13.1.1: Chapter 1

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Try It

1.1

ⓐ yes ⓑ yes ⓒ no ⓓ yes
ⓔ no

1.2

ⓐ no ⓑ yes ⓒ yes ⓓ no
ⓔ no

1.3

$2 \cdot 2 \cdot 2 \cdot 2 \cdot 5$

1.4

$2 \cdot 2 \cdot 3 \cdot 5$

1.5

$36$

1.6

$72$

1.7

1.8

1.9

1.10

1.11

ⓐ 9 ⓑ 64 ⓒ40

1.12

ⓐ 216 ⓑ 64 ⓒ 185

1.13

$10 x^{2} + 16 x + 17$

1.14

$12 y^{2} + 9 y + 7$

1.15

ⓐ $14 x^{2} - 13$ ⓑ $12 x \div 2$
ⓒ $z + 13$ ⓓ $8 x - 18$

1.16

ⓐ $17 y^{2} + 19$ ⓑ $7 y$
ⓒ $x + 11$ ⓓ $11 a - 14$

1.17

ⓐ $4 (p + q)$ ⓑ $4 p + q$

1.18

ⓐ $2 x - 8$ ⓑ $2 (x - 8)$

1.19

$w - 7$

1.20

$l - 6$

1.21

$4 q - 8$

1.22

$7 n + 3$

1.23

ⓐ $=$ ⓑ $>$ ⓒ $<$
ⓓ $=$

1.24

ⓐ $>$ ⓑ $=$ ⓒ $>$
ⓓ $<$

1.25

1.26

1.27

ⓐ $−6$ ⓑ 2 ⓒ $−2$

1.28

ⓐ $−7$ ⓑ 3 ⓒ $−3$

1.29

ⓐ 2 ⓑ $−2$ ⓒ $−10$ ⓓ 10

1.30

ⓐ 3 ⓑ $−3$ ⓒ $−11$ ⓓ 11

1.31

ⓐ $8, 8$ ⓑ $−18,$ $−18$
ⓒ $19, 19$ ⓓ $−4,$ $−4$

1.32

ⓐ $8, 8$ ⓑ $−22,$ $−22$
ⓒ $23, 23$ ⓓ $3, 3$

1.33

1.34

1.35

ⓐ 23 ⓑ 60 ⓒ $−63$ ⓓ $−9$

1.36

ⓐ 39 ⓑ 39 ⓒ −28 ⓓ −7

1.37

ⓐ 81 ⓑ $−81$

1.38

ⓐ 49 ⓑ $−49$

1.39

ⓐ 4 ⓑ 21

1.40

ⓐ 9 ⓑ 6

1.41

1.42

1.43

$(9 + (−16)) + 4; - 3$

1.44

$(−8 + (−12)) + 7; - 13$

1.45

The difference in temperatures was 45 degrees.

1.46

The difference in temperatures was 9 degrees.

