Content check — Prealgebra, Chapter 5: Decimals

Every problem in the chapter beside the book’s answer, a chapter at a time as you scroll.

Chapter 5: Decimals

540 problems · 9 figures

Be Prepared 5.1 §5.1 source ↗

Name the number

4,926,015

in words.
If you missed this problem, review Example 1.4.

Example 1.4 in the book ↗

Answer

Four million, nine hundred twenty-six thousand, fifteen

Be Prepared 5.2 §5.1 source ↗

Round

748

to the nearest ten.
If you missed this problem, review Example 1.9.

Example 1.9 in the book ↗

Answer

750

Be Prepared 5.3 §5.1 source ↗

Locate

\frac{3}{10}

on a number line.
If you missed this problem, review Example 4.16.

Example 4.16 in the book ↗

Answer

Try It 5.1 §5.1 source ↗

Name each decimal:

ⓐ $6.7$ ⓑ $19.58$ ⓒ $0.018$ ⓓ $−2.053$

Answer

ⓐ six and seven tenths

ⓑ nineteen and fifty-eight hundredths

ⓓ negative two and fifty-three thousandths

Try It 5.2 §5.1 source ↗

Name each decimal:

ⓐ $5.8$ ⓑ $3.57$ ⓒ $0.005$ ⓓ $−13.461$

Answer

ⓐ five and eight tenths

ⓑ three and fifty-seven hundredths

ⓓ negative thirteen and four hundred sixty-one thousandths

Try It 5.3 §5.1 source ↗

Write as a decimal: thirteen and sixty-eight hundredths.

Answer

13.68

Try It 5.4 §5.1 source ↗

Write as a decimal: five and eight hundred ninety-four thousandths.

Answer

5.894

Try It 5.5 §5.1 source ↗

Write as a decimal: fifty-eight thousandths.

Answer

0.058

Try It 5.6 §5.1 source ↗

Write as a decimal: sixty-seven thousandths.

Answer

0.067

Try It 5.7 §5.1 source ↗

Write as a fraction or mixed number. Simplify the answer if possible.

ⓐ $5.3$ ⓑ $6.07$ ⓒ $−0.234$

Answer

ⓐ $5 \frac{3}{10}$

ⓑ $6 \frac{7}{100}$

Try It 5.8 §5.1 source ↗

Write as a fraction or mixed number. Simplify the answer if possible.

ⓐ $8.7$ ⓑ $1.03$ ⓒ $−0.024$

Answer

ⓐ $8 \frac{7}{10}$

ⓑ $1 \frac{3}{100}$

Try It 5.9 §5.1 source ↗

Locate

0.6

on a number line.

Answer

Try It 5.10 §5.1 source ↗

Locate

0.9

on a number line.

Answer

Try It 5.11 §5.1 source ↗

Locate

−0.63

on a number line.

Answer

Try It 5.12 §5.1 source ↗

Locate

−0.25

on a number line.

Answer

Try It 5.13 §5.1 source ↗

Order each of the following pairs of numbers, using $< or >:$

ⓐ $0.42__0.4$ ⓑ $0.76__0.706$

Answer

ⓐ >

ⓑ >

Try It 5.14 §5.1 source ↗

Order each of the following pairs of numbers, using $< or >:$

ⓐ $0.1__0.18$ ⓑ $0.305__0.35$

Answer

ⓐ <

ⓑ <

Try It 5.15 §5.1 source ↗

Order each of the following pairs of numbers, using $< or >:$

$−0.3___−0.5$

Answer

Try It 5.16 §5.1 source ↗

Order each of the following pairs of numbers, using $< or >:$

$−0.6___−0.7$

Answer

Try It 5.17 §5.1 source ↗

Round to the nearest hundredth:

1.047 .

Answer

1.05

Try It 5.18 §5.1 source ↗

Round to the nearest hundredth:

9.173 .

Answer

9.17

Try It 5.19 §5.1 source ↗

Round

6.582

to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

Answer

ⓐ 6.58

ⓑ 6.6

ⓒ 7

Try It 5.20 §5.1 source ↗

Round

15.2175

to the nearest ⓐ thousandth ⓑ hundredth ⓒ tenth.

Answer

ⓐ 15.218

ⓑ 15.22

5.1-1 §5.1 source ↗

Name Decimals

In the following exercises, name each decimal.

$5.5$

Answer

five and five tenths

5.1-3 §5.1 source ↗

Name Decimals

In the following exercises, name each decimal.

$5.01$

Answer

five and one hundredth

5.1-5 §5.1 source ↗

Name Decimals

In the following exercises, name each decimal.

$8.71$

Answer

eight and seventy-one hundredths

5.1-7 §5.1 source ↗

Name Decimals

In the following exercises, name each decimal.

$0.002$

Answer

two thousandths

5.1-9 §5.1 source ↗

Name Decimals

In the following exercises, name each decimal.

$0.381$

Answer

three hundred eighty-one thousandths

5.1-11 §5.1 source ↗

Name Decimals

In the following exercises, name each decimal.

$−17.9$

Answer

negative seventeen and nine tenths

5.1-13 §5.1 source ↗

Write Decimals

In the following exercises, translate the name into a decimal number.

Eight and three hundredths

Answer

8.03

5.1-15 §5.1 source ↗

Write Decimals

In the following exercises, translate the name into a decimal number.

Twenty-nine and eighty-one hundredths

Answer

29.81

5.1-17 §5.1 source ↗

Write Decimals

In the following exercises, translate the name into a decimal number.

Seven tenths

Answer

0.7

5.1-19 §5.1 source ↗

Write Decimals

In the following exercises, translate the name into a decimal number.

One thousandth

Answer

0.001

5.1-21 §5.1 source ↗

Write Decimals

In the following exercises, translate the name into a decimal number.

Twenty-nine thousandths

Answer

0.029

5.1-23 §5.1 source ↗

Write Decimals

In the following exercises, translate the name into a decimal number.

Negative eleven and nine ten-thousandths

Answer

−11.0009

5.1-25 §5.1 source ↗

Write Decimals

In the following exercises, translate the name into a decimal number.

Thirteen and three hundred ninety-five ten thousandths

Answer

13.0395

5.1-27 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$1.99$

Answer

1 \frac{99}{100}

5.1-29 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$15.7$

Answer

15 \frac{7}{10}

5.1-31 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$0.239$

Answer

\frac{239}{1000}

5.1-33 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$0.13$

Answer

\frac{13}{100}

5.1-35 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$0.011$

Answer

\frac{11}{1000}

5.1-37 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$−0.00007$

Answer

- \frac{7}{100000}

5.1-39 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$6.4$

Answer

6 \frac{2}{5}

5.1-41 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$7.05$

Answer

7 \frac{1}{20}

5.1-43 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$4.006$

Answer

4 \frac{3}{500}

5.1-45 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$10.25$

Answer

10 \frac{1}{4}

5.1-47 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$1.324$

Answer

1 \frac{81}{250}

5.1-49 §5.1 source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction or mixed number.

