12.4.7: Chapter 7

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Be Prepared

7.1

$\frac{319}{100}$

7.2

$0. \bar{45}$

7.3

$12$

7.4

$8 y + 15$

7.5

$12$

7.6

$- 15$

7.7

$0.75$

7.8

$16$

7.9

$12 y + 15$

7.10

$4$

7.11

$\frac{2}{5}$

7.12

$\frac{27}{10}$

7.13

$4, 290$

7.14

$\frac{5}{9}$

7.15

$\frac{5}{12}$

Try It

7.1

ⓐ $\frac{−24}{1}$
ⓑ $\frac{357}{100}$

7.2

ⓐ $\frac{−19}{1}$
ⓑ $\frac{841}{100}$

7.3

ⓐ rational
ⓑ rational
ⓒ irrational

7.4

ⓐ rational
ⓑ rational
ⓒ irrational

7.5

ⓐ rational
ⓑ irrational

7.6

ⓐ irrational
ⓑ rational

7.7 $The table has seven rows and six columns. The first row is a header row that labels each column. The first column is labeled “Number”, the second column “Whole”, the third “Integer”, the fourth “Rational” the fifth “Irrational” and the sixth “Real”. Each row has a number in the “Number” column then an x in each column that corresponds to the type of number it is. The second row has the number negative 3 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The third row has the number negative square root of 2 in the “Number” column and an x marked in the “Irrational” and “Real” columns. The fourth row has the number 0.3 repeating in the “Number” column and an x marked in the “Rational” and “Real” columns. The fifth row has the number square root of negative 49 in the “Number” column with no other columns marked. The sixth row has the number 4 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns. The last row has the number 9 fifths in the “Number” column and an x marked in the “Rational” and “Real” columns.$

7.8 $The table has seven rows and six columns. The first row is a header row that labels each column. The first column is labeled “Number”, the second column “Whole”, the third “Integer”, the fourth “Rational” the fifth “Irrational” and the sixth “Real”. Each row has a number in the “Number” column then an x in each column that corresponds to the type of number it is. The second row has the number negative square root of 25 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The third row has the number negative 3 eights in the “Number” column and an x marked in the “Rational” and “Real” columns. The fourth row has the number negative 1 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The fifth row has the number 6 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns. The sixth row has the number square root of 121 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns. The last row has the number 2.041975 followed by an ellipsis in the “Number” column and an x marked in the “Irrational” and “Real” columns.$

7.9

ⓐ −4 + 7 = 7 + (−4)
ⓑ 6 · 12 = 12 · 6

7.10

ⓐ 14 + (−2) = −2 + 14
ⓑ 3(−5) = (−5)3

7.11

ⓐ $(1 + 0.7) + 0.3 = 1 + (0.7 + 0.3)$
ⓑ $(−9 \cdot 8) \cdot \frac{3}{4} = −9 (8 \cdot \frac{3}{4})$

7.12

ⓐ $(4 + 0.6) + 0.4 = 4 + (0.6 + 0.4)$
ⓑ $(−2 \cdot 12) \cdot \frac{5}{6} = −2 (12 \cdot \frac{5}{6})$

