Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis

Be Prepared

4.1

$11$

4.2

$- 2 > - 5$

4.3

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$

4.4

A circle is shown divided into 4 pieces, of which 3 are shaded.

4.5

Answers may vary. Acceptable answers include $\frac{10}{12}, \frac{15}{18}, \frac{50}{60},$ etc.

4.6

$3$

4.7

$\frac{1}{12}$

4.8

$\frac{13}{5}$

4.9

$5 x + 5$

4.10

4.11

$\frac{5}{6}$

4.12

$\frac{10}{12}, \frac{15}{18}$

4.13

$2$

4.14

Three circles are shown. They are divided into 3 equal pieces. All 3 pieces are shaded on 2 of the circles and 1 piece is shaded on the third circle.

4.15

$2 \frac{3}{4}$

4.16

$\frac{7}{2}$

4.17

$1$

4.18

$y = 6$

4.19

$- 6$

Try It

4.1

ⓐ $\frac{3}{8}$
ⓑ $\frac{4}{9}$

4.2

ⓐ $\frac{3}{5}$
ⓑ $\frac{3}{4}$

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

Three circles are shown. Each is divided into two sections. The first two circles are completely shaded. Half of the third circle is shaded.

4.9

$\frac{5}{3} = 1 \frac{2}{3}$

4.10

$\frac{13}{8} = 1 \frac{5}{8}$

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

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

4.13

$1 \frac{2}{7}$

4.14

$1 \frac{3}{4}$

4.15

$\frac{11}{8}$

4.16

$\frac{11}{6}$

4.17

$1 \frac{6}{7} .$

4.18

$1 \frac{5}{9}$

4.19

$3 \frac{2}{7}$

4.20

$4 \frac{4}{11}$

4.21

$\frac{26}{7}$

4.22

$\frac{23}{8}$

4.23

$\frac{50}{11}$

4.24

$\frac{34}{3}$

4.25

2

4.26

3

4.27

Correct answers include $\frac{6}{10}, \frac{9}{15},$ and $\frac{12}{20} .$

4.28

Correct answers include $\frac{8}{10}, \frac{12}{15},$ and $\frac{16}{20} .$

4.29

$\frac{18}{21}$

4.30

$\frac{30}{100}$

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

4.33

4.34

4.35

ⓐ >
ⓑ >
ⓒ <
ⓓ <

4.36

ⓐ >
ⓑ <
ⓒ >
ⓓ <

4.37

$\frac{2}{3}$

4.38

$\frac{3}{4}$

4.39

$- \frac{3}{4}$

4.40

$- \frac{2}{3}$

4.41

$- \frac{9}{7}$

4.42

$- \frac{9}{5}$

4.43

$\frac{23}{40}$

4.44

$\frac{5}{8}$

4.45

$\frac{x}{y}$

4.46

$\frac{a}{b}$

4.47

$\frac{3}{10}$

4.48

$\frac{5}{12}$

4.49

$\frac{2}{15}$

4.50

$\frac{21}{40}$

4.51

$\frac{5}{14}$

4.52

$\frac{14}{27}$

4.53

$- \frac{4}{21}$

4.54

$- \frac{3}{16}$

4.55

ⓐ 9
ⓑ −33a

4.56

ⓐ $24$
ⓑ $\frac{44 x}{3}$

4.57

ⓐ $\frac{7}{5}$
ⓑ $−8$
ⓒ $- \frac{4}{11}$
ⓓ $\frac{1}{14}$

4.58

ⓐ $\frac{7}{3}$
ⓑ $- 12$
ⓒ $- \frac{9}{14}$
ⓓ $\frac{1}{21}$

4.59

4.60

4.61

2

4.62

2

4.63

6

4.64

6

4.65

$- \frac{9}{14}$

4.66

$- \frac{10}{21}$

4.67

$\frac{21}{5 p}$

4.68

$\frac{15}{8 q}$

4.69

$\frac{4}{5}$

4.70

$\frac{5}{4}$

4.71

$\frac{4}{15}$

4.72

$\frac{2}{3}$