$14.125$

Answer

14 \frac{1}{8}

5.1-51 §5.1 source ↗

Locate Decimals on the Number Line

In the following exercises, locate each number on a number line.

$0.8$

Answer

5.1-53 §5.1 source ↗

Locate Decimals on the Number Line

In the following exercises, locate each number on a number line.

$−0.2$

Answer

5.1-55 §5.1 source ↗

Locate Decimals on the Number Line

In the following exercises, locate each number on a number line.

$3.1$

Answer

5.1-57 §5.1 source ↗

Locate Decimals on the Number Line

In the following exercises, locate each number on a number line.

$−2.5$

Answer

5.1-59 §5.1 source ↗

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $< or >.$

$0.9__0.6$

Answer

5.1-61 §5.1 source ↗

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $< or >.$

$0.37__0.63$

Answer

5.1-63 §5.1 source ↗

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $< or >.$

$0.6__0.59$

Answer

5.1-65 §5.1 source ↗

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $< or >.$

$0.91__0.901$

Answer

5.1-67 §5.1 source ↗

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $< or >.$

$−0.5__−0.3$

Answer

5.1-69 §5.1 source ↗

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $< or >.$

$−0.62_−0.619$

Answer

5.1-71 §5.1 source ↗

Round Decimals

In the following exercises, round each number to the nearest tenth.

$0.67$

Answer

0.7

5.1-73 §5.1 source ↗

Round Decimals

In the following exercises, round each number to the nearest tenth.

$2.84$

Answer

2.8

5.1-75 §5.1 source ↗

In the following exercises, round each number to the nearest hundredth.

$0.845$

Answer

0.85

5.1-77 §5.1 source ↗

In the following exercises, round each number to the nearest hundredth.

$5.7932$

Answer

5.79

5.1-79 §5.1 source ↗

In the following exercises, round each number to the nearest hundredth.

$0.299$

Answer

0.30

5.1-81 §5.1 source ↗

In the following exercises, round each number to the nearest hundredth.

$4.098$

Answer

4.10

5.1-83 §5.1 source ↗

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

$5.781$

Answer

ⓐ 5.78

ⓑ 5.8

ⓒ 6

5.1-85 §5.1 source ↗

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

$63.479$

Answer

ⓐ 63.48

ⓑ 63.5

5.1-87 §5.1 source ↗

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

Salary Increase Danny got a raise and now makes $$58,965.95$ a year. Round this number to the nearest:

ⓐ dollar

ⓑ thousand dollars

Answer

ⓐ $58,966

ⓑ $59,000

5.1-89 §5.1 source ↗

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

Sales Tax Hyo Jin lives in San Diego. She bought a refrigerator for $$1624.99$ and when the clerk calculated the sales tax it came out to exactly $$142.186625 .$ Round the sales tax to the nearest ⓐ penny ⓑ dollar.

Answer

ⓐ $142.19

ⓑ $142

5.1-91 §5.1 source ↗

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

How does your knowledge of money help you learn about decimals?

Answer

Answers will vary.

5.1-93 §5.1 source ↗

In the following exercises, round each number to the nearest ⓐ hundredth ⓑ tenth ⓒ whole number.

Jim ran a $100-meter$ race in $12.32 seconds .$ Tim ran the same race in $12.3 seconds .$ Who had the faster time, Jim or Tim? How do you know?

Answer

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

Be Prepared 5.4 §5.2 source ↗

Simplify

\frac{70}{100} .

If you missed this problem, review Example 4.19.

Example 4.19 in the book ↗

Answer

\frac{7}{10}

Be Prepared 5.5 §5.2 source ↗

Multiply

\frac{3}{10} \cdot \frac{9}{10} .

If you missed this problem, review Example 4.25.

Example 4.25 in the book ↗

Answer

\frac{27}{100}

Be Prepared 5.6 §5.2 source ↗

Divide

- 36 \div (−9) .

If you missed this problem, review Example 3.49.

Example 3.49 in the book ↗

Answer

4

Try It 5.21 §5.2 source ↗

Add:

5.7 + 11.9 .

Answer

17.6

Try It 5.22 §5.2 source ↗

Add:

18.32 +

14.79 .

Answer

33.11

Try It 5.23 §5.2 source ↗

Add:

4.8 + 11.69 .

Answer

16.49

Try It 5.24 §5.2 source ↗

Add:

5.123 +

18.47 .

Answer

23.593

Try It 5.25 §5.2 source ↗

Subtract:

$10 - 9.58 .$

Answer

0.42

Try It 5.26 §5.2 source ↗

Subtract:

$50 - 37.42 .$

Answer

12.58

Try It 5.27 §5.2 source ↗

Subtract:

4.77 - 6.3 .

Answer

−1.53

Try It 5.28 §5.2 source ↗

Subtract:

8.12 - 11.7 .

Answer

−3.58

Try It 5.29 §5.2 source ↗

Multiply:

4.5 (6.107).

Answer

27.4815

Try It 5.30 §5.2 source ↗

Multiply:

10.79 (8.12).

Answer

87.6148

Try It 5.31 §5.2 source ↗

Multiply:

(4.63) (−2.9) .

Answer

−13.427

Try It 5.32 §5.2 source ↗

Multiply:

(−7.78) (4.9) .

Answer

−38.122

Try It 5.33 §5.2 source ↗

Multiply:

(0.04) (0.087) .

Answer

0.00348

Try It 5.34 §5.2 source ↗

Multiply:

(0.09) (0.067) .

Answer

0.00603

Try It 5.35 §5.2 source ↗

Multiply

2.58

by factors of ⓐ

10

ⓑ

100

ⓒ

1000 .

Answer

ⓐ 25.8

ⓑ 258

Try It 5.36 §5.2 source ↗

Multiply

14.2

by factors of ⓐ

10

ⓑ

100

ⓒ

1000 .

Answer

ⓐ 142

ⓑ 1,420

Try It 5.37 §5.2 source ↗

Divide:

0.28 \div 4 .

Answer

0.07

Try It 5.38 §5.2 source ↗

Divide:

0.56 \div 7 .

Answer

0.08

Try It 5.39 §5.2 source ↗

Divide:

$6.99 \div 36 .

Answer

$0.19

Try It 5.40 §5.2 source ↗

Divide:

$4.99 \div 12 .

Answer

$0.42

Try It 5.41 §5.2 source ↗

Divide:

−1.989 \div 5.1 .

Answer

−0.39

Try It 5.42 §5.2 source ↗

Divide:

−2.04 \div 5.1 .

Answer

−0.4

Try It 5.43 §5.2 source ↗

Divide:

−23.492 \div (−0.04) .

Answer

587.3

Try It 5.44 §5.2 source ↗

Divide:

−4.11 \div (−0.12) .

Answer

34.25

Try It 5.45 §5.2 source ↗

Divide:

6 \div 0.03 .

Answer

200

Try It 5.46 §5.2 source ↗

Divide:

7 \div 0.02 .

