 Prealgebra 2e

# Chapter 4

Prealgebra 2eChapter 4

### Be Prepared

4.1

$11 11$

4.2

$− 2 > − 5 − 2 > − 5$

4.3

$2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3$

4.5

Answers may vary. Acceptable answers include $1012,1518,5060,1012,1518,5060,$ etc.

4.6

$3 3$

4.7

$1 12 1 12$

4.8

$13 5 13 5$

4.9

$5 x + 5 5 x + 5$

4.11

$5 6 5 6$

4.12

$10 12 , 15 18 10 12 , 15 18$

4.13

$2 2$

4.15

$2 3 4 2 3 4$

4.16

$7 2 7 2$

4.17

$1 1$

4.18

$y = 6 y = 6$

4.19

$- 6 - 6$

### Try It

4.1
1. $3838$
2. $4949$
4.2
1. $3535$
2. $3434$
4.3 4.4 4.5 4.6 4.7 4.8 4.9

$5 3 = 1 2 3 5 3 = 1 2 3$

4.10

$13 8 = 1 5 8 13 8 = 1 5 8$

4.11 4.12 4.13

$1 2 7 1 2 7$ 4.14

$1 3 4 1 3 4$ 4.15

$11 8 11 8$ 4.16

$11 6 11 6$ 4.17

$1 6 7 . 1 6 7 .$

4.18

$1 5 9 1 5 9$

4.19

$3 2 7 3 2 7$

4.20

$4 4 11 4 4 11$

4.21

$26 7 26 7$

4.22

$23 8 23 8$

4.23

$50 11 50 11$

4.24

$34 3 34 3$

4.25

2

4.26

3

4.27

Correct answers include $610,915,610,915,$ and $1220.1220.$

4.28

Correct answers include $810,1215,810,1215,$ and $1620.1620.$

4.29

$18 21 18 21$

4.30

$30 100 30 100$

4.31 4.32 4.33 4.34 4.35
1. >
2. >
3. <
4. <
4.36
1. >
2. <
3. >
4. <
4.37

$2 3 2 3$

4.38

$3 4 3 4$

4.39

$− 3 4 − 3 4$

4.40

$− 2 3 − 2 3$

4.41

$− 9 7 − 9 7$

4.42

$− 9 5 − 9 5$

4.43

$23 40 23 40$

4.44

$5 8 5 8$

4.45

$x y x y$

4.46

$a b a b$

4.47

$3 10 3 10$ 4.48

$5 12 5 12$ 4.49

$2 15 2 15$

4.50

$21 40 21 40$

4.51

$5 14 5 14$

4.52

$14 27 14 27$

4.53

$− 4 21 − 4 21$

4.54

$− 3 16 − 3 16$

4.55
1. 9
2. −33a
4.56
1. $2424$
2. $44x344x3$
4.57
1. $7575$
2. $−8−8$
3. $−411−411$
4. $114114$
4.58
1. $7373$
2. $−12−12$
3. $−914−914$
4. $121121$
4.59 4.60 4.61

2 4.62

2 4.63

6 4.64

6 4.65

$− 9 14 − 9 14$

4.66

$− 10 21 − 10 21$

4.67

$21 5 p 21 5 p$

4.68

$15 8 q 15 8 q$

4.69

$4 5 4 5$

4.70

$5 4 5 4$

4.71

$4 15 4 15$

4.72

$2 3 2 3$

4.73

2

4.74

$9 4 9 4$

4.75

−15

4.76

$− 85 6 − 85 6$

4.77

$5 8 5 8$

4.78

$7 8 7 8$

4.79

2

4.80

$5 2 5 2$

4.81

$9 s 14 9 s 14$

4.82

$5 y 6 5 y 6$

4.83

$a − b c d a − b c d$

4.84

$p + q r p + q r$

4.85

$4 5 4 5$

4.86

$11 14 11 14$

4.87

$− 2 7 − 2 7$

4.88

$− 10 3 − 10 3$

4.89

$3 4 b 3 4 b$

4.90

$4 q 4 q$

4.91

$25 49 . 25 49 .$

4.92

$1 2 1 2$

4.93

$− 3 5 , 3 −5 − 3 5 , 3 −5$

4.94

$−2 7 , 2 −7 −2 7 , 2 −7$

4.95

$10 9 10 9$

4.96

$1 2 1 2$

4.97

$−3 4 −3 4$

4.98

$− 2 3 − 2 3$

4.99

$2 9 2 9$

4.100

$8 5 8 5$

4.103

$5 8 5 8$ 4.104

$5 6 5 6$ 4.105

$5 6 5 6$

4.107

$x + 3 4 x + 3 4$

4.108

$y + 5 8 y + 5 8$

4.109

$1 d 1 d$

4.110

$3 m 3 m$

4.111

$9 p 8 9 p 8$

4.112

$9 q 5 9 q 5$

4.113

$− 2 3 − 2 3$

4.114

$− 2 3 − 2 3$

4.115

$3838$, models may differ.