4.73

2

4.74

$\frac{9}{4}$

4.75

−15

4.76

$- \frac{85}{6}$

4.77

$\frac{5}{8}$

4.78

$\frac{7}{8}$

4.79

2

4.80

$\frac{5}{2}$

4.81

$\frac{9 s}{14}$

4.82

$\frac{5 y}{6}$

4.83

$\frac{a - b}{c d}$

4.84

$\frac{p + q}{r}$

4.85

$\frac{4}{5}$

4.86

$\frac{11}{14}$

4.87

$- \frac{2}{7}$

4.88

$- \frac{10}{3}$

4.89

$\frac{3}{4 b}$

4.90

$\frac{4}{q}$

4.91

$\frac{25}{49} .$

4.92

$\frac{1}{2}$

4.93

$- \frac{3}{5}, \frac{3}{−5}$

4.94

$\frac{−2}{7}, \frac{2}{−7}$

4.95

$\frac{10}{9}$

4.96

$\frac{1}{2}$

4.97

$\frac{−3}{4}$

4.98

$- \frac{2}{3}$

4.99

$\frac{2}{9}$

4.100

$\frac{8}{5}$

4.101

4

4.102

2

4.103

$\frac{5}{8}$

A circle divided into 8 sections, 5 of which are shaded.

4.104

$\frac{5}{6}$

A circle divided into 6 sections, 5 of which are shaded.

4.105

$\frac{5}{6}$

4.106

1

4.107

$\frac{x + 3}{4}$

4.108

$\frac{y + 5}{8}$

4.109

$\frac{1}{d}$

4.110

$\frac{3}{m}$

4.111

$\frac{9 p}{8}$

4.112

$\frac{9 q}{5}$

4.113

$- \frac{2}{3}$

4.114

$- \frac{2}{3}$

4.115

$\frac{3}{8}$ , models may differ.

4.116

$\frac{1}{6}$ , models may differ

4.117

$\frac{3}{7}$

4.118

$\frac{1}{2}$

4.119

$\frac{x - 2}{7}$

4.120

$\frac{y - 13}{14}$

4.121

$- \frac{16}{x}$

4.122

$- \frac{22}{a}$

4.123

−1

4.124

$- \frac{2}{3}$

4.125

60

4.126

15

4.127

96

4.128

224

4.129

$\frac{9}{12}, \frac{10}{12}$

4.130

$- \frac{35}{60}, \frac{44}{60}$

4.131

$\frac{52}{96}, \frac{51}{96}$

4.132

$\frac{72}{224}, \frac{189}{224}$

4.133

$\frac{7}{12}$

4.134

$\frac{7}{10}$

4.135

$\frac{5}{8}$

4.136

$\frac{1}{2}$

4.137

$\frac{79}{60}$

4.138

$\frac{103}{60}$

4.139

$\frac{1}{96}$

4.140

$\frac{75}{224}$

4.141

$\frac{37}{210}$

4.142

$- \frac{25}{96}$

4.143

$\frac{3 y + 14}{18}$

4.144

$\frac{5 x + 14}{30}$

4.145

ⓐ $- \frac{11}{12}$
ⓑ $- \frac{1}{8}$

4.146

ⓐ $- \frac{10}{3}$
ⓑ $\frac{13}{12}$

4.147

ⓐ $\frac{(27 a - 32)}{36}$
ⓑ $\frac{2 a}{3}$

4.148

ⓐ $\frac{(24 k + 25)}{30}$
ⓑ $\frac{24 k}{5}$

4.149

$\frac{1}{90}$

4.150

272

4.151

2

4.152

$\frac{2}{7}$

4.153

ⓐ $−1$
ⓑ $- \frac{1}{2}$

4.154

ⓐ $\frac{7}{6}$
ⓑ $- \frac{1}{4}$

4.155

$- \frac{3}{4}$

4.156

$- \frac{23}{8}$

4.157

$- \frac{1}{2}$

4.158

$\frac{2}{3}$

4.159

$- \frac{5}{2}$

4.160

$\frac{3}{2}$

4.161

5

The figure shows five circles. The last one is divided into five equal sections.

4.162

5

The figure shows five circles. The last one is divided into six equal sections.

4.163

$4 \frac{2}{3}$

The figure shows five circles. The last two are divided into six equal sections. Two sections of the last circle are white.

