Prealgebra

# Chapter 5

PrealgebraChapter 5

## Try It

5.1
1. six and seven tenths
2. nineteen and fifty-eight hundredths
3. eighteen thousandths
4. negative two and fifty-three thousandths
5.2
1. five and eight tenths three and fifty-seven hundredths
2. three and fifty-seven hundredths
3. five thousandths
4. negative thirteen and four hundred sixty-one thousandths
5.3

13.68

5.4

5.894

5.5

0.058

5.6

0.067

5.7
1. $5 3 10 5 3 10$
2. $6710067100$
3. $− 234 1000 − 234 1000$
5.8
1. $8 7 10 8 7 10$
2. $1 3 100 1 3 100$
3. $− 24 1000 − 24 1000$
5.13
1. >
2. >
5.14
1. <
2. <
5.15

>

5.16

>

5.17

1.05

5.18

9.17

5.19
1. 6.58
2. 6.6
3. 7
5.20
1. 15.218
2. 15.22
3. 15.2
5.21

17.6

5.22

33.11

5.23

16.49

5.24

23.593

5.25

0.42

5.26

12.58

5.27

−1.53

5.28

−3.58

5.29

27.4815

5.30

87.6148

5.31

−13.427

5.32

38.122

5.33

0.00348

5.34

0.00603

5.35
1. 25.8
2. 258
3. 2,580
5.36
1. 142
2. 1,420
3. 14,200
5.37

0.07

5.38

0.08

5.39

$0.19 5.40$0.42

5.41

−0.39

5.42

−0.4

5.43

587.3

5.44

34.25

5.45

200

5.46

350

5.47

$16.52 5.48$65.97

5.49

$41.28 5.50$48.75

5.51

$15.47 5.52$14.25

5.53

$5.97 5.54$43.00

5.55

0.25

5.56

0.375

5.57

−2.25

5.58

−5.5

5.59

$2 . 45 — 2 . 45 —$

5.60

$2.3 18 — 2.3 18 —$

5.61

5.275

5.62

6.35

5.63

>

5.64

<

5.65

<

5.66

>

5.67

$4 5 , 0.82 , 7 8 4 5 , 0.82 , 7 8$

5.68

$3 4 , 13 16 , 0.835 3 4 , 13 16 , 0.835$

5.69
1. −183.2
2. 4.5
5.70
1. −776.25
2. 2.2
5.71

11.16

5.72

1.51

5.73
1. 314 in.
2. 7850 sq. in.
5.74
1. 628 ft.
2. 31,400 sq. ft.
5.75
1. 325.304 cm
2. 8425.3736 sq. cm
5.76
1. 165.792 m
2. 2188.4544 sq. m
5.77
1. $220 147 m 220 147 m$
2. $550 3087 sq. m 550 3087 sq. m$
5.78
1. $40 21 in. 40 21 in.$
2. $200 693 sq.in. 200 693 sq.in.$
5.79
1. no
2. yes
3. no
5.80
1. yes
2. no
3. no
5.81

y = −8

5.82

y = −8.4

5.83

a = 1.07

5.84

n = 0.83

5.85

b = −12

5.86

c = −8

5.87

c = 11.7

5.88

b = 6.48

5.89

y − 4.9 = 2.8; y = 7.7

5.90

z − 5.7 = 3.4; z = 9.1

5.91

−4.3x = 12.04; x = −2.8

5.92

−3.1m = 26.66; m = −8.6

5.93

$q −3.4 = 4.5 ; q = −15.3 q −3.4 = 4.5 ; q = −15.3$

5.94

$r −2.6 = 2.5 ; r = −6.5 r −2.6 = 2.5 ; r = −6.5$

5.95

j + 3.8 = 2.6; j = −1.2

5.96

k + 4.7 = 0.3; k = −4.4

5.97

8.5

5.98

9

5.99

21.5 years years

5.100

10

5.101

$7.19 5.102$39.62

5.103

43

5.104

30

5.105

8.5

5.106

20.5

5.109

21

5.111
1. $1 10 1 10$
2. $0.1 0.1$
5.112
1. $1 20 1 20$
2. $0.05 0.05$
5.113
1. $5 8 5 8$
2. $0.625 0.625$
5.114
1. $2 8 2 8$
2. $0.25 0.25$
5.115
1. $3838$
2. $3232$
5.116
1. $3838$
2. $3232$
5.117
1. $2 5 2 5$
2. $10 3 10 3$
5.118
1. $2929$
2. $5151$
5.119