7.13

8(4x) = (8 · 4)x = 32x

7.14

−9(7y) = (−9 · 7)y = −63y

7.15

ⓐ 0.84
ⓑ 0.84

7.16

ⓐ 0.975
ⓑ 0.975

7.17

ⓐ 24
ⓑ 24

7.18

ⓐ 15
ⓑ 15

7.19

−48a

7.20

−92x

7.21

$\frac{5}{49}$

7.22

$\frac{11}{25}$

7.23

$\frac{22}{15}$

7.24

$\frac{11}{9}$

7.25

15.58c

7.26

17.79d

7.27

10.53

7.28

70.4

7.29

24y

7.30

60z

7.31

32r − s

7.32

41m + 6n

7.33

4x + 8

7.34

6x + 42

7.35

27y + 72

7.36

25w + 45

7.37

7x − 42

7.38

8x − 40

7.39

$\frac{2}{5} p + 4$

7.40

$\frac{3}{7} u + 9$

7.41

5y + 3

7.42

4n + 9

7.43

70 + 15p

7.44

4 + 35d

7.45

rs − 2r

7.46

yz − 8y

7.47

xp + 2p

7.48

yq + 4q

7.49

−18m − 15

7.50

−48n − 66

7.51

−10 + 15a

7.52

−56 + 105y

7.53

−z + 11

7.54

−x + 4

7.55

−3x + 3

7.56

2x − 20

7.57

5x − 66

7.58

7x − 13

7.59

ⓐ 120
ⓑ 120

7.60

ⓐ 126
ⓑ 126

7.61

ⓐ 30
ⓑ 30

7.62

ⓐ 3
ⓑ 3

7.63

ⓐ −32
ⓑ −32

7.64

ⓐ −45
ⓑ −45

7.65

ⓐ identity property of addition
ⓑ identity property of multiplication

7.66

ⓐ identity property of multiplication
ⓑ identity property of addition

7.67

ⓐ $−18$
ⓑ $- \frac{7}{9}$
ⓒ $−1.2$

7.68

ⓐ $−47$
ⓑ $- \frac{7}{13}$
ⓒ $−8.4$

7.69

ⓐ $\frac{1}{5}$
ⓑ $−7$
ⓒ $\frac{10}{3}$

7.70

ⓐ $\frac{1}{18}$
ⓑ $- \frac{5}{4}$
ⓒ $\frac{5}{3}$

7.71

ⓐ 0
ⓑ 0
ⓒ 0

7.72

ⓐ 0
ⓑ 0
ⓒ 0

7.73

ⓐ 0
ⓑ 0
ⓒ 0

7.74

ⓐ 0
ⓑ 0
ⓒ 0

7.75

ⓐ undefined
ⓑ undefined
ⓒ undefined

7.76

ⓐ undefined
ⓑ undefined
ⓒ undefined

7.77

7.78

−18

7.79

7.80

7.81

7.82

7.83

undefined

7.84

undefined

7.85

20y + 50

7.86

12z + 16

7.87

2.5 feet

7.88

54 feet

7.89

8600 pounds

7.90

102,000,000 pounds

7.91

440,000,000 yards

7.92

151,200 minutes

7.93

16 cups

7.94

48 teaspoons

7.95

9 lbs. 8 oz

7.96

21 ft. 6 in.

7.97

4 lbs. 8 oz.

7.98

11 gal. 2 qts.

7.99

5000 m

7.100

250 cm

7.101

2.8 kilograms

7.102

4.5 kilograms

7.103

ⓐ 0.00725 kL
ⓑ 6300 mL

7.104

ⓐ 35,000 L
ⓑ 410 cL

7.105

83 cm

7.106

1.04 m

7.107

2 L

7.108

2.4 kg

7.109

2.12 quarts

7.110

3.8 liters

7.111

19,328 ft

7.112

3,470 mi

7.113

15°C

7.114

5°C

7.115

59°F

7.116

50°F

Section 7.1 Exercises

ⓐ $\frac{5}{1}$
ⓑ $\frac{319}{100}$

ⓐ $\frac{−12}{1}$
ⓑ $\frac{9279}{1000}$

Rational: $0.75, 0.22 \overset{–}{3}$ . Irrational: $1.39174…$

Rational: $0 . \overset{—}{45}$ , $3.59$ . Irrational: $1.919293…$

ⓐ rational
ⓑ irrational

11.

ⓐ irrational
ⓑ rational

13. $The table has seven rows and six columns. The first row is a header row that labels each column. The first column is labeled “Number”, the second column “Whole”, the third “Integer”, the fourth “Rational” the fifth “Irrational” and the sixth “Real”. Each row has a number in the “Number” column then an x in each column that corresponds to the type of number it is. The second row has the number negative 8 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The third row has the number 0 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns. The fourth row has the number 1.95286 followed by and ellipsis in the “Number” column and an x marked in the “Irrational” and “Real” columns. The fifth row has the number 12 fifths in the “Number” column and an x marked in the “Rational” and “Real” columns. The sixth row has the number square root of 36 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns. The last row has the number 9 in the “Number” column and an x marked in the “Whole”, “Integer”, “Rational” and “Real” columns.$