4.164

$3 \frac{1}{2}$

The figure shows four circles. The last two are divided into eight equal sections. Four sections of the last circle are white.

4.165

$5 \frac{6}{7}$

4.166

$7 \frac{9}{11}$

4.167

$16 \frac{1}{2}$

4.168

$15 \frac{1}{3}$

4.169

$9 \frac{1}{3}$

4.170

$6 \frac{3}{5}$

4.171

$\frac{3}{4}$

4.172

$\frac{4}{5}$

4.173

$\frac{9}{5}$

4.174

$\frac{5}{3}$

4.175

$\frac{2}{3}$

4.176

$\frac{3}{4}$

4.177

$\frac{2}{3}$

A circle divided into three sections, two of which are shaded.

4.178

$\frac{2}{5}$

A circle divided into 5 sections, 2 of which are shaded.

4.179

$2 \frac{2}{3}$

4.180

$1 \frac{5}{7}$

4.181

$2 \frac{2}{3}$

4.182

$1 \frac{5}{7}$

4.183

$6 \frac{7}{12}$

4.184

$12 \frac{3}{10}$

4.185

$4 \frac{7}{10}$

4.186

$2 \frac{11}{12}$

4.187

$- \frac{41}{8}$

4.188

$- \frac{757}{63}$

4.189

ⓐ no
ⓑ yes
ⓒ no

4.190

ⓐ no
ⓑ no
ⓒ yes

4.191

$- \frac{1}{2}$

4.192

$- \frac{4}{15}$

4.193

−1

4.194

$- \frac{6}{7}$

4.195

$- \frac{19}{3}$

4.196

$\frac{23}{2}$

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

$\frac{n}{7} = −21; n = −147$

4.208

$\frac{n}{8} = −56; n = −448$

4.209

$\frac{q}{−8} = 72; q = −576$

4.210

$\frac{p}{−9} = 81; p = −729$

4.211

$\frac{2}{5} f = 16; f = 40$

4.212

$\frac{3}{4} f = 21; f = 28$

4.213

$\frac{n}{\frac{2}{3}} = \frac{5}{12}; n = \frac{5}{18}$

4.214

$\frac{c}{\frac{3}{8}} = \frac{4}{9}; c = \frac{1}{6}$

4.215

$\frac{5}{8} + x = \frac{1}{4}; x = - \frac{3}{8}$

4.216

$1 \frac{3}{4} - x = \frac{5}{6}; x = \frac{11}{12}$

Section 4.1 Exercises

1.

ⓐ $\frac{1}{4}$
ⓑ $\frac{3}{4}$
ⓒ $\frac{3}{8}$
ⓓ $\frac{5}{8}$

3.

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.

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.

ⓐ $\frac{5}{4} = 1 \frac{1}{4}$
ⓑ $\frac{7}{4} = 1 \frac{3}{4}$
ⓒ $\frac{11}{8} = 1 \frac{3}{8}$

19.

ⓐ $\frac{11}{4} = 2 \frac{3}{4}$
ⓑ $\frac{19}{8} = 2 \frac{3}{8}$

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.

$1 \frac{2}{3}$

31.

$2 \frac{3}{5}$

33.

$3 \frac{1}{9}$

35.

$3 \frac{2}{15}$

37.

$\frac{7}{5}$

39.

$\frac{17}{6}$

41.

$\frac{19}{7}$

43.

$\frac{32}{9}$

45.

4

47.

9

49.

9

51.

Answers may vary. Correct answers include $\frac{2}{6}, \frac{3}{9}, \frac{4}{12} .$

53.

Answers may vary. Correct answers include $\frac{10}{12}, \frac{15}{18}, \frac{20}{24} .$

55.

Answers may vary. Correct answers include $\frac{10}{18}, \frac{15}{27}, \frac{20}{36} .$

57.

59.

61.

63.

65.

<

67.

>

69.

<

71.

<

73.

ⓐ 2
ⓑ $6 \frac{1}{4}$

75.

Answers will vary.

Section 4.2 Exercises

77.

$\frac{1}{3}$

79.

$\frac{3}{4}$

81.

$- \frac{5}{11}$

83.

$- \frac{12}{7}$

85.

$\frac{10}{21}$

87.

