = 7

481.

m + 4 = −48; m = −52

Practice Test

485.
  1. ⓐ <
  2. ⓑ >
487.
  1. ⓐ 7
  2. ⓑ −8
489.

5

491.

−27

493.

11

495.

54

497.

−8

499.

22

501.

39

503.

34

505.

−7 − (−4) = −3

507.

4°F

509.

n = −1

511.

r = 6

513.

y − 8 = −32; y = −24

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