1.47

$- \frac{23}{40}$

1.48

$- \frac{5}{8}$

1.49

$−33 a$

1.50

$−26 b$

1.51

$\frac{4}{15}$

1.52

$\frac{2}{3}$

1.53

$\frac{3}{4 b}$

1.54

$\frac{4}{q}$

1.55

$\frac{79}{60}$

1.56

$\frac{103}{60}$

1.57

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

1.58

ⓐ $\frac{24 k - 5}{30}$ ⓑ $\frac{2 k}{15}$

1.59

1.60

1.61

$\frac{1}{90}$

1.62

272

1.63

1.64

$\frac{2}{7}$

1.65

$- \frac{1}{2}$

1.66

$\frac{2}{3}$

1.67

ⓐ $6.58$ ⓑ $6.6$ ⓒ 7

1.68

ⓐ $15.218$ ⓑ $15.22$
ⓒ $15.2$

1.69

ⓐ $−16.49$ ⓑ $−0.42$

1.70

ⓐ $−23.593$ ⓑ $−12.58$

1.71

$−27.4815$

1.72

$−87.6148$

1.73

ⓐ 25.8 ⓑ 258 ⓒ 2,580

1.74

ⓐ 142 ⓑ 1,420 ⓒ 14,200

1.75

$587.3$

1.76

$34.25$

1.77

ⓐ $\frac{117}{500}$ ⓑ $−0.875$

1.78

ⓐ $\frac{3}{125}$ ⓑ $−0.375$

1.79

ⓐ 0.09, 0.87, 0.039 ⓑ 17%, 175%, 8.25%

1.80

ⓐ 0.03, 0.91, 0.083 ⓑ 41%, 225%, 9.25%

1.81

ⓐ 6 ⓑ 13 ⓒ $−15$

1.82

ⓐ 4 ⓑ 14 ⓒ $−10$

1.83

ⓐ $4, \sqrt{49}$ ⓑ $−3, 4, \sqrt{49}$
ⓒ $−3, 0. \bar{3}, \frac{9}{5}, 4, \sqrt{49}$ ⓓ $− \sqrt{2}$
ⓔ $−3, − \sqrt{2}, 0. \bar{3}, \frac{9}{5}, 4, \sqrt{49}$

1.84

ⓐ $6, \sqrt{121}$
ⓑ $− \sqrt{25}, −1, 6, \sqrt{121}$
ⓒ $− \sqrt{25}, - \frac{3}{8}, −1, 6, \sqrt{121}$
ⓓ $2.041975.. .$
ⓔ $− \sqrt{25}, - \frac{3}{8}, −1, 6, \sqrt{121}, 2.041975.. .$

1.85

$Figure shows a number line with numbers ranging from minus 4 to 5. Various points on the line are highlighted. From left to right, these are: minus 8 by 3, minus 7 by 4, minus 1, 1 by 3, 6 by 5, 9 by 2 and 5.$

1.86

$Figure shows a number line with numbers ranging from minus 4 to 5. Various points on the line are highlighted. From left to right, these are: minus 7 by 3, minus 2, minus 7 by 4, 2 by 3, 7 by 5, 3 and 7 by 2.$

1.87

ⓐ

$Figure shows a number line with numbers ranging from 0 to 1. 0.6 is highlighted.$

ⓑ

$Figure shows a number line with numbers ranging from minus 1.00 to 0.00. Minus 0.74 is highlighted, minus 0.25 is highlighted.$

1.88

ⓐ

$Figure shows a number line with numbers ranging from 0 to 1. 0.9 is highlighted.$

ⓑ

$Figure shows a number line with numbers ranging from minus 1.00 to 0.00. Minus 0.74 is highlighted.$

1.89

$32 r + 29 s$

1.90

$41 m + 6 n$

1.91

$1 \frac{7}{15}$

1.92

$1 \frac{2}{9}$

1.93

$−48 a$

1.94

$−92 x$

1.95

$\frac{5}{49}$

1.96

$\frac{11}{25}$

1.97

ⓐ 0 ⓑ undefined

1.98

ⓐ 0 ⓑ undefined

1.99

$4 x + 8$

1.100

$6 x + 42$

1.101

$5 y + 3$

1.102

$4 n + 9$

1.103

$70 + 15 p$

1.104

$4 + 35 d$

1.105

$−10 + 15 a$

1.106

$−56 + 105 y$

1.107

$− z + 11$

1.108

$− x + 4$

1.109

$3 - 3 x$

1.110

$2 x - 20$

1.111

$5 x - 66$

1.112

$7 x - 13$

Section 1.1 Exercises

Divisible by 2, 3, 6

Divisible by 2

Divisible by 3, 5

$2 \cdot 43$

$5 \cdot 7 \cdot 13$

11.

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

13.

15.

280

17.

440

19.

21.

23.

25.

149

27.

29.

31.

ⓐ 64 ⓑ 16 ⓒ 7

33.

35.

37.

$10 x + 6$

39.

$22 a + 1$

41.

$17 x^{2} + 20 x + 16$

43.

ⓐ $5 x^{2} - 6 x y$ ⓑ $\frac{6 y^{2}}{5 x}$
ⓒ $y^{2} + 21$ ⓓ $81 x^{2} - 6 x$

45.

ⓐ $4 a b^{2} + 3 a^{2} b$ ⓑ $20 x y^{2}$
ⓒ $m + 15$ ⓓ $121 x^{2} - 9 x$

47.

ⓐ $8 (y - 9)$ ⓑ $8 y - 9$

49.

ⓐ $5 (3 x + y)$ ⓑ $15 x + y$

51.

$2 c + 14$

53.

$3 n - 7$

55.

Answers will vary.

57.

Answers will vary.

Section 1.2 Exercises

59.

ⓐ $>$ ⓑ $>$ ⓒ $>$ ⓓ $>$

61.

ⓐ $=$ ⓑ $=$ ⓒ $>$ ⓓ $=$

63.

65.

67.

69.