Answer

350

Try It 5.47 §5.2 source ↗

Nicole earned

$35

for babysitting her cousins, then went to the bookstore and spent

$18.48

on books and coffee. How much of her babysitting money was left?

Answer

$16.52

Try It 5.48 §5.2 source ↗

Amber bought a pair of shoes for

$24.75

and a purse for

$36.90 .

The sales tax was

$4.32 .

How much did Amber spend?

Answer

$65.97

Try It 5.49 §5.2 source ↗

Hector put

13

gallons of gas into his car. One gallon of gas costs

$3.175 .

How much did Hector owe for the gas? Round to the nearest cent.

Answer

$41.28

Try It 5.50 §5.2 source ↗

Christopher bought

5

pizzas for the team. Each pizza cost

$9.75 .

How much did all the pizzas cost?

Answer

$48.75

Try It 5.51 §5.2 source ↗

Six friends went out for dinner. The total cost of their dinner was

$92.82 .

If they divide the bill equally, how much should each friend pay?

Answer

$15.47

Try It 5.52 §5.2 source ↗

Chad worked

40

hours last week and his paycheck was

$570 .

How much does he earn per hour?

Answer

$14.25

Try It 5.53 §5.2 source ↗

Suzanne buys

3

cans of beans that cost

$0.75

each and

6

cans of corn that cost

$0.62

each. How much is the total cost of these groceries?

Answer

$5.97

Try It 5.54 §5.2 source ↗

Lydia bought movie tickets for the family. She bought two adult tickets for

$9.50

each and four children’s tickets for

$6.00

each. How much did the tickets cost Lydia in all?

Answer

$43.00

5.2-95 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$16.92 + 7.56$

Answer

24.48

5.2-97 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$256.37 -$ $85.49$

Answer

170.88

5.2-99 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$21.76 - 30.99$

Answer

−9.23

5.2-101 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$37.5 + 12.23$

Answer

49.73

5.2-103 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$-$ $16.53 -$ $24.38$

Answer

−40.91

5.2-105 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$-$ $38.69 +$ $31.47$

Answer

−7.22

5.2-107 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$- 4.2 + (- 9.3)$

Answer

−13.5

5.2-109 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$100 - 64.2$

Answer

35.8

5.2-111 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$72.5 - 100$

Answer

−27.5

5.2-113 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$15 + 0.73$

Answer

15.73

5.2-115 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$2.51 + 40$

Answer

42.51

5.2-117 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$91.75 -$ $(- 10.462)$

Answer

102.212

5.2-119 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$55.01 - 3.7$

Answer

51.31

5.2-121 §5.2 source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$2.51 - 7.4$

Answer

−4.89

5.2-123 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(0.3) (0.4)$

Answer

0.12

5.2-125 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(0.24) (0.6)$

Answer

0.144

5.2-127 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(5.9) (7.12)$

Answer

42.008

5.2-129 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(8.52) (3.14)$

Answer

26.7528

5.2-131 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(−4.3)(2.71)$

Answer

−11.653

5.2-133 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(−5.18)(−65.23)$

Answer

337.8914

5.2-135 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(0.09) (24.78)$

Answer

2.2302

5.2-137 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(0.06) (21.75)$

Answer

1.305

5.2-139 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(9.24) (10)$

Answer

92.4

5.2-141 §5.2 source ↗

Multiply Decimals

In the following exercises, multiply.

$(55.2) (1,000)$

Answer

55,200

5.2-143 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$0.15 \div 5$

Answer

0.03

5.2-145 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$4.75 \div 25$

Answer

0.19

5.2-147 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$$8.49 \div 12$

Answer

$0.71

5.2-149 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$$117.25 \div 48$

Answer

$2.44

5.2-151 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$0.6 \div 0.2$

Answer

5.2-153 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$1.44 \div (- 0.3)$

Answer

−4.8

5.2-155 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$-$ $1.75 \div (- 0.05)$

Answer

5.2-157 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$5.2 \div 2.5$

Answer

2.08

5.2-159 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$12 \div 0.08$

Answer

150

5.2-161 §5.2 source ↗

Divide Decimals

In the following exercises, divide.

$11 \div 0.55$

Answer

5.2-163 §5.2 source ↗

Mixed Practice

In the following exercises, simplify.

$6 (12.4 - 9.2)$

Answer

19.2

5.2-165 §5.2 source ↗

Mixed Practice

In the following exercises, simplify.

$24 (0.5) +$ ${(0.3)}^{2}$

Answer

12.09

5.2-167 §5.2 source ↗

Mixed Practice

In the following exercises, simplify.

$1.15 (26.83 + 1.61)$

Answer

32.706

5.2-169 §5.2 source ↗

Mixed Practice

In the following exercises, simplify.

$$45 +$ $0.08 ($45)$

Answer

$48.60

5.2-171 §5.2 source ↗

Mixed Practice

In the following exercises, simplify.

$18 \div (0.75 + 0.15)$

Answer

5.2-173 §5.2 source ↗

Mixed Practice

In the following exercises, simplify.

$(1.43 + 0.27) \div (0.9 - 0.05)$

Answer

5.2-175 §5.2 source ↗

Mixed Practice

In the following exercises, simplify.

$[$75.42 + 0.18 ($75.42)] \div 5$

Answer

$17.80

5.2-177 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Spending money Brenda got $$40$ from the ATM. She spent $$15.11$ on a pair of earrings. How much money did she have left?

Answer

$24.89

5.2-179 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Shopping Adam bought a t-shirt for $$18.49$ and a book for $$8.92$ The sales tax was $$1.65 .$ How much did Adam spend?

Answer

$29.06

5.2-181 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Coupon Emily bought a box of cereal that cost $$4.29 .$ She had a coupon for $$0.55$ off, and the store doubled the coupon. How much did she pay for the box of cereal?

Answer

$3.19

5.2-183 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Diet Leo took part in a diet program. He weighed $190$ pounds at the start of the program. During the first week, he lost $4.3$ pounds. During the second week, he had lost $2.8$ pounds. The third week, he gained $0.7$ pounds. The fourth week, he lost $1.9$ pounds. What did Leo weigh at the end of the fourth week?

Answer

181.7 pounds

5.2-185 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Coffee Noriko bought $4$ coffees for herself and her co-workers. Each coffee was $$3.75 .$ How much did she pay for all the coffees?

Answer

$15.00

5.2-187 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Income Mayra earns $$9.25$ per hour. Last week she worked $32$ hours. How much did she earn?

Answer

$296.00

5.2-189 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Hourly Wage Alan got his first paycheck from his new job. He worked $30$ hours and earned $$382.50 .$ How much does he earn per hour?

Answer

$12.75

5.2-191 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Restaurant Jeannette and her friends love to order mud pie at their favorite restaurant. They always share just one piece of pie among themselves. With tax and tip, the total cost is $$6.00 .$ How much does each girl pay if the total number sharing the mud pie is

ⓐ $2 ?$

ⓑ $3 ?$

ⓓ $5 ?$

ⓔ $6 ?$

Answer

ⓐ $3

ⓑ $2

ⓓ $1.20

ⓔ $1

5.2-193 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Fast Food At their favorite fast food restaurant, the Carlson family orders $4$ burgers that cost $$3.29$ each and $2$ orders of fries at $$2.74$ each. What is the total cost of the order?