4.116

$1616$, models may differ

4.117

$3 7 3 7$

4.118

$1 2 1 2$

4.119

$x − 2 7 x − 2 7$

4.120

$y − 13 14 y − 13 14$

4.121

$− 16 x − 16 x$

4.122

$− 22 a − 22 a$

4.123

−1

4.124

$− 2 3 − 2 3$

4.125

60

4.126

15

4.127

96

4.128

224

4.129

$9 12 , 10 12 9 12 , 10 12$

4.130

$− 35 60 , 44 60 − 35 60 , 44 60$

4.131

$52 96 , 51 96 52 96 , 51 96$

4.132

$72 224 , 189 224 72 224 , 189 224$

4.133

$7 12 7 12$

4.134

$7 10 7 10$

4.135

$5 8 5 8$

4.136

$1 2 1 2$

4.137

$79 60 79 60$

4.138

$103 60 103 60$

4.139

$1 96 1 96$

4.140

$75 224 75 224$

4.141

$37 210 37 210$

4.142

$− 25 96 − 25 96$

4.143

$3 y + 14 18 3 y + 14 18$

4.144

$5 x + 14 30 5 x + 14 30$

4.145
1. $−1112−1112$
2. $−18−18$
4.146
1. $−103−103$
2. $13121312$
4.147
1. $(27a−32)36(27a−32)36$
2. $2a32a3$
4.148
1. $(24k+25)30(24k+25)30$
2. $24k2524k25$
4.149

