Chapter 5

Four million, nine hundred twenty-six thousand, fifteen

$750$

$\frac{7}{10}$

$\frac{27}{100}$

$4$

$0.03$

$>$

$<$

$\frac{5}{12}$

$20$

$-294$

$5$

$50$

$2.5$

$\frac{2}{3}$

$0.24$

$\frac{6}{11}$

$81$

$3.85$

$960$

13.68

5.894

0.058

0.067

>

>

1.05

9.17

17.6

33.11

16.49

23.593

0.42

12.58

−1.53

−3.58

27.4815

87.6148

−13.427

−38.122

0.00348

0.00603

0.07

0.08

$0.19

$0.42

−0.39

−0.4

587.3

34.25

200

350

$16.52

$65.97

$41.28

$48.75

$15.47

$14.25

$5.97

$43.00

0.25

0.375

−2.25

−5.5

$2.\stackrel{\text{—}}{45}$

$2.3\stackrel{\text{—}}{18}$

5.275

6.35

>

<

<

>

$\frac{4}{5},0.82,\frac{7}{8}$

$\frac{3}{4},\frac{13}{16},0.835$

11.16

1.51

y = −8

y = −8.4

a = 1.07

n = 0.83

b = −12

c = −8

c = 11.7

b = 6.48

y − 4.9 = 2.8; y = 7.7

z − 5.7 = 3.4; z = 9.1

−4.3x = 12.04; x = −2.8

−3.1m = 26.66; m = −8.6

$\frac{q}{\mathrm{-3.4}}=4.5;q=\mathrm{-15.3}$

$\frac{r}{\mathrm{-2.6}}=2.5;r=\mathrm{-6.5}$

j + 3.8 = 2.6; j = −1.2

k + 4.7 = 0.3; k = −4.4

8.5

9

21.5 years

10

$7.19

$39.62

43

30

8.5

20.5

2

5

21

5

$\frac{2}{3}$

$\frac{9}{22}$

$\frac{37}{8}$

$\frac{102}{19}$

$\frac{8}{3}$

$\frac{2}{9}$

$\frac{\text{123 miles}}{\text{2 hours}}$

$\frac{\text{121 miles}}{\text{3 hours}}$

$18.00/hour

$19.00/hour

23.5 mpg

28 mpg

$0.29/box

$0.53/bottle

Brand A costs $0.11 per bag. Brand B costs $0.13 per bag. Brand A is the better buy.

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

$6<\sqrt{38}<7$

$9<\sqrt{84}<10$

≈ 3.32

≈ 3.61

y

m

8x

13y

−11y

−10p

10ab

15mn

19.2 feet

52 centimeters

9 seconds

3.5 seconds

42.7 mph

54.1 mph

five and five tenths

five and one hundredth

eight and seventy-one hundredths

two thousandths

three hundred eighty-one thousandths

negative seventeen and nine tenths

8.03

29.81

0.7

0.001

0.029

−11.0009

13.0395

$1\frac{99}{100}$

$15\frac{7}{10}$

$\frac{239}{1000}$

$\frac{13}{100}$

$\frac{11}{1000}$

$-\frac{7}{100000}$

$6\frac{2}{5}$

$7\frac{1}{20}$

$4\frac{3}{500}$

$10\frac{1}{4}$

$1\frac{81}{250}$

$14\frac{1}{8}$

>

<

>

>

<

<

0.7

2.8

0.85

5.79

0.30

4.10

Answers will vary.

Tim had the faster time. 12.3 is less than 12.32, so Tim had the faster time.

24.48

170.88

−9.23

49.73

−40.91

−7.22

−13.5

35.8

−27.5

15.73

42.51

102.212

51.31

−4.89

0.12

0.144

42.008

26.7528

−11.653

337.8914

2.2302

1.305

92.4

55,200

0.03

0.19

$0.71

$2.44

3

−4.8

35

2.08

150

20

19.2

12.09

32.706

$48.60

20

2

$17.80

$24.89

$29.06

$3.19

181.7 pounds

$15.00

$296.00

$12.75

$18.64

$259.45

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

0.4

−0.375

0.85

2.75

−12.4

$0.\bar{5}$

$1.\stackrel{\text{—}}{36}$

$0.\stackrel{\text{—}}{135}$

7

3.025

10.58

<

>

<

<

>

>

$0.55,\frac{9}{16},\frac{3}{5}$

$\frac{5}{8},\frac{13}{20},0.702$

$-\frac{7}{20},-\frac{1}{3},-0.3$

$-\frac{7}{9},-\frac{3}{4},\mathrm{-0.7}$

−187

295.12

6.15

20.2

107.11

449

9.14

−0.23

−3.25

16.29

632.045

−5.742

$56.66

Answers will vary.

y = 2.8

f = −0.85

a = −7.9

c = −4.65

n = 4.4

x = −3.5

j = −4.68

m = −1.42

x = 7

c = −5

p = 3

q = −80

x = 20

z = 2.7

a = −8

x = −0.28

p = 8.25

r = 7.2

x = −6

p = −10

m = 8

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

$m=\frac{4}{35}$

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

$f=-\frac{11}{20}$

a = −0.8

r = −1.45

h = 24

$n-1.9=3.4;5.3$

−6.2x = −4.96; 0.8

$\frac{y}{-1.7}=\mathrm{-5};8.5$

n + (−7.3) = 2.4; 9.7

$104

Answers will vary.