71.

ⓐ $−11$ ⓑ $−3$ ⓒ $3$

73.

75.

$−22$

77.

$29$

79.

ⓐ 6 ⓑ $−6$ ⓒ $−20$ ⓓ $20$

81.

$−59$

83.

85.

ⓐ 16 ⓑ16

87.

ⓐ 45 ⓑ45

89.

91.

93.

95.

ⓐ $−32$ ⓑ $−65$ ⓒ $−4$
ⓓ $13$

97.

ⓐ $−4$ ⓑ $−12$ ⓒ $−39$
ⓓ $14$

99.

ⓐ $64$ ⓑ $−64$

101.

$−47$

103.

$90$

105.

$9$

107.

$41$

109.

$−9$

111.

$−29$

113.

$1$

115.

$−3$

117.

$5$

119.

ⓐ $−47$ ⓑ $16$

121.

$121$

123.

$−56$

125.

$6$

127.

$(3 + (−15)) + 7; - 5$

129.

ⓐ $10 - (−18); 28$
ⓑ $−25 - 11; - 36$

131.

$\frac{−6}{a + b}$

133.

$96 °$

135.

21 yards

137.

$− $ 28$

139.

Answers will vary.

141.

Answers will vary.

Section 1.3 Exercises

143.

$- \frac{12}{7}$

145.

$\frac{10}{21}$

147.

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

149.

$- \frac{21 a^{2}}{11 b^{2}}$

151.

$\frac{1}{3}$

153.

$- \frac{21}{50}$

155.

$\frac{11}{30}$

157.

$9 n$

159.

$\frac{33}{4 x}$

161.

$- \frac{4}{9}$

163.

$\frac{10 u}{9 v}$

165.

$- \frac{1}{16}$

167.

$- \frac{10}{9}$

169.

$- \frac{2}{5}$

171.

$\frac{2 m}{3 n}$

173.

$\frac{29}{24}$

175.

$\frac{1}{48}$

177.

$\frac{17}{105}$

179.

$- \frac{53}{40}$

181.

$\frac{1}{12}$

183.

$\frac{4 x + 3}{12}$

185.

ⓐ $\frac{5}{6}$ ⓑ $4$

187.

ⓐ $\frac{25 n}{16}$ ⓑ $\frac{25 n - 16}{30}$

189.

ⓐ $\frac{−8 x - 15}{18}$ ⓑ $- \frac{10 k}{27}$

191.

ⓐ $\frac{−5 (a + 1)}{3}$ ⓑ $a$

193.

$\frac{9}{7}$

195.

$−8$

197.

$\frac{11}{6}$

199.

$\frac{5}{2}$

201.

$54$

203.

$\frac{49}{25}$

205.

$\frac{15}{4}$

207.

$\frac{5}{21}$

209.

$\frac{5}{4}$

211.

$\frac{1}{24}$

213.

$\frac{−28 - 15 y}{60}$

215.

$\frac{33}{64}$

217.

$\frac{7}{9}$

219.

$−5$

221.

$\frac{23}{24}$

223.

$\frac{11}{5}$

225.

$1$

227.

$\frac{13}{3}$

229.

ⓐ $\frac{1}{5}$ ⓑ $\frac{6}{5}$

231.

$- \frac{1}{9}$

233.

$- \frac{5}{11}$

235.

Answers will vary.

237.

Answers will vary.

Section 1.4 Exercises

239.

ⓐ 5.78 ⓑ 5.8 ⓒ 6

241.

ⓐ 0.30 ⓑ 0.3 ⓒ 0

243.

ⓐ 63.48 ⓑ 63.5 ⓒ 63

245.

$−40.91$

247.

$−7.22$

249.

$−27.5$

251.

$102.212$

253.

$51.31$

255.

$−4.89$

257.

$−1200.47982$

259.

$337.8914$

261.

$1.305$

263.

$92.4$

265.

2.5

267.

55200

269.

$$ 2.44$

271.

$−4.8$

273.

$2.08$

275.

$\frac{1}{25}$

277.

$\frac{19}{200}$

279.

$0.85$

281.

$−12.4$

283.

$0.71$

285.

$0.393$

287.

$156 %$

289.

$6.25 %$

291.

293.

295.

$−10$

297.

ⓐ $0, \sqrt{36}, 9$ ⓑ $−8, 0, \sqrt{36}, 9$ ⓒ $−8, 0, \frac{12}{5}, \sqrt{36}, 9$ ⓓ $1.95286...,$ ⓔ $−8, 0, 1.95286..., \frac{12}{5}, \sqrt{36}, 9$

299.