15. $The table has seven rows and six columns. The first row is a header row that labels each column. The first column is labeled “Number”, the second column “Whole”, the third “Integer”, the fourth “Rational” the fifth “Irrational” and the sixth “Real”. Each row has a number in the “Number” column then an x in each column that corresponds to the type of number it is. The second row has the number negative 100 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The third row has the number negative 7 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The fourth row has the number negative 8 thirds in the “Number” column and an x marked in the “Rational” and “Real” columns. The fifth row has the number negative 1 in the “Number” column and an x marked in the “Integer”, “Rational” and “Real” columns. The sixth row has the number 0.77 in the “Number” column and an x marked in the “Rational” and “Real” columns. The last row has the number 3 and 1 quarter in the “Number” column and an x marked in the “Rational” and “Real” columns.$

17.

ⓐ 4
ⓑ Teachers cannot be divided
ⓒ It would result in a lower number.

19.

Answers will vary.

Section 7.2 Exercises

21.

7 + 6 = 6 + 7

23.

7(−13) = (−13)7

25.

(−12)(−18) = (−18)(−12)

27.

−15 + 7 = 7 + (−15)

29.

y + 1 = 1 + y

31.

−3m = m(−3)

33.

(21 + 14) + 9 = 21 + (14 + 9)

35.

(14 · 6) · 9 = 14(6 · 9)

37.

(−2 + 6) + 7 = −2 + (6 + 7)

39.

$(13 \cdot \frac{2}{3}) \cdot 18 = 13 (\frac{2}{3} \cdot 18)$

41.

4(7x) = (4 · 7)x

43.

(17 + y) + 33 = 17 + (y + 33)

45.

ⓐ 0.97
ⓑ 0.97

47.

ⓐ 2.375
ⓑ 2.375

49.

ⓐ 21
ⓑ 21

51.

ⓐ −8
ⓑ −8

53.

55.

$\frac{5}{12}$

57.

$\frac{25}{7}$

59.

$\frac{65}{23}$

61.

−176

63.

$\frac{13}{12}$

65.

$\frac{23}{15}$

67.

9.89d

69.

71.

29.193

73.

72w

75.

−46n

77.

12q

79.

42u + 30v

81.

−57p + (−10q)

83.

$a + \frac{6}{5} b$

85.

7.41m + 6.57n

87.

ⓐ $975
ⓑ $700
ⓒ $1675
ⓓ $185
ⓔ $270
ⓕ $1220

89.

Answers will vary.

Section 7.3 Exercises

91.

3a + 27

93.

27w + 63

95.

7y − 91

97.

35u − 20

99.

$\frac{1}{3} u + 3$

101.

$\frac{4}{5} m + 4$

103.

3x − 4

105.

2 + 9s

107.

uv − 10u

109.

ax + 7x

111.

−3a − 33

113.

−81a − 36

115.

−4q + 28

117.

−42x + 48

119.

−q − 11

121.

−5p + 4

123.

8u + 4

125.

−4x + 10

127.

−42n + 39

129.

−r + 15

131.

−c + 6

133.

3y + 1

135.

47u + 60

137.

24x + 4

139.

6n − 72

141.

17n + 76

143.

ⓐ 56
ⓑ 56

145.

ⓐ $\frac{9}{2}$
ⓑ $\frac{9}{2}$

147.

ⓐ −89
ⓑ −89

149.

ⓐ −525
ⓑ −525

151.

ⓐ 160
ⓑ 160

153.

ⓐ −1.03
ⓑ −1.03

155.

ⓐ 3(4 − 0.03) = 11.91
ⓑ $1.42

157.

Answers will vary.

Section 7.4 Exercises

159.

identity property of multiplication

161.

identity property of addition

163.

$\frac{1}{14}$

165.

$- \frac{1}{19}$

167.

$\frac{13}{8}$

169.

$- \frac{12}{5}$

171.