Answer

$18.64

5.2-195 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Zoo The Lewis and Chousmith families are planning to go to the zoo together. Adult tickets cost $$29.95$ and children’s tickets cost $$19.95 .$ What will the total cost be for $4$ adults and $7$ children?

Answer

$259.45

5.2-197 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Paycheck Annie has two jobs. She gets paid $$14.04$ per hour for tutoring at City College and $$8.75$ per hour at a coffee shop. Last week she tutored for $8$ hours and worked at the coffee shop for $15$ hours.

ⓐ How much did she earn?

ⓑ If she had worked all $23$ hours as a tutor instead of working both jobs, how much more would she have earned?

Answer

ⓐ $243.57

ⓑ $79.35

5.2-199 §5.2 source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

At the 2010 winter Olympics, two skiers took the silver and bronze medals in the Men's Super-G ski event. Miller's time was $1$ minute $30.62$ seconds and Weibrecht's time was $1$ minute $30.65$ seconds. Find the difference in their times and then write the name of that decimal.

Answer

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

Be Prepared 5.7 §5.3 source ↗

Divide:

0.24 \div 8 .

If you missed this problem, review Example 5.19.

Example 5.19 in the book ↗

Answer

0.03

Be Prepared 5.8 §5.3 source ↗

Order

0.64__0.6

using

<

>.

If you missed this problem, review Example 5.7.

Example 5.7 in the book ↗

Answer

>

Be Prepared 5.9 §5.3 source ↗

Order

−0.2__−0.1

using

<

>.

If you missed this problem, review Example 5.8.

Example 5.8 in the book ↗

Answer

<

Try It 5.55 §5.3 source ↗

Write the fraction as a decimal:

\frac{1}{4} .

Answer

0.25

Try It 5.56 §5.3 source ↗

Write the fraction as a decimal:

\frac{3}{8} .

Answer

0.375

Try It 5.57 §5.3 source ↗

Write the fraction as a decimal:

- \frac{9}{4} .

Answer

−2.25

Try It 5.58 §5.3 source ↗

Write the fraction as a decimal:

- \frac{11}{2} .

Answer

−5.5

Try It 5.59 §5.3 source ↗

Write as a decimal:

\frac{27}{11} .

Answer

2 . \overset{—}{45}

Try It 5.60 §5.3 source ↗

Write as a decimal:

\frac{51}{22} .

Answer

2.3 \overset{—}{18}

Try It 5.61 §5.3 source ↗

Simplify:

\frac{3}{8} + 4.9 .

Answer

5.275

Try It 5.62 §5.3 source ↗

Simplify:

5.7 + \frac{13}{20} .

Answer

6.35

Try It 5.63 §5.3 source ↗

Order each of the following pairs of numbers, using $<$ or $>.$

$\frac{17}{20}__0.82$

Answer

Try It 5.64 §5.3 source ↗

Order each of the following pairs of numbers, using $<$ or $>.$

$\frac{3}{4}__0.785$

Answer

Try It 5.65 §5.3 source ↗

Order each of the following pairs of numbers, using $<$ or $>:$

$- \frac{5}{8}__−0.58$

Answer

Try It 5.66 §5.3 source ↗

Order each of the following pairs of numbers, using $<$ or $>:$

$−0.53__-$ $\frac{11}{20}$

Answer

Try It 5.67 §5.3 source ↗

Write each set of numbers in order from smallest to largest:

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

Answer

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

Try It 5.68 §5.3 source ↗

Write each set of numbers in order from smallest to largest:

0.835,

\frac{13}{16},

\frac{3}{4} .

Answer

\frac{3}{4},

\frac{13}{16},

0.835

Try It 5.69 §5.3 source ↗

Simplify: ⓐ

8 (14.6 - 37.5)

ⓑ

\frac{3}{5} (9.6 - 2.1) .

Answer

ⓐ −183.2

ⓑ 4.5

Try It 5.70 §5.3 source ↗

Simplify: ⓐ

25 (25.69 - 56.74)

ⓑ

\frac{2}{7} (11.9 - 4.2) .

Answer

ⓐ −776.25

ⓑ 2.2

Try It 5.71 §5.3 source ↗

Simplify:

9 \div 0.9 +

(0.4) 3 -

{(0.2)}^{2} .

Answer

11.16

Try It 5.72 §5.3 source ↗

Simplify:

{(\frac{1}{2})}^{2} +

(0.3) (4.2) .

Answer

1.51

Try It 5.73 §5.3 source ↗

A circle has radius

50

inches. Approximate its ⓐ circumference and ⓑ area.

Answer

ⓐ 314 in.

ⓑ 7850 sq. in.

Try It 5.74 §5.3 source ↗

A circle has radius

100

feet. Approximate its ⓐ circumference and ⓑ area.

Answer

ⓐ 628 ft.

ⓑ 31,400 sq. ft.

Try It 5.75 §5.3 source ↗

A circle has radius

51.8

centimeters. Approximate its ⓐ circumference and ⓑ area.

Answer

ⓐ 325.304 cm

ⓑ 8425.3736 sq. cm

Try It 5.76 §5.3 source ↗

A circle has radius

26.4

meters. Approximate its ⓐ circumference and ⓑ area.

Answer

ⓐ 165.792 m

ⓑ 2188.4544 sq. m

Try It 5.77 §5.3 source ↗

A circle has radius

\frac{5}{21}

meters. Approximate its ⓐ circumference and ⓑ area.

Answer

ⓐ $\frac{220}{147} m$

ⓑ $\frac{550}{3087} sq. m$

Try It 5.78 §5.3 source ↗

A circle has radius

\frac{10}{33}

inches. Approximate its ⓐ circumference and ⓑ area.

Answer

ⓐ $\frac{40}{21} in.$

ⓑ $\frac{200}{693} sq.in.$

5.3-201 §5.3 source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{2}{5}$

Answer

0.4

5.3-203 §5.3 source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$- \frac{3}{8}$

Answer

−0.375

5.3-205 §5.3 source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{17}{20}$

Answer

0.85

5.3-207 §5.3 source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{11}{4}$

Answer

2.75

5.3-209 §5.3 source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$- \frac{310}{25}$

Answer

−12.4

5.3-211 §5.3 source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{5}{9}$

Answer

0 . \bar{5}

5.3-213 §5.3 source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{15}{11}$

Answer

1 . \overset{—}{36}

5.3-215 §5.3 source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{15}{111}$

Answer

0 . \overset{—}{135}

5.3-217 §5.3 source ↗

In the following exercises, simplify the expression.

$\frac{1}{2} + 6.5$

Answer

5.3-219 §5.3 source ↗

In the following exercises, simplify the expression.

$2.4 + \frac{5}{8}$

Answer

3.025

5.3-221 §5.3 source ↗

In the following exercises, simplify the expression.