$- \frac{7}{8}$

89.

$\frac{x}{y}$

91.

$- \frac{x}{4 y}$

93.

$\frac{2 x^{2}}{3 y}$

95.

$\frac{1}{3}$

97.

$\frac{5}{18}$

99.

$\frac{2}{15}$

101.

$\frac{27}{40}$

103.

$\frac{1}{4}$

105.

$- \frac{1}{6}$

107.

$- \frac{2}{9}$

109.

$- \frac{21}{50}$

111.

$\frac{11}{30}$

113.

$\frac{20}{11}$

115.

9n

117.

7p

119.

−34

121.

$\frac{3}{8}$

123.

$\frac{8}{27}$

125.

$\frac{1296}{625}$

127.

$\frac{4}{3}$

129.

$- \frac{17}{5}$

131.

$\frac{8}{11}$

133.

$- \frac{1}{19}$

135.

1

136.

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.

4

141.

12

143.

4

145.

$\frac{16}{15}$

147.

$- \frac{5}{4}$

149.

1

151.

$\frac{18}{5 y}$

153.

$\frac{25}{2 c}$

155.

$- \frac{3}{4}$

157.

$\frac{2}{9}$

159.

$\frac{14 r}{15 s}$

161.

−12

163.

$- \frac{1}{25}$

165.

9

167.

$\frac{8}{7}$

169.

ⓐ $4 \cdot \frac{2}{3}$ cups $= \frac{8}{3}$ cups $= 2 \frac{2}{3}$ cups
ⓑ Answers will vary.

171.

$\frac{1}{8}$ yard

173.

Answers will vary.

175.

Answers will vary.

Section 4.3 Exercises

177.

$\frac{44}{21}$

179.

$\frac{35}{8}$

181.

$- \frac{16}{3}$

183.

$- \frac{63}{16}$

185.

$\frac{3}{2}$

187.

$- \frac{4}{3}$

189.

2

191.

5

193.

$\frac{7 v}{13}$

195.

$\frac{a}{b}$

197.

$\frac{A}{3 - B}$

199.

$\frac{3}{2}$

201.

$- \frac{15}{22}$

203.

$- \frac{3}{10}$

205.

$\frac{1}{6}$

207.

$\frac{3 r}{5 s}$

209.

$\frac{9}{2 y}$

211.

28

213.

$- \frac{1}{18}$

215.

$\frac{−4}{9}, - \frac{4}{9}$

217.

$\frac{13}{−6}, \frac{−13}{6}$

219.

$\frac{12}{7}$

221.

$\frac{5}{2}$

223.

$\frac{23}{4}$

225.

$- \frac{1}{3}$

227.

$\frac{4}{5}$

229.

$- \frac{1}{2}$

231.

2

233.

$\frac{5}{6}$

235.

$\frac{26}{25}$

237.

$\frac{11}{6}$

239.

$\frac{5}{2}$

241.

−10

243.

−2

245.

$\frac{51}{20}$

247.

$\frac{18}{7}$

249.

ⓐ $\frac{4}{3} = 1 \frac{1}{3}$ cups
ⓑ $\frac{80}{3} = 26 \frac{2}{3}$ 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.

$\frac{7}{10}$

257.

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

$\frac{3}{4}$

259.

$\frac{7}{9}$

261.

$\frac{16}{15}$

263.

$\frac{y + 2}{3}$

265.

$\frac{14}{q}$

267.

$\frac{9 a}{7}$

269.

$\frac{−4 x}{5}$

271.

$- \frac{3}{4}$

273.

$- \frac{7}{8}$

275.

$\frac{8}{19}$

277.

$- \frac{13}{12}$

279.

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

$\frac{1}{2}$

281.

$\frac{1}{5}$

283.

$\frac{5}{13}$

285.

$\frac{1}{6}$

287.

$- \frac{8}{3}$

289.

$\frac{x - 8}{19}$

291.

$\frac{11 z - 8}{13}$

293.

$- \frac{14}{c}$

295.

$- \frac{55}{v}$

297.

$\frac{3 d}{11}$

299.

$- \frac{14 s}{3}$

301.

$\frac{2}{7}$

303.

$- \frac{3}{11}$

305.