$2 3 2 3$

5.120

$9 22 9 22$

5.121

$37 8 37 8$

5.122

$102 19 102 19$

5.123

$8 3 8 3$

5.124

$2 9 2 9$

5.125

$123 miles 2 hours 123 miles 2 hours$

5.126

$121 miles 3 hours 121 miles 3 hours$

5.127

$18.00/hour 5.128$19.00/hour

5.129

23.5 mpg

5.130

28 mpg

5.131

$0.29/box 5.132$0.53/bottle

5.133

Brand A costs $0.12 per bag. Brand B costs$0.13 per bag. Brand A is the better buy.

5.134

Brand C costs $0.07 per ounce. Brand D costs$0.09 per ounce. Brand C is the better buy.

5.135
1. 689 mi/h hours
2. y parents/22 students
3. $d/9 min 5.136 1. m mi/9 h 2. x students/8 buses 3.$y/40 h
5.137
1. 6
2. 13
5.138
1. 4
2. 14
5.139
1. −2
2. −15
5.140
1. −9
2. −8
5.141
1. not a real number
2. −9
5.142
1. −7
2. not a real number
5.143
1. 7
2. 5
5.144
1. 17
2. 23
5.145

$6 < 38 < 7 6 < 38 < 7$

5.146

$9 < 84 < 10 9 < 84 < 10$

5.147

≈ 3.32

5.148

≈ 3.61

5.151

8x

5.152

13y

5.153

−11y

5.154

−10p

5.155

10ab

5.156

15mn

5.157

19.2 feet

5.158

52 centimeters

5.159

9 seconds

5.160

3.5 seconds

5.161

42.7 mph

5.162

54.1 mph

## Section 5.1 Exercises

1.

five and five tenths

3.

five and one hundredth

5.

eight and seventy-one hundredths

7.

two thousandths

9.

three hundred eighty-one thousandths

11.

negative seventeen and nine tenths

13.

8.03

15.

29.81

17.

0.7

19.

0.001

21.

0.029

23.

−11.0009

25.

13.0395

27.

$1 99 100 1 99 100$

29.

$15 7 10 15 7 10$

31.

$239 1000 239 1000$

33.

$13 100 13 100$

35.

$11 1000 11 1000$

37.

$− 7 100000 − 7 100000$

39.

$6 2 5 6 2 5$

41.

$7 1 20 7 1 20$

43.

$4 3 500 4 3 500$

45.

$10 1 4 10 1 4$

47.

$1 81 250 1 81 250$

49.

$14 1 8 14 1 8$

51.

53.

55.

57.

59.

>

61.

<

63.

>

65.

>

67.

<

69.

<

71.

0.7

73.

2.8

75.

0.85

77.

5.79

79.

0.30

81.

4.10

83.
1. 5.78
2. 5.8
3. 6
85.
1. 63.48
2. 63.5
3. 63
87.
1. $58,966 2.$59,000
3. $60,000 89. 1.$142.19
2. $142 91. Answers will vary. 93. Tim had the faster time. 12.3 is less than 12.32, so Tim had the faster time. ## Section 5.2 Exercises 95. 24.48 97. 170.88 99. −9.23 101. 49.73 103. −40.91 105. −7.22 107. −13.5 109. 35.8 111. −27.5 113. 15.73 115. 42.51 117. 102.212 119. 51.31 121. −4.89 123. 0.12 125. 0.144 127. 42.008 129. 26.7528 131. −11.653 133. 337.8914 135. 2.2302 137. 1.305 139. 92.4 141. 55,200 143. 0.03 145. 0.19 147.$0.71

149.

$2.44 151. 3 153. −4.8 155. 35 157. 2.08 159. 150 161. 20 163. 19.2 165. 12.09 167. 32.706 169.$48.60

171.