$1 90 1 90$

4.150

272

4.152

$2 7 2 7$

4.153
1. $−1−1$
2. $−12−12$
4.154
1. $7676$
2. $−14−14$
4.155

$− 3 4 − 3 4$

4.156

$− 23 8 − 23 8$

4.157

$− 1 2 − 1 2$

4.158

$2 3 2 3$

4.159

$− 5 2 − 5 2$

4.160

$3 2 3 2$

4.161

5 4.162

5 4.163

$423423$ 4.164

$312312$ 4.165

$5 6 7 5 6 7$

4.166

$7 9 11 7 9 11$

4.167

$16 1 2 16 1 2$

4.168

$15 1 3 15 1 3$

4.169

$9 1 3 9 1 3$

4.170

$6 3 5 6 3 5$

4.171

$3434$ 4.172

$4545$ 4.173

$9595$ 4.174

$5353$ 4.175

$2323$ 4.176

$3434$ 4.177

$2323$ 4.178

$2525$ 4.179

$2 2 3 2 2 3$

4.180

$1 5 7 1 5 7$

4.181

$2 2 3 2 2 3$

4.182

$1 5 7 1 5 7$

4.183

$6 7 12 6 7 12$

4.184

$12 3 10 12 3 10$

4.185

$4 7 10 4 7 10$

4.186

$2 11 12 2 11 12$

4.187

$− 41 8 − 41 8$

4.188

$− 757 63 − 757 63$

4.189
1. no
2. yes
3. no
4.190
1. no
2. no
3. yes
4.191

$− 1 2 − 1 2$

4.192

$− 4 15 − 4 15$

4.193

−1

4.194

$− 6 7 − 6 7$

4.195

$− 19 3 − 19 3$

4.196

$23 2 23 2$

4.197

−125

4.198

−243

4.199

245

4.200

132

4.201

−48

4.202

23

4.203

35

4.204

18

4.205

−91

4.206

−108

4.207

$n 7 = −21 ; n = −147 n 7 = −21 ; n = −147$

4.208

$n 8 = −56 ; n = −448 n 8 = −56 ; n = −448$

4.209

$q −8 = 72 ; q = −576 q −8 = 72 ; q = −576$

4.210

$p −9 = 81 ; p = −729 p −9 = 81 ; p = −729$

4.211

$2 5 f = 16 ; f = 40 2 5 f = 16 ; f = 40$

4.212

$3 4 f = 21 ; f = 28 3 4 f = 21 ; f = 28$

4.213

$n 2 3 = 5 12 ; n = 5 18 n 2 3 = 5 12 ; n = 5 18$

4.214

$c 3 8 = 4 9 ; c = 1 6 c 3 8 = 4 9 ; c = 1 6$

4.215

$5 8 + x = 1 4 ; x = − 3 8 5 8 + x = 1 4 ; x = − 3 8$

4.216

$1 3 4 − x = 5 6 ; x = 11 12 1 3 4 − x = 5 6 ; x = 11 12$

### Section 4.1 Exercises

1.
1. $1414$
2. $3434$
3. $3838$
4. $5858$
3. 5. 7. 9. 11. 13. 15. 17.
1. $54=11454=114$
2. $74=13474=134$
3. $118=138118=138$
19.
1. $114=234114=234$
2. $198=238198=238$
21. 23. 25. 27. 29.

$1 2 3 1 2 3$

31.

$2 3 5 2 3 5$

33.

$3 1 9 3 1 9$

35.

$3 2 15 3 2 15$

37.

$7 5 7 5$

39.

$17 6 17 6$

41.

$19 7 19 7$

43.

$32 9 32 9$

45.

4

47.

9

49.

9

51.

Answers may vary. Correct answers include $26,39,412.26,39,412.$

53.

Answers may vary. Correct answers include $1012,1518,2024.1012,1518,2024.$

55.

Answers may vary. Correct answers include $1018,1527,2036.1018,1527,2036.$

57. 59. 61. 63. 65.

<

67.

>

69.

<

71.

<

73.
1. 2
2. $614614$
75.

### Section 4.2 Exercises

77.

$1 3 1 3$

79.

$3 4 3 4$

81.

$− 5 11 − 5 11$

83.

$− 12 7 − 12 7$

85.

$10 21 10 21$

87.

$− 7 8 − 7 8$

89.

$x y x y$

91.

$− x 4 y − x 4 y$

93.

$2 x 2 3 y 2 x 2 3 y$

95.

$1313$ 97.

$518518$ 99.

$2 15 2 15$

101.

$27 40 27 40$

103.

$1 4 1 4$

105.

$− 1 6 − 1 6$

107.

$− 2 9 − 2 9$

109.

$− 21 50 − 21 50$

111.

$11 30 11 30$

113.

$20 11 20 11$

115.

9n

117.

7p

119.

−34

121.

$3 8 3 8$

123.

$8 27 8 27$

125.

$1296 625 1296 625$

127.

$4 3 4 3$

129.

$− 17 5 − 17 5$

131.

$8 11 8 11$

133.

$− 1 19 − 1 19$

135.

1

136. 137. 139.

4 141.

12 143.

4

145.

$16 15 16 15$

147.

$− 5 4 − 5 4$

149.

1

151.

$18 5 y 18 5 y$

153.

$25 2 c 25 2 c$

155.

$− 3 4 − 3 4$

157.

$2 9 2 9$

159.

$14 r 15 s 14 r 15 s$

161.

−12

163.

$− 1 25 − 1 25$

165.

9

167.

$8 7 8 7$

169.
• $4·234·23$ cups$=83=83$ cups$=223=223$ cups
171.

$1818$ yard

173.

175.

### Section 4.3 Exercises

177.

$44 21 44 21$

179.

$35 8 35 8$

181.

$− 16 3 − 16 3$

183.

$− 63 16 − 63 16$

185.

$3 2 3 2$

187.

$− 4 3 − 4 3$

189.

2

191.

5

193.

$7 v 13 7 v 13$

195.

$a b a b$

197.

$A 3 − B A 3 − B$

199.

$3 2 3 2$

201.

$− 15 22 − 15 22$

203.

$− 3 10 − 3 10$

205.

$1 6 1 6$

207.

$3 r 5 s 3 r 5 s$

209.

$9 2 y 9 2 y$

211.

28

213.

$− 1 18 − 1 18$

215.

$−4 9 , − 4 9 −4 9 , − 4 9$

217.

$13 −6 , −13 6 13 −6 , −13 6$

219.

$12 7 12 7$

221.

$5 2 5 2$

223.

$23 4 23 4$

225.

$− 1 3 − 1 3$

227.

$4 5 4 5$

229.

$− 1 2 − 1 2$

231.

2

233.

$5 6 5 6$

235.

$26 25 26 25$

237.

$11 6 11 6$

239.

$5 2 5 2$

241.

−10

243.

−2

245.

$51 20 51 20$

247.

$18 7 18 7$

249.
1. $43=11343=113$ cups
2. $803=2623803=2623$ cups
251.

