 Prealgebra 2e

# Chapter 4

Prealgebra 2eChapter 4

### Be Prepared

4.1

$1111$

4.2

$−2>−5−2>−5$

4.3

$2⋅2⋅2⋅2⋅32⋅2⋅2⋅2⋅3$

4.5

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

4.6

$33$

4.7

$112112$

4.8

$135135$

4.9

$5x+55x+5$

4.11

$5656$

4.12

$1012,15181012,1518$

4.13

$22$

4.15

$234234$

4.16

$7272$

4.17

$11$

4.18

$y=6y=6$

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

$53=12353=123$

4.10

$138=158138=158$

4.11 4.12 4.13

$127127$ 4.14

$134134$ 4.15

$118118$ 4.16

$116116$ 4.17

$167.167.$

4.18

$159159$

4.19

$327327$

4.20

$44114411$

4.21

$267267$

4.22

$238238$

4.23

$50115011$

4.24

$343343$

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

$18211821$

4.30

$3010030100$

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

$2323$

4.38

$3434$

4.39

$−34−34$

4.40

$−23−23$

4.41

$−97−97$

4.42

$−95−95$

4.43

$23402340$

4.44

$5858$

4.45

$xyxy$

4.46

$abab$

4.47

$310310$ 4.48

$512512$ 4.49

$215215$

4.50

$21402140$

4.51

$514514$

4.52

$14271427$

4.53

$−421−421$

4.54

$−316−316$

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

$−914−914$

4.66

$−1021−1021$

4.67

$215p215p$

4.68

$158q158q$

4.69

$4545$

4.70

$5454$

4.71

$415415$

4.72

$2323$

4.73

2

4.74

$9494$

4.75

−15

4.76

$−856−856$

4.77

$5858$

4.78

$7878$

4.79

2

4.80

$5252$

4.81

$9s149s14$

4.82

$5y65y6$

4.83

$a−bcda−bcd$

4.84

$p+qrp+qr$

4.85

$4545$

4.86

$11141114$

4.87

$−27−27$

4.88

$−103−103$

4.89

$34b34b$

4.90

$4q4q$

4.91

$2549.2549.$

4.92

$1212$

4.93

$−35,3−5−35,3−5$

4.94

$−27,2−7−27,2−7$

4.95

$109109$

4.96

$1212$

4.97

$−34−34$

4.98

$−23−23$

4.99

$2929$

4.100

$8585$

4.103

$5858$ 4.104

$5656$ 4.105

$5656$

4.107

$x+34x+34$

4.108

$y+58y+58$

4.109

$1d1d$

4.110

$3m3m$

4.111

$9p89p8$

4.112

$9q59q5$

4.113

$−23−23$

4.114

$−23−23$

4.115

$3838$, models may differ.