20

173.

2

175.

$17.80 177.$24.89

179.

$29.06 181.$3.19

183.

181.7 pounds

185.

$15.00 187.$296.00

189.

$12.75 191. 1.$3
2. $2 3.$1.50
4. $1.20 5.$1
193.

$18.64 195.$259.45

197.
1. $243.57 2.$79.35
199.

The difference: 0.03 seconds. Three hundredths of a second.

## Section 5.3 Exercises

201.

0.4

203.

−0.375

205.

0.85

207.

2.75

209.

−12.4

211.

$0 . 5 – 0 . 5 –$

213.

$1 . 36 — 1 . 36 —$

215.

$0 . 135 — 0 . 135 —$

217.

7

219.

3.025

221.

10.58

223.

<

225.

>

227.

<

229.

<

231.

>

233.

>

235.

$0.55 , 9 16 , 3 5 0.55 , 9 16 , 3 5$

237.

$5 8 , 13 20 , 0.702 5 8 , 13 20 , 0.702$

239.

$− 7 20 , − 1 3 , − 0.3 − 7 20 , − 1 3 , − 0.3$

241.

$− 7 9 , − 3 4 , −0.7 − 7 9 , − 3 4 , −0.7$

243.

−187

245.

295.12

247.

6.15

249.

20.2

251.

107.11

253.

449

255.

9.14

257.

−0.23

259.

−3.25

261.

16.29

263.

632.045

265.

−5.742

267.
1. 31.4 in
2. 78.5 sq.in.
269.
1. 56.52.ft.
2. 254.34 sq.ft.
271.
1. 288.88 cm
2. 6644.24 sq.cm
273.
1. 116.808 m
2. 1086.3144 sq.m
275.
1. $22 5 mile 22 5 mile$
2. $77 50 sq.mile 77 50 sq.mile$
277.
1. $33 14 yard 33 14 yard$
2. $99 224 sq.yard 99 224 sq.yard$
279.
1. $55 21 m 55 21 m$
2. $275 504 sq.m 275 504 sq.m$
281.

355.

## Section 5.5 Exercises

357.

4

359.

35

361.

245.5

363.

11.65

365.

$18.84 367. 19.5 minutes 369. 0.329 371. 21 373. 45 375. 4.5 377. 99.65 379.$6.50

381.

40.5 months

383.

2

385.

22

387.

2 children

389.

11 units

391.

$1 20 , 0.05 1 20 , 0.05$

393.

$1 24 , 0.041 6 – ≈ 0.042 1 24 , 0.041 6 – ≈ 0.042$

395.

$4 10 , 0.4 4 10 , 0.4$

397.

$10 14 , 0 . 714285 ——— ≈ 0.714 10 14 , 0 . 714285 ——— ≈ 0.714$

399.
1. $285.47 2.$275.63
3. $236.25 401. Answers will vary. ## Section 5.6 Exercises 403. $5 9 5 9$ 405. $7 8 7 8$ 407. $7 3 7 3$ 409. $7 3 7 3$ 411. $1 5 1 5$ 413. $10 17 10 17$ 415. $5 4 5 4$ 417. $2 7 2 7$ 419. $11 4 11 4$ 421. $1 3 1 3$ 423. $6 23 6 23$ 425. $82 15 82 15$ 427. $35 9 35 9$ 429. $9 4 9 4$ 431. $35 calories 3 ounces 35 calories 3 ounces$ 433. $41 lbs 15 sq. in . 41 lbs 15 sq. in .$ 435. $488 miles 7 hours 488 miles 7 hours$ 437. $119 8 hours 119 8 hours$ 439. 11.67 calories/ounce 441. 2.73 lbs./sq. in. 443. 69.71 mph 445.$14.88/hour

447.

32 mpg

449.

2.69 lbs./week

451.

92 beats/minute

453.

8,000

455.

$1.09/bar 457.$1.33/pair

459.

$0.48/pack 461.$0.60/disc

463.