253.

### Section 4.4 Exercises

255. $710710$

257. $3434$

259.

$7 9 7 9$

261.

$16 15 16 15$

263.

$y + 2 3 y + 2 3$

265.

$14 q 14 q$

267.

$9 a 7 9 a 7$

269.

$−4 x 5 −4 x 5$

271.

$− 3 4 − 3 4$

273.

$− 7 8 − 7 8$

275.

$8 19 8 19$

277.

$− 13 12 − 13 12$

279. $1212$

281.

$1 5 1 5$

283.

$5 13 5 13$

285.

$1 6 1 6$

287.

$− 8 3 − 8 3$

289.

$x − 8 19 x − 8 19$

291.

$11 z − 8 13 11 z − 8 13$

293.

$− 14 c − 14 c$

295.

$− 55 v − 55 v$

297.

$3 d 11 3 d 11$

299.

$− 14 s 3 − 14 s 3$

301.

$2 7 2 7$

303.

$− 3 11 − 3 11$

305.

$− 1 8 − 1 8$

307.

$6 − s 11 6 − s 11$

309.

$− 2 9 − 2 9$

311.

$49 27 49 27$

313.

$1414$ cup

315.

No, adding up the number of pieces gives $13121312$, which is greater than 1. (Answers may vary.)

### Section 4.5 Exercises

317.

20

319.

48

321.

240

323.

245

325.

60

327.

$5 20 , 4 20 5 20 , 4 20$

329.

$14 24 , 15 24 14 24 , 15 24$

331.

$33 48 , − 20 48 33 48 , − 20 48$

333.

$20 60 , 45 60 , 36 60 20 60 , 45 60 , 36 60$

335.

$9 20 9 20$

337.

$11 24 11 24$

339.

$3 8 3 8$

341.

$2 3 2 3$

343.

$23 20 23 20$

345.

$19 24 19 24$

347.

$1 48 1 48$

349.

$1 24 1 24$

351.

$1 12 1 12$

353.

$7 60 7 60$

355.

$− 53 80 − 53 80$

357.

$− 291 245 − 291 245$

359.

$1 20 1 20$

361.

$11 40 11 40$

363.

$11 6 11 6$

365.

$7 10 7 10$

367.

$3 y + 4 6 3 y + 4 6$

369.

$4 x − 5 20 4 x − 5 20$

371.
1. $5656$
2. $44$
373.
1. $−3740−3740$
2. $−110−110$
375.
1. $9a149a14$
2. $9a−14249a−1424$
377.
1. $−4q27−4q27$
2. $12−25q4512−25q45$
381.

$11 24 11 24$

383.

$7 18 7 18$

385.

$− 2 15 − 2 15$

387.

$−33 − 8 x 88 −33 − 8 x 88$

389.

$16 39 16 39$

391.

$1 81 1 81$

393.

32

395.

$36 25 36 25$

397.

$60 7 60 7$

399.

$15 2 15 2$

401.

$3 13 3 13$

403.

$19 30 19 30$

405.

−9

407.

$91 60 91 60$

409.

$11 40 11 40$

411.

$5 6 5 6$

413.

1

415.

$22 7 22 7$

417.
1. $1212$
2. $−1−1$
419.
1. $0 0$
2. $−16−16$
421.
1. $1313$
2. $−1−1$
423.
1. $1616$
2. $2323$
425.

$4 15 4 15$

427.

$− 9 16 − 9 16$

429.

−2

431.

3

433.

She needs $238238$ cups

435.

### Section 4.6 Exercises

437. $323323$

439. $323323$

441.

$7 5 9 7 5 9$

443.

11

445.

$11 1 3 11 1 3$

447.

$11 1 3 11 1 3$

449. $1212$

451.

$1 1 6 1 1 6$

453.

$6 2 5 6 2 5$

455.

$1 7 9 1 7 9$

457.

$5 6 5 6$

459.

$7 11 12 7 11 12$

461.

$16 1 6 16 1 6$

463.

$5 11 20 5 11 20$

465.

$−1 11 24 −1 11 24$

467.

$6 17 18 6 17 18$

469.

$7 9 7 9$

471.

23

473.

$8 3 4 8 3 4$

475.

$4 15 4 15$

477.

$5 3 5 5 3 5$

479.

$1 16 1 16$

481.

$13 1 13 13 1 13$

483.

$7 1 30 7 1 30$

485.

$10 27 10 27$

487.

$2 7 45 2 7 45$

489.

