12.4.4: Chapter 4

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May 28, 2023
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Be Prepared

1111

−2>−5−2>−5

2⋅2⋅2⋅2⋅32⋅2⋅2⋅2⋅3

4.4

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

112112

135135

5x+55x+5

4.10

5656

1012,15181012,1518

4.14

234234

7272

y=6y=6

−6-6

Try It

ⓐ3838
ⓑ4949

ⓐ3535
ⓑ3434

4.3

$A circle is shown divided into 8 pieces, of which 6 are shaded.$ 4.4

$A rectangle is divided into 5 sections, of which 2 are shaded.$ 4.5

$A circle is shown. It is divided into 3 equal pieces. All 3 pieces are shaded.$ 4.6

$A circle is divided into 8 sections, of which all are shaded.$ 4.7

$Two circles are shown. Each is divided into three sections. All of the first circle is shaded. 2 out of 3 sections of the second circle are shaded.$ 4.8

53=12353=123

138=158138=158

4.11

$Two circles are shown. Each is divided into six sections. All of the first circle is shaded and one section of the second circle is shaded.$ 4.12

127127

134134

118118

116116

167.167.

159159

327327

44114411

267267

238238

50115011

343343

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

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

18211821

3010030100

4.31

$A number line is shown. It shows the whole numbers 0 through 6. Between 0 and 1, 1 third is labeled and shown with a red dot. Between 1 and 2, 5 fourths and 7 fourths are labeled and shown with red dots. Between 2 and 3, 2 and 3 fifths is labeled and shown with a red dot. Between 4 and 5, 9 halves is labeled and shown with a red dot.$ 4.32

$A number line is shown. It shows the whole numbers 0 through 6. Between 0 and 1, 2 thirds is labeled and shown with a red dot. Between 2 and 3, 9 fourths, 5 halves, and 11 fourths are labeled and shown with red dots. Between 3 and 4, 3 and 2 fifths is labeled and shown with a red dot.$ 4.33

$A number line is shown. The integers from negative 5 to 5 are labeled. Between negative 3 and negative 2, negative 2 and 1 fourth is labeled and marked with a red dot. Between negative 2 and negative 1, negative 3 halves is labeled and marked with a red dot. Between negative 1 and 0, negative 2 thirds is labeled and marked with a red dot. Between 0 and 1, 2 thirds is labeled and marked with a red dot. Between 1 and 2, 3 halves is labeled and marked with a red dot. Between 2 and 3, 2 and 1 fourth is labeled and marked with a red dot.$ 4.34

ⓐ >
ⓑ >
ⓒ <
ⓓ <

ⓐ >
ⓑ <
ⓒ >
ⓓ <

2323

3434

−34−34

−23−23

−97−97

−95−95

23402340

5858

xyxy

abab

310310

512512

215215

21402140

514514

14271427

−421−421

−316−316

ⓐ 9
ⓑ −33a

ⓐ2424
ⓑ44x344x3

ⓐ7575
ⓑ−8−8
ⓒ−411−411
ⓓ114114

ⓐ7373
ⓑ−12−12
ⓒ−914−914
ⓓ121121

4.59

$No alt text$ 4.60

−914−914

−1021−1021

215p215p

158q158q

4545

5454

415415

2323

9494

−15

−856−856

5858

7878

5252

9s149s14

5y65y6

a−bcda−bcd

p+qrp+qr

4545

11141114

−27−27

−103−103

34b34b

4q4q

2549.2549.

1212

−35,3−5−35,3−5

−27,2−7−27,2−7

109109

1212

−34−34

−23−23

2929

8585

5858

5656

x+34x+34

y+58y+58

1d1d

3m3m

9p89p8

9q59q5

−23−23

3838, models may differ.

1616, models may differ

3737

1212

x−27x−27

y−1314y−1314

−16x−16x

−22a−22a

−1

−23−23

224

912,1012912,1012

−3560,4460−3560,4460

5296,51965296,5196

72224,18922472224,189224

712712

710710

5858

1212

79607960

1036010360

196196

7522475224

3721037210

−2596−2596

3y+14183y+1418

5x+14305x+1430

ⓐ −1112−1112
ⓑ −18−18

ⓐ−103−103
ⓑ13121312

ⓐ(27a−32)36(27a−32)36
ⓑ2a32a3

ⓐ(24k+25)30(24k+25)30
ⓑ24k2524k25

190190

272

2727

ⓐ −1−1
ⓑ −12−12

ⓐ7676
ⓑ−14−14

−34−34

−238−238

−12−12

2323

−52−52

3232

423423

312312

567567

79117911

16121612

15131513

913913

635635

3434

4545

9595

5353

2323

3434

2323

2525

223223

157157

223223

157157

67126712

1231012310

47104710

2111221112

−418−418

−75763−75763

ⓐ no
ⓑ yes
ⓒ no

ⓐ no
ⓑ no
ⓒ yes

−12−12

−415−415

−1

−67−67

−193−193

232232

−125

−243

245

132

−48

−91

−108

n7=−21;n=−147n7=−21;n=−147

n8=−56;n=−448n8=−56;n=−448

q−8=72;q=−576q−8=72;q=−576

p−9=81;p=−729p−9=81;p=−729

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

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

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

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

58+x=14;x=−3858+x=14;x=−38

134−x=56;x=1112134−x=56;x=1112

Section 4.1 Exercises

ⓐ1414
ⓑ3434
ⓒ3838
ⓓ5858

$A circle is shown. It is divided into 2 equal pieces. 1 piece is shaded.$ 5.