ⓐ none ⓑ $− \sqrt{100}, −7, −1$
ⓒ $− \sqrt{100}, −7, - \frac{8}{3}, −1, 0.77, 3 \frac{1}{4}$
ⓓ none
ⓔ $− \sqrt{100}, −7, - \frac{8}{3}, −1, 0.77, 3 \frac{1}{4}$

301.

$Figure shows a number line with numbers ranging from 0 to 6. Some values are highlighted. From left to right, these are: 3 by 10, 11 by 6, 7 by 2 and 4.$

303.

$Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted. From left to right, these are: minus 5 by 2, minus 1 and two thirds, minus 3 by 4, 3 by 4, 1 and two thirds, and 5 by 2.$

305.

$Figure shows a number line with numbers ranging from minus 4 to 4. Two values are highlighted. One is between minus 2 and minus 1. The other is between 0 and 1.$

307.

$Figure shows a number line with numbers ranging from minus 4 to 4. Two values are highlighted. One is between minus 2 and minus 1. The other is between 3 and 4.$

309.

Answers will vary.

311.

Answers will vary.

Section 1.5 Exercises

313.

$27 m + (−21 n)$

315.

$\frac{5}{4} g + \frac{1}{2} h$

317.

$2.43 p + 8.26 q$

319.

$−63$

321.

$1 \frac{5}{6}$

323.

$17$

325.

$14.88$

327.

$10 p$

329.

$44$

331.

$\frac{7}{8}$

333.

$d$

335.

$\frac{49}{11}$

337.

339.

undefined

341.

undefined

343.

$32 y + 72$

345.

$6 c - 78$

347.

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

349.

$5 y - 3$

351.

$3 + 8 r$

353.

$36 d + 90$

355.

$r s - 18 r$

357.

$y p + 4 p$

359.

$−28 p - 7$

361.

$−3 x + 18$

363.

$−3 x + 7$

365.

$−3 y - 8$

367.

$−33 c + 26$

369.

$− a + 19$

371.

$4 m - 10$

373.

$72 x - 25$

375.

$22 n + 9$

377.

$6 c + 34$

379.

$12 y + 63$

381.

Answers will vary.

383.

Answers will vary.

Review Exercises

385.

Divisible by $2, 3, 5, 6, 10$

387.

120

389.

391.

393.

$6 x^{2} - x + 5$

395.

ⓐ $11 (y - 2)$ ⓑ $11 y - 2$

397.

399.

$−9$

401.

403.

ⓐ 40 ⓑ 40

405.

407.

409.

$−12$

411.

413.

$(−4 + (−9)) + 23; 10$

415.

$46^{°}$

417.

$- \frac{15 x^{3}}{11 y^{2}}$

419.

$\frac{8 x}{15 y}$

421.

$\frac{31}{36}$

423.

ⓐ $\frac{11}{8}$ ⓑ $\frac{5}{6}$

425.

$- \frac{1}{6}$

427.

429.

$- \frac{1}{5}$

431.

$6.17$

433.

$96.978$

435.

488.1813

437.

$56.3$

439.

$−2.3$

441.

$- \frac{48}{5}$

443.

$1. \bar{27}$

445.

$4.75 %$

447.

no real number

449.

$Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted.$

451.

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

453.

$1 \frac{11}{15}$

455.

$\frac{9}{17}$

457.

undefined

459.

$8 b + 10$

461.

$x p - 5 p$

463.

$−6 x - 6$

465.

$6 y + 16$

Practice Test

467.

$7 n + 7$

469.

$−8 - 11; - 19$

$(−8 - (−3)) + 5; 0$

471.

ⓐ $28.15$ ⓑ $28.146$

473.

$Figure shows a number line with numbers ranging from minus 4 to 4. Some values are highlighted.$

475.

477.

$−8$

479.

$\frac{15}{17}$

481.

$- \frac{5}{3}$

483.

$3$

485.

$- \frac{7}{6}$

487.

$−65.4$

489.

−160

491.

$1 \frac{8}{13}$

493.

ⓐ 0 ⓑ undefined

495.

$13 y - 3$

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Section 1.1 Exercises

Section 1.2 Exercises

Section 1.3 Exercises

Section 1.4 Exercises

Section 1.5 Exercises

Review Exercises

Practice Test