$17 24 17 24$

491.

$712712$ yards

493.

$13141314$ inches

495.

497.

### Section 4.7 Exercises

499.
1. no
2. yes
3. no
501.
1. no
2. yes
3. no
503.

$m = 1 2 m = 1 2$

505.

$h = − 2 3 h = − 2 3$

507.

c = −1

509.

z = −1

511.

$p = 37 40 p = 37 40$

513.

$k = − 7 15 k = − 7 15$

515.

$k = 18 7 k = 18 7$

517.

$v = − 11 3 v = − 11 3$

519.

b = −27

521.

x = −256

523.

q = 160

525.

s = 45

527.

y = −42

529.

$k = 17 20 k = 17 20$

531.

p = 100

533.

m = −16

535.

b = −21

537.

v = 36

539.

y = 0

541.

$g = 1 9 g = 1 9$

543.

$q = − 3 4 q = − 3 4$

545.

$n = 14 5 n = 14 5$

547.

$y = − 25 24 y = − 25 24$

549.

$d = − 8 15 d = − 8 15$

551.

$n 6 = −24 ; n = −144 n 6 = −24 ; n = −144$

553.

$m −7 = −8 ; m = 56 m −7 = −8 ; m = 56$

555.

$f −4 = −20 ; f = 80 f −4 = −20 ; f = 80$

557.

$g 9 = 14 ; g = 126 g 9 = 14 ; g = 126$

559.

$2 5 q = 20 ; q = 50 2 5 q = 20 ; q = 50$

561.

$4 9 p = −28 ; p = −63 4 9 p = −28 ; p = −63$

563.

$h 2 = 43 ; h = 86 h 2 = 43 ; h = 86$

565.

$a 2 3 = 3 4 ; a = 1 2 a 2 3 = 3 4 ; a = 1 2$

567.

$3 4 + x = 1 8 ; x = − 5 8 3 4 + x = 1 8 ; x = − 5 8$

569.

$y − 1 3 = − 1 6 ; y = 1 6 y − 1 3 = − 1 6 ; y = 1 6$

571.

30 inches

573.

### Review Exercises

575.

$5 9 5 9$

577.

$3 2 = 1 1 2 3 2 = 1 1 2$

579.

$5 8 11 5 8 11$

581.

$49 5 49 5$

583.

585. 587.

>

589.

$− 3 4 − 3 4$

591.

$− x y − x y$

593.

$− 4 7 − 4 7$

595.

$24 m 11 24 m 11$

597.

6

599.

$4 15 4 15$

601.

−4

603.

4

605.

$4 15 4 15$

607.

$− 5 2 b − 5 2 b$

609.

$− 268 11 − 268 11$

611.

8

613.

$V h − 6 V h − 6$

615.

$− 2 9 − 2 9$

617.

22

619.

$7 36 7 36$

621.

$5 8 5 8$

623.

$3 5 3 5$

625.

$x + 7 10 x + 7 10$

627.

$1 2 1 2$

629.

$− 19 15 − 19 15$

631.

$8 15 8 15$

633.

15

635.

60

637.

$924924$ and $20242024$

639.

$2060,45602060,4560$ and $48604860$

641.

$1 4 1 4$

643.

$− 77 90 − 77 90$

645.

$3 y − 10 30 3 y − 10 30$

647.

$14 d 11 14 d 11$

649.

$256 225 256 225$

651.
1. $−85−85$
2. $−1120−1120$
653.

$13 2 3 13 2 3$

655.

$8 1 11 8 1 11$

657.

$5 1 10 5 1 10$

659.

$1 1 3 1 1 3$

661.
1. no
2. yes
3. no
663.

$n = − 5 11 n = − 5 11$

665.

$h = − 51 40 h = − 51 40$

667.

z = −23

669.

$q − 1 10 = 1 2 ; q = 3 5 q − 1 10 = 1 2 ; q = 3 5$

671.

$3 8 y = 24 ; y = 64 3 8 y = 24 ; y = 64$

### Practice Test

673.

$23 7 23 7$

675.

$1 4 1 4$

677.

$1 4 1 4$

679.

16u

681.

−2

683.

$12 25 12 25$

685.

5

687.

$5 p 2 q 5 p 2 q$

689.

13

691.

$− 7 13 − 7 13$

693.

−1

695.

$− 9 4 x − 9 4 x$

697.

3

699.

$y = 4 5 y = 4 5$

701.

$f = 13 12 f = 13 12$

703.

c = −27 Do you know how you learn best?
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