4.116

$1616$, models may differ

4.117

$3737$

4.118

$1212$

4.119

$x−27x−27$

4.120

$y−1314y−1314$

4.121

$−16x−16x$

4.122

$−22a−22a$

4.123

−1

4.124

$−23−23$

4.125

60

4.126

15

4.127

96

4.128

224

4.129

$912,1012912,1012$

4.130

$−3560,4460−3560,4460$

4.131

$5296,51965296,5196$

4.132

$72224,18922472224,189224$

4.133

$712712$

4.134

$710710$

4.135

$5858$

4.136

$1212$

4.137

$79607960$

4.138

$1036010360$

4.139

$196196$

4.140

$7522475224$

4.141

$3721037210$

4.142

$−2596−2596$

4.143

$3y+14183y+1418$

4.144

$5x+14305x+1430$

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

$190190$

4.150

272

4.152

$2727$

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

$−34−34$

4.156

$−238−238$

4.157

$−12−12$

4.158

$2323$

4.159

$−52−52$

4.160

$3232$

4.161

5 4.162

5 4.163

$423423$ 4.164

$312312$ 4.165

$567567$

4.166

$79117911$

4.167

$16121612$

4.168

$15131513$

4.169

$913913$

4.170

$635635$

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

$223223$

4.180

$157157$

4.181

$223223$

4.182

$157157$

4.183

$67126712$

4.184

$1231012310$

4.185

$47104710$

4.186

$2111221112$

4.187

$−418−418$

4.188

$−75763−75763$

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

$−12−12$

4.192

$−415−415$

4.193

−1

4.194

$−67−67$

4.195

$−193−193$

4.196

$232232$

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

$n7=−21;n=−147n7=−21;n=−147$

4.208

$n8=−56;n=−448n8=−56;n=−448$

4.209

$q−8=72;q=−576q−8=72;q=−576$

4.210

$p−9=81;p=−729p−9=81;p=−729$

4.211

$25f=16;f=4025f=16;f=40$

4.212

$34f=21;f=2834f=21;f=28$

4.213

$n23=512;n=518n23=512;n=518$

4.214

$c38=49;c=16c38=49;c=16$

4.215

$58+x=14;x=−3858+x=14;x=−38$

4.216

$134−x=56;x=1112134−x=56;x=1112$

### 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.

$123123$

31.

$235235$

33.

$319319$

35.

$32153215$

37.

$7575$

39.

$176176$

41.

$197197$

43.

$329329$

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.

$1313$

79.

$3434$

81.

$−511−511$

83.

$−127−127$

85.

$10211021$

87.

$−78−78$

89.

$xyxy$

91.

$−x4y−x4y$

93.

$2x23y2x23y$

95.

$1313$ 97.

$518518$ 99.

$215215$

101.

$27402740$

103.

$1414$

105.

$−16−16$

107.

$−29−29$

109.

$−2150−2150$

111.

$11301130$

113.

$20112011$

115.

9n

117.

7p

119.

−34

121.

$3838$

123.

$827827$

125.

$12966251296625$

127.

$4343$

129.

$−175−175$

131.

$811811$

133.

$−119−119$

135.

1

136. 137. 139.

4 141.

12 143.

4

145.

$16151615$

147.

$−54−54$

149.

1

151.

$185y185y$

153.

$252c252c$

155.

$−34−34$

157.

$2929$

159.

$14r15s14r15s$

161.

−12

163.

$−125−125$

165.

9

167.

$8787$

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

$1818$ yard

173.

175.

### Section 4.3 Exercises

177.

$44214421$

179.

$358358$

181.

$−163−163$

183.

$−6316−6316$

185.

$3232$

187.

$−43−43$

189.

2

191.

5

193.

$7v137v13$

195.

$abab$

197.

$A3−BA3−B$

199.

$3232$

201.

$−1522−1522$

203.

$−310−310$

205.

$1616$

207.

$3r5s3r5s$

209.

$92y92y$

211.

28

213.

$−118−118$

215.

$−49,−49−49,−49$

217.

$13−6,−13613−6,−136$

219.

$127127$

221.

$5252$

223.

$234234$

225.

$−13−13$

227.

$4545$

229.

$−12−12$

231.

2

233.

$5656$

235.

$26252625$

237.

$116116$

239.

$5252$

241.

−10

243.

−2

245.

$51205120$

247.

$187187$

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

253.

### Section 4.4 Exercises

255. $710710$

257. $3434$

259.

$7979$

261.

$16151615$

263.

$y+23y+23$

265.

$14q14q$

267.

$9a79a7$

269.

$−4x5−4x5$

271.

$−34−34$

273.

$−78−78$

275.

$819819$

277.

$−1312−1312$

279. $1212$

281.

$1515$

283.

$513513$

285.

$1616$

287.

$−83−83$

289.

$x−819x−819$

291.

$11z−81311z−813$

293.

$−14c−14c$

295.

$−55v−55v$

297.

$3d113d11$

299.

$−14s3−14s3$

301.

$2727$

303.

$−311−311$

305.

$−18−18$

307.

$6−s116−s11$

309.

$−29−29$

311.

$49274927$

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.

$520,420520,420$

329.

$1424,15241424,1524$

331.

$3348,−20483348,−2048$

333.

$2060,4560,36602060,4560,3660$

335.

$920920$

337.

$11241124$

339.

$3838$

341.

$2323$

343.

$23202320$

345.

$19241924$

347.

$148148$

349.

$124124$

351.

$112112$

353.

$760760$

355.

$−5380−5380$

357.

$−291245−291245$

359.

$120120$

361.

$11401140$

363.