$- \frac{1}{8}$

307.

$\frac{6 - s}{11}$

309.

$- \frac{2}{9}$

311.

$\frac{49}{27}$

313.

$\frac{1}{4}$ cup

315.

No, adding up the number of pieces gives $\frac{13}{12}$ , which is greater than 1. (Answers may vary.)

Section 4.5 Exercises

317.

20

319.

48

321.

240

323.

245

325.

60

327.

$\frac{5}{20}, \frac{4}{20}$

329.

$\frac{14}{24}, \frac{15}{24}$

331.

$\frac{33}{48}, - \frac{20}{48}$

333.

$\frac{20}{60}, \frac{45}{60}, \frac{36}{60}$

335.

$\frac{9}{20}$

337.

$\frac{11}{24}$

339.

$\frac{3}{8}$

341.

$\frac{2}{3}$

343.

$\frac{23}{20}$

345.

$\frac{19}{24}$

347.

$\frac{1}{48}$

349.

$\frac{1}{24}$

351.

$\frac{1}{12}$

353.

$\frac{7}{60}$

355.

$- \frac{53}{80}$

357.

$- \frac{291}{245}$

359.

$\frac{1}{20}$

361.

$\frac{11}{40}$

363.

$\frac{11}{6}$

365.

$\frac{7}{10}$

367.

$\frac{3 y + 4}{6}$

369.

$\frac{4 x - 5}{20}$

371.

ⓐ $\frac{5}{6}$
ⓑ $4$

373.

ⓐ $- \frac{37}{40}$
ⓑ $- \frac{1}{10}$

375.

ⓐ $\frac{9 a}{14}$
ⓑ $\frac{9 a - 14}{24}$

377.

ⓐ $- \frac{4 q}{27}$
ⓑ $\frac{12 - 25 q}{45}$

379.

$\frac{3}{4}$

381.

$\frac{11}{24}$

383.

$\frac{7}{18}$

385.

$- \frac{2}{15}$

387.

$\frac{−33 - 8 x}{88}$

389.

$\frac{16}{39}$

391.

$\frac{1}{81}$

393.

32

395.

$\frac{36}{25}$

397.

$\frac{60}{7}$

399.

$\frac{15}{2}$

401.

$\frac{3}{13}$

403.

$\frac{19}{30}$

405.

−9

407.

$\frac{91}{60}$

409.

$\frac{11}{40}$

411.

$\frac{5}{6}$

413.

1

415.

$\frac{22}{7}$

417.

ⓐ $\frac{1}{2}$
ⓑ $−1$

419.

ⓐ $0$
ⓑ $- \frac{1}{6}$

421.

ⓐ $\frac{1}{3}$
ⓑ $−1$

423.

ⓐ $\frac{1}{6}$
ⓑ $\frac{2}{3}$

425.

$\frac{4}{15}$

427.

$- \frac{9}{16}$

429.

−2

431.

3

433.

She needs $2 \frac{3}{8}$ 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.

$3 \frac{2}{3}$

439.

$3 \frac{2}{3}$

441.

$7 \frac{5}{9}$

443.

11

445.

$11 \frac{1}{3}$

447.

$11 \frac{1}{3}$

449.

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

$\frac{1}{2}$

451.

$1 \frac{1}{6}$

453.

$6 \frac{2}{5}$

455.

$1 \frac{7}{9}$

457.

$\frac{5}{6}$

459.

$7 \frac{11}{12}$

461.

$16 \frac{1}{6}$

463.

$5 \frac{11}{20}$

465.

$−1 \frac{11}{24}$

467.

$6 \frac{17}{18}$

469.

$\frac{7}{9}$

471.

23

473.

$8 \frac{3}{4}$

475.

$\frac{4}{15}$

477.

$5 \frac{3}{5}$

479.

$\frac{1}{16}$

481.

$13 \frac{1}{13}$

483.

$7 \frac{1}{30}$

485.

$\frac{10}{27}$

487.

$2 \frac{7}{45}$

489.

$\frac{17}{24}$

491.

$\frac{7}{12}$ yards

493.

$13 \frac{1}{4}$ inches

495.

Answers will vary.

497.

Answers will vary.

Section 4.7 Exercises

499.