$9.73 + \frac{17}{20}$

Answer

10.58

5.3-223 §5.3 source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$\frac{1}{8}___0.8$

Answer

5.3-225 §5.3 source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$\frac{2}{5}___0.25$

Answer

5.3-227 §5.3 source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$0.725___\frac{3}{4}$

Answer

5.3-229 §5.3 source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$0.66___\frac{2}{3}$

Answer

5.3-231 §5.3 source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$−0.75___- \frac{4}{5}$

Answer

5.3-233 §5.3 source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$-$ $\frac{3}{4}___−0.925$

Answer

5.3-235 §5.3 source ↗

In the following exercises, write each set of numbers in order from least to greatest.

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

Answer

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

5.3-237 §5.3 source ↗

In the following exercises, write each set of numbers in order from least to greatest.

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

Answer

\frac{5}{8},

\frac{13}{20},

0.702

5.3-239 §5.3 source ↗

In the following exercises, write each set of numbers in order from least to greatest.

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

Answer

-

\frac{7}{20},

-

\frac{1}{3},

-

0.3

5.3-241 §5.3 source ↗

In the following exercises, write each set of numbers in order from least to greatest.

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

Answer

-

\frac{7}{9},

-

\frac{3}{4},

−0.7

5.3-243 §5.3 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$10 (25.1 - 43.8)$

Answer

−187

5.3-245 §5.3 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$62 (9.75 - 4.99)$

Answer

295.12

5.3-247 §5.3 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$\frac{3}{4} (12.4 - 4.2)$

Answer

6.15

5.3-249 §5.3 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$\frac{5}{12} (30.58 + 17.9)$

Answer

20.2

5.3-251 §5.3 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$10 \div 0.1 +$ $(1.8) 4 -$ ${(0.3)}^{2}$

Answer

107.11

5.3-253 §5.3 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$(37.1 + 52.7) \div (12.5 \div 62.5)$

Answer

449

5.3-255 §5.3 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

${(\frac{1}{5})}^{2} +$ $(1.4) (6.5)$

Answer

9.14

5.3-257 §5.3 source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify.

$-$ $\frac{9}{10} \cdot \frac{8}{15} +$ $0.25$

Answer

−0.23

5.3-259 §5.3 source ↗

Mixed Practice

In the following exercises, simplify. Give the answer as a decimal.

$3 \frac{1}{4} - 6.5$

Answer

−3.25

5.3-261 §5.3 source ↗

Mixed Practice

In the following exercises, simplify. Give the answer as a decimal.

$10.86 \div \frac{2}{3}$

Answer

16.29

5.3-263 §5.3 source ↗

Mixed Practice

In the following exercises, simplify. Give the answer as a decimal.

$\frac{7}{8} (103.48) +$ $1 \frac{1}{2} (361)$

Answer

632.045

5.3-265 §5.3 source ↗

Mixed Practice

In the following exercises, simplify. Give the answer as a decimal.

$3.6 (\frac{9}{8} - 2.72)$

Answer

−5.742

5.3-267 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

$radius = 5 in.$

Answer

ⓐ 31.4 in

ⓑ 78.5 sq.in.

5.3-269 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

$radius = 9 ft.$

Answer

ⓐ 56.52.ft.

ⓑ 254.34 sq.ft.

5.3-271 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

$radius = 46 cm$

Answer

ⓐ 288.88 cm

ⓑ 6644.24 sq.cm

5.3-273 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

$radius =$ $18.6 m$

Answer

ⓐ 116.808 m

ⓑ 1086.3144 sq.m

5.3-275 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

$radius =$ $\frac{7}{10} mile$

Answer

ⓐ $\frac{22}{5} mile$

ⓑ $\frac{77}{50} sq.mile$

5.3-277 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

$radius =$ $\frac{3}{8} yard$

Answer

ⓐ $\frac{33}{14} yard$

ⓑ $\frac{99}{224} sq.yard$

5.3-279 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

$diameter =$ $\frac{5}{6} m$

Answer

ⓐ $\frac{55}{21} m$

ⓑ $\frac{275}{504} sq.m$

5.3-281 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

Kelly wants to buy a pair of boots that are on sale for $\frac{2}{3}$ of the original price. The original price of the boots is $$84.99 .$ What is the sale price of the shoes?

Answer

$56.66

5.3-283 §5.3 source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle. If measurements are given in fractions, leave answers in fraction form.

Is it easier for you to convert a decimal to a fraction or a fraction to a decimal? Explain.

Answer

Answers will vary.

Be Prepared 5.10 §5.4 source ↗

Evaluate

x +

\frac{2}{3} when x =

-

\frac{1}{4} .

If you missed this problem, review Example 4.77.

Example 4.77 in the book ↗

Answer

\frac{5}{12}

Be Prepared 5.11 §5.4 source ↗

Evaluate

15 - y

when

y = −5 .

If you missed this problem, review Example 3.41.

Example 3.41 in the book ↗

Answer

20

Be Prepared 5.12 §5.4 source ↗

Solve

\frac{n}{- 7} = 42 .

If you missed this problem, review Example 4.99.

Example 4.99 in the book ↗

Answer

- 294

Try It 5.79 §5.4 source ↗

Determine whether each value is a solution of the given equation.

$x - 0.6 = 1.3 :$ ⓐ $x = 0.7$ ⓑ $x = 1.9$ ⓒ $x = −0.7$

Answer

ⓐ no

ⓑ yes

Try It 5.80 §5.4 source ↗

Determine whether each value is a solution of the given equation.

$y - 0.4 = 1.7 :$ ⓐ $y = 2.1$ ⓑ $y = 1.3$ ⓒ $−1.3$

Answer

ⓐ yes

ⓑ no

Try It 5.81 §5.4 source ↗

Solve:

y + 2.7 = −5.3 .

Answer

y = −8

Try It 5.82 §5.4 source ↗

Solve:

y + 3.6 = −4.8 .

Answer

y = −8.4

Try It 5.83 §5.4 source ↗

Solve:

a -

3.93 =

−2.86 .

Answer

a = 1.07

Try It 5.84 §5.4 source ↗

Solve:

n -

3.47 =

−2.64 .

Answer

n = 0.83

Try It 5.85 §5.4 source ↗

Solve:

−8.4 = 0.7 b .

Answer

b = −12

Try It 5.86 §5.4 source ↗

Solve:

−5.6 = 0.7 c .

Answer

c = −8

Try It 5.87 §5.4 source ↗

Solve:

\frac{c}{−2.6} = −4.5 .

Answer

c = 11.7

Try It 5.88 §5.4 source ↗

Solve:

\frac{b}{−1.2} = −5.4 .

Answer

b = 6.48

Try It 5.89 §5.4 source ↗

Translate and solve: The difference of

y

and

4.9

2.8 .

Answer

y − 4.9 = 2.8; y = 7.7

Try It 5.90 §5.4 source ↗

Translate and solve: The difference of

z

and

5.7

3.4 .