4

35

245.5

11.65

$18.84

19.5 minutes

0.329

21

45

4.5

99.65

$6.50

40.5 months

2

22

2 children

11 units

$\frac{1}{20},0.05$

$\frac{1}{24},0.041\bar{6}\approx 0.042$

$\frac{2}{5},0.4$

$\frac{5}{7},0.\stackrel{\text{———}}{714285}\approx 0.714$

Answers will vary.

$\frac{5}{9}$

$\frac{7}{8}$

$\frac{7}{3}$

$\frac{7}{3}$

$\frac{1}{5}$

$\frac{10}{17}$

$\frac{5}{4}$

$\frac{2}{7}$

$\frac{11}{4}$

$\frac{1}{3}$

$\frac{6}{23}$

$\frac{82}{15}$

$\frac{35}{9}$

$\frac{9}{4}$

$\frac{\text{35 calories}}{\text{3 ounces}}$

$\frac{\text{41 lbs}}{\text{15 sq. in}.}$

$\frac{\text{488 miles}}{\text{7 hours}}$

$\frac{\text{\$119}}{\text{8 hours}}$

11.67 calories/ounce

2.73 lbs./sq. in.

69.71 mph

$14.88/hour

32 mpg

2.69 lbs./week

92 beats/minute

8,000

$1.09/bar

$1.33/pair

$0.48/pack

$0.60/disc

$1.29/box

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.

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.

The regular bottle costs $0.075 per ounce. The squeeze bottle costs $0.069 per ounce. The squeeze bottle is a better buy.

The half-pound block costs $6.78/lb, so the 1-lb. block is a better buy.

$\frac{\text{793 miles}}{p\text{hours}}$

$\frac{\text{\$3}}{\text{0.5 lbs}.}$

$\frac{\text{105 calories}}{x\text{ounces}}$

$\frac{y}{5x}$

15.2 students per teacher

Answers will vary.

Kathryn should swim for approximately 16.35 minutes. Explanations will vary.

6

8

−2

−1

not a real number

not a real number

5

7

$8<\sqrt{70}<9$

$14<\sqrt{200}<15$

4.36

7.28

y

7x

−8a

12xy

8.7 feet

8 seconds

15.8 seconds

72 mph

53.0 mph

45 inches

Answers will vary. 9² reads: “nine squared” and means nine times itself. The expression $\sqrt{9}$ 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.

three hundred seventy-five thousandths

five and twenty-four hundredths

negative four and nine hundredths

0.09

10.035

−0.05

$\frac{33}{40}$

$3\frac{16}{25}$

<

<

24.67

24.831

−2.37

−1.6

15,400

0.18

4

200

$28.22

$1.79

0.875

−5.25

$0.\stackrel{\text{—}}{54}$

>

>

>

$\frac{11}{15},0.75,\frac{7}{9}$

6.03

1.975

−0.22

h = −3.51

p = 2.65

j = 3.72

x = −4

a = −7.2

s = 25

−5.9x = −3.54; x = 0.6

m + (−4.03) = 6.8; m = 10.83

$269.10

$40.94

24.5

16 clients

2

$\frac{1}{5};0.2$

$\frac{7}{4}$

$\frac{2}{3}$

$\frac{4}{9}$

$\frac{7}{9}$

$\frac{12\text{pounds}}{1\text{square inch}}$

$\frac{\text{\$35}}{2\text{hours}}$

12 pounds/sq.in.

$17.50/hour

$0.42

$1.65

$0.11, $0.12; 60 tablets for $6.49

$\frac{a\text{adults}}{45\text{children}}$

$\frac{19}{3+n}$

12

−9

not a real number

17

$12<\sqrt{155}<13$

7.55

8b

15mn

7y

11cd

5.5 feet

72 mph

$1\frac{73}{100}$

18.42

0.192

−0.08

2

200

1.975

−1.2

8.8

$26.45

The unit prices are $0.172 per ounce for 64 ounces, and $0.177 per ounce for 48 ounces; 64 ounces is the better buy.

12n

15 feet