$1.29/box 465. The 50.7-ounce size costs$0.138 per ounce. The 33.8-ounce size costs $0.142 per ounce. The 50.7-ounce size is the better buy. 467. The 18-ounce size costs$0.222 per ounce. The 14-ounce size costs $0.235 per ounce. The 18-ounce size is a better buy. 469. The regular bottle costs$0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy. 471. The half-pound block costs$6.78/lb, so the 1-lb. block is a better buy.

473.

$793 miles p hours 793 miles p hours$

475.

$3 0.5 lbs . 3 0.5 lbs .$

477.

$105 calories x ounces 105 calories x ounces$

479.

$y 5 x y 5 x$

481.

15.2 students per teacher

483.
1. 72 calories/ounce
2. 3.87 grams of fat/ounce
3. 5.73 grams carbs/once
4. 3.33 grams protein/ounce
485.

487.

## Section 5.7 Exercises

489.

6

491.

8

493.

−2

495.

−1

497.

not a real number

499.

not a real number

501.

5

503.

7

505.

$8 < 70 < 9 8 < 70 < 9$

507.

$14 < 200 < 15 14 < 200 < 15$

509.

4.36

511.

7.28

513.

y

515.

7x

517.

−8a

519.

12xy

521.

8.7 feet

523.

8 seconds

525.

15.8 seconds

527.

72 mph

529.

53.0 mph

531.

45 inches

533.

Answers will vary. 92 reads: “nine squared” and means nine times itself. The expression $99$ reads: “the square root of nine” which gives us the number such that if it were multiplied by itself would give you the number inside of the square root.

## Review Exercises

535.

three hundred seventy-five thousandths

537.

five and twenty-four hundredths

539.

negative four and nine hundredths

541.

0.09

543.

10.035

545.

−0.05

547.

$33 40 33 40$

549.

$3 16 25 3 16 25$

551.

<

553.

<

555.
1. 12.53
2. 12.5
3. 13
557.
1. 5.90
2. 5.9
3. 6
559.

24.67

561.

24.831

563.

−2.37

565.

−1.6

567.

15,400

569.

0.18

571.

4

573.

200

575.

$28.22 577.$1.79

579.

0.875

581.

−5.25

583.

$0 . 54 — 0 . 54 —$

585.

>

587.

>

589.

>

591.

$11 15 , 0.75 , 7 9 11 15 , 0.75 , 7 9$

593.

6.03

595.

1.975

597.

−0.22

599.
1. 21.98 ft.
2. 38.465 sq.ft.
601.
1. 34.54 cm
2. 379.94 sq.cm
603.
1. no
2. yes
605.
1. no
2. yes
607.

h = −3.51

609.

p = 2.65

611.

j = 3.72

613.

x = −4

615.

a = −7.2

617.

s = 25

619.

−5.9x = −3.54; x = 0.6

621.

m + (−4.03) = 6.8; m = 0.83

623.

$269.10 625.$40.94

627.

24.5

629.

16 clients

631.

2

633.

$1 5 ; 0.2 1 5 ; 0.2$

635.

$7 4 7 4$

637.

$2 3 2 3$

639.

$4 9 4 9$

641.

$7 9 7 9$

643.

$90 pounds 7.5 square inches 90 pounds 7.5 square inches$

645.

$612.50 35 hours 612.50 35 hours$

647.

12 pounds/sq.in.

649.

$17.50/hour 651.$0.42

653.

$1.65 655.$0.11, $0.12; 60 tablets for$6.49

657.

$a adults 45 children a adults 45 children$

659.

$19 3 + n 19 3 + n$

661.

12

663.

−9

665.

not a real number

667.

17

669.

$12 < 155 < 13 12 < 155 < 13$

671.

7.55

673.

8b

675.

15mn

677.

7y

679.

11cd

681.

5.5 feet

683.

72 mph

## Practice Test

685.

$1 73 100 1 73 100$

687.
1. 16.7
2. 16.75
3. 17
689.

18.42

691.

0.192

693.

−0.08

695.

2

697.

200

699.

1.975

701.

−1.2

703.

8.8

705.

$26.45 707. 1. 59 2. 51.5 3. 55 709. 64 ounces for$10.99 is the better buy

711.

12n

713.

15 feet

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