$116116$

365.

$710710$

367.

$3y+463y+46$

369.

$4x−5204x−520$

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.

$11241124$

383.

$718718$

385.

$−215−215$

387.

$−33−8x88−33−8x88$

389.

$16391639$

391.

$181181$

393.

32

395.

$36253625$

397.

$607607$

399.

$152152$

401.

$313313$

403.

$19301930$

405.

−9

407.

$91609160$

409.

$11401140$

411.

$5656$

413.

1

415.

$227227$

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.

$415415$

427.

$−916−916$

429.

−2

431.

3

433.

She needs $238238$ cups

435.

### Section 4.6 Exercises

437. $323323$

439. $323323$

441.

$759759$

443.

11

445.

$11131113$

447.

$11131113$

449. $1212$

451.

$116116$

453.

$625625$

455.

$179179$

457.

$5656$

459.

$7111271112$

461.

$16161616$

463.

$5112051120$

465.

$−11124−11124$

467.

$6171861718$

469.

$7979$

471.

23

473.

$834834$

475.

$415415$

477.

$535535$

479.

$116116$

481.

$1311313113$

483.

$71307130$

485.

$10271027$

487.

$27452745$

489.

$17241724$

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.

$m=12m=12$

505.

$h=−23h=−23$

507.

c = −1

509.

z = −1

511.

$p=3740p=3740$

513.

$k=−715k=−715$

515.

$k=187k=187$

517.

$v=−113v=−113$

519.

b = −27

521.

x = −256

523.

q = 160

525.

s = 45

527.

y = −42

529.

$k=1720k=1720$

531.

p = 100

533.

m = −16

535.

b = −21

537.

v = 36

539.

y = 0

541.

$g=19g=19$

543.

$q=−34q=−34$

545.

$n=145n=145$

547.

$y=−2524y=−2524$

549.

$d=−815d=−815$

551.

$n6=−24;n=−144n6=−24;n=−144$

553.

$m−7=−8;m=56m−7=−8;m=56$

555.

$f−4=−20;f=80f−4=−20;f=80$

557.

$g9=14;g=126g9=14;g=126$

559.

$25q=20;q=5025q=20;q=50$

561.

$49p=−28;p=−6349p=−28;p=−63$

563.

$h2=43;h=86h2=43;h=86$

565.

$a23=34;a=12a23=34;a=12$

567.

$34+x=18;x=−5834+x=18;x=−58$

569.

$y−13=−16;y=16y−13=−16;y=16$

571.

30 inches

573.

### Review Exercises

575.

$5959$

577.

$32=11232=112$

579.

$58115811$

581.

$495495$

583.

585. 587.

>

589.

$−34−34$

591.

$−xy−xy$

593.

$−47−47$

595.

$24m1124m11$

597.

6

599.

$415415$

601.

−4

603.

4

605.

$415415$

607.

$−52b−52b$

609.

$−26811−26811$

611.

8

613.

$Vh−6Vh−6$

615.

$−29−29$

617.

22

619.

$736736$

621.

$5858$

623.

$3535$

625.

$x+710x+710$

627.

$1212$

629.

$−1915−1915$

631.

$815815$

633.

15

635.

60

637.

$924924$ and $20242024$

639.

$2060,45602060,4560$ and $48604860$

641.

$1414$

643.

$−7790−7790$

645.

$3y−10303y−1030$

647.

$14d1114d11$

649.

$256225256225$

651.
1. $−85−85$
2. $−1120−1120$
653.

$13231323$

655.

$81118111$

657.

$51105110$

659.

$113113$

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

$n=−511n=−511$

665.

$h=−5140h=−5140$

667.

z = −23

669.

$q−110=12;q=35q−110=12;q=35$

671.

$38y=24;y=6438y=24;y=64$

### Practice Test

673.

$237237$

675.

$1414$

677.

$1414$

679.

16u

681.

−2

683.

$12251225$

685.

5

687.

$5p2q5p2q$

689.

13

691.

$−713−713$

693.

−1

695.

$−94x−94x$

697.

3

699.

$y=45y=45$

701.

$f=1312f=1312$

703.

c = −27

Order a print copy

As an Amazon Associate we earn from qualifying purchases.