ⓐ no
ⓑ yes
ⓒ no

501.

ⓐ no
ⓑ yes
ⓒ no

503.

$m = \frac{1}{2}$

505.

$h = - \frac{2}{3}$

507.

c = −1

509.

z = −1

511.

$p = \frac{37}{40}$

513.

$k = - \frac{7}{15}$

515.

$k = \frac{18}{7}$

517.

$v = - \frac{11}{3}$

519.

b = −27

521.

x = −256

523.

q = 160

525.

s = 45

527.

y = −42

529.

$k = \frac{17}{20}$

531.

p = 100

533.

m = −16

535.

b = −21

537.

v = 36

539.

y = 0

541.

$g = \frac{1}{9}$

543.

$q = - \frac{3}{4}$

545.

$n = \frac{14}{5}$

547.

$y = - \frac{25}{24}$

549.

$d = - \frac{8}{15}$

551.

$\frac{n}{6} = −24; n = −144$

553.

$\frac{m}{−7} = −8; m = 56$

555.

$\frac{f}{−4} = −20; f = 80$

557.

$\frac{g}{9} = 14; g = 126$

559.

$\frac{2}{5} q = 20; q = 50$

561.

$\frac{4}{9} p = −28; p = −63$

563.

$\frac{h}{2} = 43; h = 86$

565.

$\frac{a}{\frac{2}{3}} = \frac{3}{4}; a = \frac{1}{2}$

567.

$\frac{3}{4} + x = \frac{1}{8}; x = - \frac{5}{8}$

569.

$y - \frac{1}{3} = - \frac{1}{6}; y = \frac{1}{6}$

571.

30 inches

573.

Answers will vary.

Review Exercises

575.

$\frac{5}{9}$

577.

$\frac{3}{2} = 1 \frac{1}{2}$

579.

$5 \frac{8}{11}$

581.

$\frac{49}{5}$

583.

Answers may vary.

585.

587.

>

589.

$- \frac{3}{4}$

591.

$- \frac{x}{y}$

593.

$- \frac{4}{7}$

595.

$\frac{24 m}{11}$

597.

6

599.

$\frac{4}{15}$

601.

−4

603.

4

605.

$\frac{4}{15}$

607.

$- \frac{5}{2 b}$

609.

$- \frac{268}{11}$

611.

8

613.

$\frac{V}{h - 6}$

615.

$- \frac{2}{9}$

617.

22

619.

$\frac{7}{36}$

621.

$\frac{5}{8}$

623.

$\frac{3}{5}$

625.

$\frac{x + 7}{10}$

627.

$\frac{1}{2}$

629.

$- \frac{19}{15}$

631.

$\frac{8}{15}$

633.

15

635.

60

637.

$\frac{9}{24}$ and $\frac{20}{24}$

639.

$\frac{20}{60}, \frac{45}{60}$ and $\frac{48}{60}$

641.

$\frac{1}{4}$

643.

$- \frac{77}{90}$

645.

$\frac{3 y - 10}{30}$

647.

$\frac{14 d}{11}$

649.

$\frac{256}{225}$

651.

ⓐ $- \frac{8}{5}$
ⓑ $- \frac{11}{20}$

653.

$13 \frac{2}{3}$

655.

$8 \frac{1}{11}$

657.

$5 \frac{1}{10}$

659.

$1 \frac{1}{3}$

661.

ⓐ no
ⓑ yes
ⓒ no

663.

$n = - \frac{5}{11}$

665.

$h = - \frac{51}{40}$

667.

z = −23

669.

$q - \frac{1}{10} = \frac{1}{2}; q = \frac{3}{5}$

671.

$\frac{3}{8} y = 24; y = 64$

Practice Test

673.

$\frac{23}{7}$

675.

$\frac{1}{4}$

677.

$\frac{1}{4}$

679.

16u

681.

−2

683.

$\frac{12}{25}$

685.

5

687.

$\frac{5 p}{2 q}$

689.

13

691.

$- \frac{7}{13}$

693.

−1

695.

$- \frac{9}{4 x}$

697.

3

699.

$y = \frac{4}{5}$

701.

$f = \frac{13}{12}$

703.

c = −27

Chapter 4

Be Prepared

Try It

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