Answer

z − 5.7 = 3.4; z = 9.1

Try It 5.91 §5.4 source ↗

Translate and solve: The product of

−4.3

and

x

12.04 .

Answer

−4.3x = 12.04; x = −2.8

Try It 5.92 §5.4 source ↗

Translate and solve: The product of

−3.1

and

m

26.66 .

Answer

−3.1m = 26.66; m = −8.6

Try It 5.93 §5.4 source ↗

Translate and solve: The quotient of

q

and

−3.4

4.5 .

Answer

\frac{q}{−3.4} =

4.5;

q =

−15.3

Try It 5.94 §5.4 source ↗

Translate and solve: The quotient of

r

and

−2.6

2.5 .

Answer

\frac{r}{−2.6} =

2.5;

r =

−6.5

Try It 5.95 §5.4 source ↗

Translate and solve: The sum of

j

and

3.8

2.6 .

Answer

j + 3.8 = 2.6; j = −1.2

Try It 5.96 §5.4 source ↗

Translate and solve: The sum of

k

and

4.7

0.3 .

Answer

k + 4.7 = 0.3; k = −4.4

5.4-285 §5.4 source ↗

Determine Whether a Decimal is a Solution of an Equation

In the following exercises, determine whether each number is a solution of the given equation.

$x - 0.8 = 2.3$
ⓐ $x = 2$ ⓑ $x = −1.5$ ⓒ $x = 3.1$

Answer

ⓐ no

ⓑ no

5.4-287 §5.4 source ↗

Determine Whether a Decimal is a Solution of an Equation

In the following exercises, determine whether each number is a solution of the given equation.

$\frac{h}{1.5} = −4.3$
ⓐ $h = 6.45$ ⓑ $h = −6.45$ ⓒ $h = −2.1$

Answer

ⓐ no

ⓑ yes

5.4-289 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$y + 2.9 = 5.7$

Answer

y = 2.8

5.4-291 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$f + 3.45 = 2.6$

Answer

f = −0.85

5.4-293 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$a + 6.2 = −1.7$

Answer

a = −7.9

5.4-295 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$c + 1.15 = −3.5$

Answer

c = −4.65

5.4-297 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$n - 2.6 = 1.8$

Answer

n = 4.4

5.4-299 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$x - 0.4 = −3.9$

Answer

x = −3.5

5.4-301 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$j - 1.82 = −6.5$

Answer

j = −4.68

5.4-303 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$m -$ $0.25 =$ $−1.67$

Answer

m = −1.42

5.4-305 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$0.5 x = 3.5$

Answer

x = 7

5.4-307 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$−1.7 c = 8.5$

Answer

c = −5

5.4-309 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$−1.4 p = −4.2$

Answer

p = 3

5.4-311 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$−120 = 1.5 q$

Answer

q = −80

5.4-313 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$0.24 x = 4.8$

Answer

x = 20

5.4-315 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$−3.4 z = −9.18$

Answer

z = 2.7

5.4-317 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$\frac{a}{0.4} = −20$

Answer

a = −8

5.4-319 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$\frac{x}{0.7} = −0.4$

Answer

x = −0.28

5.4-321 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$\frac{p}{- 5} = −1.65$

Answer

p = 8.25

5.4-323 §5.4 source ↗

Solve Equations with Decimals

In the following exercises, solve the equation.

$\frac{r}{- 1.2} = −6$

Answer

r = 7.2

5.4-325 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$x - 5 = −11$

Answer

x = −6

5.4-327 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$p + 8 = −2$

Answer

p = −10

5.4-329 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$−4.2 m = −33.6$

Answer

m = 8

5.4-331 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$q + \frac{5}{6} = \frac{1}{12}$

Answer

q = - \frac{3}{4}

5.4-333 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$\frac{7}{8} m = \frac{1}{10}$

Answer

m = \frac{4}{35}

5.4-335 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$- \frac{2}{3} = y + \frac{3}{8}$

Answer

y = - \frac{25}{24}

5.4-337 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

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

Answer

f = - \frac{11}{20}

5.4-339 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$−4.2 a = 3.36$

Answer

a = −0.8

5.4-341 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$r - 1.25 = −2.7$

Answer

r = −1.45

5.4-343 §5.4 source ↗

Mixed Practice

In the following exercises, solve the equation. Then check your solution.

$\frac{h}{- 3} = −8$

Answer

h = 24

5.4-345 §5.4 source ↗

Translate to an Equation and Solve

In the following exercises, translate and solve.

The difference of $n$ and $1.9$ is $3.4 .$

Answer

n -

1.9 =

3.4;

5.3

5.4-347 §5.4 source ↗

Translate to an Equation and Solve

In the following exercises, translate and solve.

The product of $−6.2$ and $x$ is $−4.96 .$

Answer

−6.2x = −4.96; 0.8

5.4-349 §5.4 source ↗

Translate to an Equation and Solve

In the following exercises, translate and solve.

The quotient of $y$ and $−1.7$ is $−5 .$

Answer

\frac{y}{- 1.7} =

−5;

8.5

5.4-351 §5.4 source ↗

Translate to an Equation and Solve

In the following exercises, translate and solve.

The sum of $n$ and $−7.3$ is $2.4.$

Answer

n + (−7.3) = 2.4; 9.7

5.4-353 §5.4 source ↗

Translate to an Equation and Solve

In the following exercises, translate and solve.

Shawn bought a pair of shoes on sale for $$78$ . Solve the equation $0.75 p = 78$ to find the original price of the shoes, $p .$

Answer

$104

5.4-355 §5.4 source ↗

Translate to an Equation and Solve

In the following exercises, translate and solve.

Think about solving the equation $1.2 y = 60,$ but do not actually solve it. Do you think the solution should be greater than $60$ or less than $60 ?$ Explain your reasoning. Then solve the equation to see if your thinking was correct.

Answer

Answers will vary.

Be Prepared 5.13 §5.5 source ↗

Simplify:

\frac{4 + 9 + 2}{3} .

If you missed this problem, review Example 4.48.

Example 4.48 in the book ↗

Answer

5

Be Prepared 5.14 §5.5 source ↗

Simplify:

4 (8) + 6 (3) .

If you missed this problem, review Example 2.8.

Example 2.8 in the book ↗

Answer

50

Be Prepared 5.15 §5.5 source ↗

Convert

\frac{5}{2}

to a decimal.
If you missed this problem, review Example 5.28.

Example 5.28 in the book ↗

Answer

2.5

Try It 5.97 §5.5 source ↗

Find the mean of the numbers:

8,

9,

7,

12,

10,

5 .

Answer

8.5

Try It 5.98 §5.5 source ↗

Find the mean of the numbers:

9,

13,

11,

7,

5 .

Answer

Try It 5.99 §5.5 source ↗

The ages of the four students in Ben’s carpool are

25,

18,

21,

and 22 .

Find the mean age of the students.

Answer

21.5 years

Try It 5.100 §5.5 source ↗

Yen counted the number of emails she received last week. The numbers were

4,

9,

15,

12,

10,

12,

and 8 .