$A circle is shown. It is divided into 4 equal pieces. 3 pieces are shaded.$ 7.

$A circle is shown. It is divided into 6 equal pieces. 5 pieces are shaded.$ 9.

$A circle is shown. It is divided into 8 equal pieces. 5 pieces are shaded.$ 11.

$A circle is shown. It is divided into 3 equal pieces. All 3 pieces are shaded.$ 13.

$Two circles are shown. Each is divided into 6 equal pieces. All 6 pieces are shaded in the circle on the left. 1 piece is shaded in the circle on the right.$ 15.

$Two circles are shown. Each is divided into 5 equal pieces. All 5 pieces are shaded in the circle on the left. 2 pieces are shaded in the circle on the right.$ 17.

ⓐ54=11454=114
ⓑ74=13474=134
ⓒ118=138118=138

19.

ⓐ114=234114=234
ⓑ198=238198=238

21.

$A circle is shown. It is divided into 4 equal pieces. All 4 pieces are shaded.$ 23.

$Two circles are shown. Each is divided into 3 equal pieces. All 3 pieces are shaded in the circle on the left. 2 pieces are shaded in the circle on the right.$ 25.

$Two circles are shown. Each is divided into 8 equal pieces. All 8 pieces are shaded in the circle on the left. 5 pieces are shaded in the circle on the right.$ 27.

$Three circles are shown. Each is divided into 4 equal pieces. All 4 pieces are shaded in the two circles on the left. 1 piece is shaded in the circle on the right.$ 29.

123123

31.

235235

33.

319319

35.

32153215

37.

7575

39.

176176

41.

197197

43.

329329

45.

47.

49.

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.

$A number line is shown. The numbers 0, 1, 2, 3, 4, 5, and 6 are labeled. Between 0 and 1, 1 third is labeled and shown with a red dot. Between 1 and 2, 7 fourths is labeled and shown with a red dot. Between 2 and 3, 13 fifths is labeled and shown with a red dot.$ 59.

$A number line is shown. The numbers 0, 1, 2, 3, 4, 5, and 6 are labeled. Between 0 and 1, 7 tenths is labeled and shown with a red dot. Between 1 and 2, 13 eighths is labeled and shown with a red dot. Between 2 and 3, 5 halves is labeled and shown with a red dot. 3 is labeled and shown with a red dot.$ 61.

$A number line is shown. The numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4 are labeled. Between negative 3 and negative 2, negative 2 and 1 third is labeled and shown with a red dot. Between 2 and 3, 2 and 1 third is labeled and shown with a red dot.$ 63.

$A number line is shown. The numbers negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, and 4 are labeled. Between negative 3 and negative 2, negative 8 thirds is labeled and shown with a red dot. Between negative 2 and negative 1, negative 1 and 3 fourths is labeled and shown with a red dot. Between negative 1 and 0, negative 2 fifths is labeled and shown with a red dot. Between 0 and 1, 2 fifths is labeled and shown with a red dot. Between 1 and 2, 1 and 3 fourths is labeled and shown with a red dot. Between 2 and 3, 8 thirds is labeled and shown with a red dot.$ 65.

67.

69.

71.

73.

ⓐ 2
ⓑ 614614

75.

Answers will vary.

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

$No alt text$ 97.

518518

$No alt text$ 99.

215215

101.

27402740

103.

1414

105.

−16−16

107.

−29−29

109.

−2150−2150

111.

11301130

113.

20112011

115.

117.

119.

−34

121.

3838

123.

827827

125.

12966251296625

127.

4343

129.

−175−175

131.

811811

133.

−119−119

135.

136.

$No alt text$ 137.

$A table is shown with four columns and five rows. The first row reads Number, Opposite, Absolute Value, and Reciprocal. The second row reads negative three thirteenths, three thirteenths, three thirteenths, negative thirteen thirds. The third row reads nine fourteenths, negative nine fourteenths, nine fourteenths, and fourteen ninths. The fourth row reads fifteen sevenths, negative fifteen sevenths, fifteen sevenths, and seven fifteenths. The last row reads negative nine, nine, nine, negative one ninth.$ 139.

$No alt text$ 141.

$No alt text$ 143.

145.

16151615

147.

−54−54

149.

151.

185y185y

153.

252c252c

155.

−34−34

157.