$\frac{5}{2}$

173.

−2

175.

177.

179.

undefined

181.

183.

185.

undefined

187.

189.

31s

191.

193.

195.

197.

199.

201.

undefined

203.

undefined

205.

undefined

207.

20q − 35

209.

225h + 360

211.

ⓐ 8 hours
ⓑ 8
ⓒ associative property of multiplication

213.

Answers will vary.

Section 7.5 Exercises

215.

24 inches

217.

3.75 feet

219.

58 inches

221.

90 feet

223.

0.98 miles

225.

300,000 pounds

227.

110 tons

229.

162 hours

231.

8100 seconds

233.

256 tablespoons

235.

128 ounces

237.

111 ounces

239.

31.25 gallons

241.

4 lbs. 1 oz.

243.

5 weeks and 1 day

245.

9 ft 2 in

247.

8 yards

249.

8000 meters

251.

245 centimeters

253.

10.911 kilometers

255.

3000 milligrams

257.

25,000 milligrams

259.

3800 grams

261.

0.3 liters

263.

65 centimeters

265.

1.82 kilograms

267.

16.8 grams

269.

42,000 milligrams

271.

106.7 centimeters

273.

8.2 meters

275.

40,900 kilograms

277.

5.2 feet

279.

33 pounds

281.

30.2 liters

283.

25°C

285.

−10°C

287.

−15.6°C

289.

48.9°C

291.

77°F

293.

5°F

295.

46.4°F

297.

60.8°F

299.

110 reflectors

Review Exercises

303.

$\frac{- 5}{1}$

305.

$\frac{18}{10}$

307.

$0. \overset{—}{16}, 1.95$

309.

ⓐ irrational
ⓑ rational

311.

ⓐ $4$
ⓑ $- 5, - \sqrt{4}, 4$
ⓓ none
ⓔ $- 5, - 2 \frac{1}{4}, - \sqrt{4}, 0. \overset{—}{25}, \frac{13}{5}, 4$

313.

−14·5 = 5(−14)

315.

a + 8 = 8 + a

317.

(22 + 7) + 3 = 22 + (7 + 3)

319.

$\frac{1}{2} (22 y) = (\frac{1}{2} \cdot 22) y$

321.

ⓐ 5.39
ⓑ 5.39

323.

ⓐ 13
ⓑ 13

325.

$\frac{11}{15}$

327.

−60

329.

5.98 d

331.

25 q

333.

34 m + (−25 n)

335.

9y − 36

337.

56a + 96

339.

yp + 10p

341.

−4x + 68

343.

ⓐ 9
ⓑ 9

345.

ⓐ 36
ⓑ 36

347.

identity property of addition

349.

identity property of multiplication

351.

−19.4

353.

$\frac{7}{15}$

355.

$- \frac{1}{5}$

357.

$- \frac{9}{4}$

359.

361.

363.

n + 7

365.

367.

54x − 84

369.

3.5 feet

371.

15 yards

373.

9000 pounds

375.

64 tablespoons

377.

1.9 gallons

379.

7 hours 10 minutes

381.

3 yards, 12 inches

383.

8.85 kilometers

385.

13,000 milligrams

387.

0.65 liters

389.

855 milliliters

391.

10,000 milligrams

393.

25.6 meters

395.

171.6 pounds

397.

11.4 kilograms

399.

−5°C

401.

17.8°C

403.

23°F

405.

75.2°F

Practice Test

407.

$\sqrt{144} = 12 therefore rational.$

409.

x·14 = 14·x

411.

(8·2)·5 = 8·(2·5)

413.

ⓐ $- \frac{2}{5}$
ⓑ $\frac{5}{2}$

415.

15y

417.

$\frac{23}{15}$

419.

30y − 4z

421.

30x − 24

423.

2a + 3

425.

66p − 2

427.

429.

431.

.276 grams

433.

9.317 miles

435.

95°F

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Be Prepared

Try It

Section 7.1 Exercises

Section 7.2 Exercises

Section 7.3 Exercises

Section 7.4 Exercises

Section 7.5 Exercises

Review Exercises

Practice Test