Find the mean number of emails.

Answer

Try It 5.101 §5.5 source ↗

Last week Ray recorded how much he spent for lunch each workday. He spent

$6.50,

$7.25,

$4.90,

$5.30,

and $12.00 .

Find the mean of how much he spent each day.

Answer

$7.19

Try It 5.102 §5.5 source ↗

Lisa has kept the receipts from the past four trips to the gas station. The receipts show the following amounts:

$34.87,

$42.31,

$38.04,

and $43.26 .

Find the mean.

Answer

$39.62

Try It 5.103 §5.5 source ↗

Find the median of the data set:

43,

38,

51,

40,

46 .

Answer

Try It 5.104 §5.5 source ↗

Find the median of the data set:

15,

35,

20,

45,

50,

25,

30 .

Answer

Try It 5.105 §5.5 source ↗

Find the median of the data set:

8,

7,

5,

10,

9,

12 .

Answer

8.5

Try It 5.106 §5.5 source ↗

Find the median of the data set:

21,

25,

19,

17,

22,

18,

20,

24 .

Answer

20.5

Try It 5.107 §5.5 source ↗

The number of sick days employees used last year:

3,

6,

2,

3,

7,

5,

6,

2,

4,

2 .

Identify the mode.

Answer

Try It 5.108 §5.5 source ↗

The number of handbags owned by women in a book club:

5,

6,

3,

1,

5,

8,

1,

5,

8,

5 .

Identify the mode.

Answer

Try It 5.109 §5.5 source ↗

The ages of the students in a statistics class are listed here:

19

20

23

23

38

21

19

21

19

21

20

43

20

23

17

21

21

20

29

18

28

. What is the mode?

Answer

Try It 5.110 §5.5 source ↗

Students listed the number of members in their household as follows:

6

2

5

6

3

7

5

6

5

3

4

4

5

7

6

4

5

2

1

5

. What is the mode?

Answer

Try It 5.111 §5.5 source ↗

Ignaly is attending a fashion show where the guests are seated at tables of ten. One guest from each table will be selected at random to receive a door prize. ⓐ Find the probability Ignaly will win the door prize for her table. ⓑ Convert the fraction to a decimal.

Answer

ⓐ $\frac{1}{10}$

ⓑ $0.1$

Try It 5.112 §5.5 source ↗

Hoang is among

20

people available to sit on a jury. One person will be chosen at random from the

20 .

ⓐ Find the probability Hoang will be chosen. ⓑ Convert the fraction to a decimal.

Answer

ⓐ $\frac{1}{20}$

ⓑ $0.05$

Try It 5.113 §5.5 source ↗

A bowl of Halloween candy contains

5

chocolate candies and

3

lemon candies. Tanya will choose one piece of candy at random. ⓐ Find the probability Tanya will choose a chocolate candy. ⓑ Convert the fraction to a decimal.

Answer

ⓐ $\frac{5}{8}$

ⓑ $0.625$

Try It 5.114 §5.5 source ↗

Dan has

2

pairs of black socks and

6

pairs of blue socks. He will choose one pair at random to wear tomorrow. ⓐ Find the probability Dan will choose a pair of black socks ⓑ Convert the fraction to a decimal.

Answer

ⓐ $\frac{2}{8}$

ⓑ $0.25$

5.5-357 §5.5 source ↗

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

$3$ , $8$ , $2$ , $2$ , $5$

Answer

5.5-359 §5.5 source ↗

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

$65$ , $13$ , $48$ , $32$ , $19$ , $33$

Answer

5.5-361 §5.5 source ↗

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

$202$ , $241$ , $265$ , $274$

Answer

245.5

5.5-363 §5.5 source ↗

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

$12.45$ , $12.99$ , $10.50$ , $11.25$ , $9.99$ , $12.72$

Answer

11.65

5.5-365 §5.5 source ↗

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

Four girls leaving a mall were asked how much money they had just spent. The amounts were $$0$ , $$14.95$ , $$35.25$ , and $$25.16$ . Find the mean amount of money spent.

Answer

$18.84

5.5-367 §5.5 source ↗

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

The number of minutes it took Jim to ride his bike to school for each of the past six days was $21$ , $18$ , $16$ , $19$ , $24$ , and $19$ . Find the mean number of minutes.

Answer

19.5 minutes

5.5-369 §5.5 source ↗

Calculate the Mean of a Set of Numbers

In the following exercises, find the mean.

The top eight hitters in a softball league have batting averages of $.373$ , $.360$ , $.321$ , $.321$ , $.320$ , $.312$ , $.311$ , and $.311$ . Find the mean of the batting averages. Round your answer to the nearest thousandth.

Answer

0.329

5.5-371 §5.5 source ↗

Find the Median of a Set of Numbers

In the following exercises, find the median.

$24$ , $19$ , $18$ , $29$ , $21$

Answer

5.5-373 §5.5 source ↗

Find the Median of a Set of Numbers

In the following exercises, find the median.

$65$ , $56$ , $35$ , $34$ , $44$ , $39$ , $55$ , $52$ , $45$

Answer

5.5-375 §5.5 source ↗

Find the Median of a Set of Numbers

In the following exercises, find the median.

$4$ , $8$ , $1$ , $5$ , $14$ , $3$ , $1$ , $12$

Answer

4.5

5.5-377 §5.5 source ↗

Find the Median of a Set of Numbers

In the following exercises, find the median.

$99.2$ , $101.9$ , $98.6$ , $99.5$ , $100.8$ , $99.8$

Answer

99.65

5.5-379 §5.5 source ↗

Find the Median of a Set of Numbers

In the following exercises, find the median.

Last week Ray recorded how much he spent for lunch each workday. He spent $$6.50$ , $$7.25$ , $$4.90$ , $$5.30$ , and $$12.00$ . Find the median.

Answer

$6.50

5.5-381 §5.5 source ↗

Find the Median of a Set of Numbers

In the following exercises, find the median.

Brian is teaching a swim class for $6$ three-year olds. Their ages, in months, are $38,$ $41,$ $45,$ $36,$ $40,$ $and 42 .$ Find the median age.

Answer

40.5 months

5.5-383 §5.5 source ↗

Identify the Mode of a Set of Numbers

In the following exercises, identify the mode.

$2$ , $5$ , $1$ , $5$ , $2$ , $1$ , $2$ , $3$ , $2$ , $3$ , $1$

Answer

5.5-385 §5.5 source ↗

Identify the Mode of a Set of Numbers

In the following exercises, identify the mode.

$18$ , $22$ , $17$ , $20$ , $19$ , $20$ , $22$ , $19$ , $29$ , $18$ , $23$ , $25$ , $22$ , $24$ , $23$ , $22$ , $18$ , $20$ , $22$ , $20$

Answer

5.5-387 §5.5 source ↗

Identify the Mode of a Set of Numbers

In the following exercises, identify the mode.