2929

159.

14r15s14r15s

161.

−12

163.

−125−125

165.

167.

8787

169.

ⓐ 4⋅234·23 cups=83=83 cups=223=223 cups
ⓑ Answers will vary.

171.

1818 yard

173.

Answers will vary.

175.

Answers will vary.

Section 4.3 Exercises

177.

44214421

179.

358358

181.

−163−163

183.

−6316−6316

185.

3232

187.

−43−43

189.

191.

193.

7v137v13

195.

abab

197.

A3−BA3−B

199.

3232

201.

−1522−1522

203.

−310−310

205.

1616

207.

3r5s3r5s

209.

92y92y

211.

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.

233.

5656

235.

26252625

237.

116116

239.

5252

241.

−10

243.

−2

245.

51205120

247.

187187

249.

ⓐ43=11343=113 cups
ⓑ803=2623803=2623 cups

251.

Answers will vary.

253.

Answers will vary.

Section 4.4 Exercises

255.

$A circle is divided into 10 equal pieces. 7 of the pieces are shaded.$

710710

257.

$A circle is divided into 8 equal pieces. 6 of the pieces are shaded.$

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.

$A circle is divided into eight sections, three of which are shaded.$

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.

319.

321.

240

323.

245

325.

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.

ⓐ5656
ⓑ44

373.

ⓐ−3740−3740
ⓑ−110−110

375.

ⓐ9a149a14
ⓑ9a−14249a−1424

377.

ⓐ−4q27−4q27
ⓑ12−25q4512−25q45

381.

11241124

383.

718718

385.

−215−215

387.

−33−8x88−33−8x88

389.

16391639

391.

181181

393.

395.

36253625

397.

607607

399.

152152

401.

313313

403.

19301930

405.

−9

407.

91609160

409.

11401140

411.

5656

413.

415.

227227

417.

ⓐ1212
ⓑ−1−1

419.

ⓐ00
ⓑ−16−16

421.

ⓐ1313
ⓑ−1−1

423.

ⓐ1616
ⓑ2323

425.

415415

427.

−916−916

429.

−2

431.

433.

She needs 238238 cups

435.

Answers will vary.

Section 4.6 Exercises

437.

$Four circles are shown. The first three are shaded. The last circle is divided into 3 equal parts. 2 parts are shaded.$

323323

439.

$Four circles are shown. The first three are shaded. The last circle is divided into 3 equal parts. 2 parts are shaded.$

323323

441.

759759

443.

445.

11131113

447.

11131113

449.

$A circle is shown. It is divided into 8 equal pieces. 4 pieces are shaded.$

1212

451.

116116

453.

625625

455.

179179

457.

5656

459.

7111271112

461.

16161616

463.

5112051120

465.

−11124−11124

467.

6171861718

469.

7979

471.

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.

Answers will vary.

497.

Answers will vary.

Section 4.7 Exercises

499.

ⓐ no
ⓑ yes
ⓒ no

501.

ⓐ no
ⓑ yes
ⓒ 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.

Answers will vary.

Review Exercises

575.

5959

577.

32=11232=112

579.

58115811

581.

495495

583.

Answers may vary.

585.

$A number line is shown. Integers from negative 4 to 4 are labeled. Between negative 4 and negative 3, negative 7 halves is labeled and marked with a red dot. Between negative 2 and negative 1, negative 1 and 1 third is labeled and marked with a red dot. Between negative 1 and 0, negative 1 fourth is labeled and marked with a red dot. Between 0 and 1, 1 fourth is labeled and marked with a red dot. Between 1 and 2, 1 and 1 third is labeled and marked with a red dot. Between 3 and 4, 7 halves is labeled and marked with a red dot.$ 587.

589.

−34−34

591.

−xy−xy

593.

−47−47

595.

24m1124m11

597.

599.

415415

601.

−4

603.

605.

415415

607.

−52b−52b

609.

−26811−26811

611.

613.

Vh−6Vh−6

615.

−29−29

617.

619.

736736

621.

5858

623.

3535

625.

x+710x+710

627.

1212

629.

−1915−1915

631.

815815

633.

635.

637.

924924 and 20242024

639.

2060,45602060,4560 and 48604860

641.

1414

643.

−7790−7790

645.

3y−10303y−1030

647.

14d1114d11

649.

256225256225

651.

ⓐ−85−85
ⓑ−1120−1120

653.

13231323

655.

81118111

657.

51105110

659.

113113

661.

ⓐ no
ⓑ yes
ⓒ 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.

687.

5p2q5p2q

689.

691.

−713−713

693.

−1

695.

−94x−94x

697.

699.

y=45y=45

701.

f=1312f=1312

703.

c = −27

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Section 4.1 Exercises

Section 4.2 Exercises

Section 4.3 Exercises

Section 4.4 Exercises

Section 4.5 Exercises

Section 4.6 Exercises

Section 4.7 Exercises

Review Exercises

Practice Test

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