The number of children per house on one block: $1$ , $4$ , $2$ , $3$ , $3$ , $2$ , $6$ , $2$ , $4$ , $2$ , $0$ , $3$ , $0 .$

Answer

2 children

5.5-389 §5.5 source ↗

Identify the Mode of a Set of Numbers

In the following exercises, identify the mode.

The number of units being taken by students in one class: $12$ , $5$ , $11$ , $10$ , $10$ , $11$ , $5$ , $11$ , $11$ , $11$ , $10$ , $12$ .

Answer

11 units

5.5-391 §5.5 source ↗

Use the Basic Definition of Probability

In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Josue is in a book club with $20$ members. One member is chosen at random each month to select the next month’s book. Find the probability that Josue will be chosen next month.

Answer

\frac{1}{20}, 0.05

5.5-393 §5.5 source ↗

Use the Basic Definition of Probability

In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

There are $24$ people who work in Dane’s department. Next week, one person will be selected at random to bring in doughnuts. Find the probability that Dane will be selected. Round your answer to the nearest thousandth.

Answer

\frac{1}{24},

0.041 \bar{6} \approx

0.042

5.5-395 §5.5 source ↗

Use the Basic Definition of Probability

In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Michel has four rock CDs and six country CDs in his car. He will pick one CD to play on his way to work. Find the probability Michel will pick a rock CD.

Answer

\frac{2}{5}, 0.4

5.5-397 §5.5 source ↗

Use the Basic Definition of Probability

In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Donovan is considering transferring to a $4-year college .$ He is considering $10$ out-of state colleges and $4$ colleges in his state. He will choose one college at random to visit during spring break. Find the probability that Donovan will choose an out-of-state college.

Answer

\frac{5}{7},

0 . \overset{———}{714285} \approx

0.714

5.5-399 §5.5 source ↗

Use the Basic Definition of Probability

In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Joaquin gets paid every Friday. His paychecks for the past $8$ Fridays were $$315,$ $$236.25,$ $$236.25,$ $$236.25,$ $$315,$ $$315,$ $$236.25,$ $$393.75 .$ Find the ⓐ mean, ⓑ median, and ⓒ mode.

Answer

ⓐ $285.47

ⓑ $275.63

5.5-401 §5.5 source ↗

Use the Basic Definition of Probability

In the following exercises, express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Explain in your own words the difference between the mean, median, and mode of a set of numbers.

Answer

Answers will vary.

Be Prepared 5.16 §5.6 source ↗

Simplify:

\frac{16}{24} .

If you missed this problem, review Example 4.19.

Example 4.19 in the book ↗

Answer

\frac{2}{3}

Be Prepared 5.17 §5.6 source ↗

Divide:

2.76 \div 11.5 .

If you missed this problem, review Example 5.19.

Example 5.19 in the book ↗

Answer

0.24

Be Prepared 5.18 §5.6 source ↗

Simplify:

\frac{1 \frac{1}{2}}{2 \frac{3}{4}} .

If you missed this problem, review Example 4.43.

Example 4.43 in the book ↗

Answer

\frac{6}{11}

Try It 5.115 §5.6 source ↗

Write each ratio as a fraction: ⓐ

21 to 56

ⓑ

48 to 32 .

Answer

ⓐ $\frac{3}{8}$

ⓑ $\frac{3}{2}$

Try It 5.116 §5.6 source ↗

Write each ratio as a fraction: ⓐ

27 to 72

ⓑ

51 to 34 .

Answer

ⓐ $\frac{3}{8}$

ⓑ $\frac{3}{2}$

Try It 5.117 §5.6 source ↗

Write each ratio as a fraction: ⓐ

4.6 to 11.5

ⓑ

2.3 to 0.69 .

Answer

ⓐ $\frac{2}{5}$

ⓑ $\frac{10}{3}$

Try It 5.118 §5.6 source ↗

Write each ratio as a fraction: ⓐ

3.4 to 15.3

ⓑ

3.4 to 0.68 .

Answer

ⓐ $\frac{2}{9}$

ⓑ $\frac{5}{1}$

Try It 5.119 §5.6 source ↗

Write each ratio as a fraction:

1 \frac{3}{4} to 2 \frac{5}{8} .

Answer

\frac{2}{3}

Try It 5.120 §5.6 source ↗

Write each ratio as a fraction:

1 \frac{1}{8} to 2 \frac{3}{4} .

Answer

\frac{9}{22}

Try It 5.121 §5.6 source ↗

Find the patient's ratio of total cholesterol to HDL cholesterol using the given information.

Total cholesterol is $185$ mg/dL and HDL cholesterol is $40$ mg/dL.

Answer

\frac{37}{8}

Try It 5.122 §5.6 source ↗

Find the patient’s ratio of total cholesterol to HDL cholesterol using the given information.

Total cholesterol is $204$ mg/dL and HDL cholesterol is $38$ mg/dL.

Answer

\frac{102}{19}

Try It 5.123 §5.6 source ↗

Find the ratio of the first length to the second length:

32

inches to

1

foot.

Answer

\frac{8}{3}

Try It 5.124 §5.6 source ↗

Find the ratio of the first length to the second length:

1

foot to

54

inches.

Answer

\frac{2}{9}

Try It 5.125 §5.6 source ↗

Write the rate as a fraction:

492

miles in

8

hours.

Answer

\frac{123 miles}{2 hours}

Try It 5.126 §5.6 source ↗

Write the rate as a fraction:

242

miles in

6

hours.

Answer

\frac{121 miles}{3 hours}

Try It 5.127 §5.6 source ↗

Find the unit rate:

$630

for

35

hours.

Answer

$18.00/hour

Try It 5.128 §5.6 source ↗

Find the unit rate:

$684

for

36

hours.

Answer

$19.00/hour

Try It 5.129 §5.6 source ↗

Find the unit rate:

423

miles to

18

gallons of gas.

Answer

23.5 mpg

Try It 5.130 §5.6 source ↗

Find the unit rate:

406

miles to

14.5

gallons of gas.

Answer

28 mpg

Try It 5.131 §5.6 source ↗

Find the unit price. Round your answer to the nearest cent if necessary.

$24-pack$ of juice boxes for $$6.99$

Answer

$0.29/box

Try It 5.132 §5.6 source ↗

Find the unit price. Round your answer to the nearest cent if necessary.

$24-pack$ of bottles of ice tea for $$12.72$

Answer

$0.53/bottle

Try It 5.133 §5.6 source ↗

Find each unit price and then determine the better buy. Round to the nearest cent if necessary.

Brand A Storage Bags, $$4.59$ for $40$ count, or Brand B Storage Bags, $$3.99$ for $30$ count

Answer

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

Try It 5.134 §5.6 source ↗

Find each unit price and then determine the better buy. Round to the nearest cent if necessary.

Brand C Chicken Noodle Soup, $$1.89$ for $26$ ounces, or Brand D Chicken Noodle Soup, $$0.95$ for $10.75$ ounces

Answer

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

Try It 5.135 §5.6 source ↗

Translate the word phrase into an algebraic expression.

ⓐ $689$ miles per $h$ hours ⓑ $y$ parents to $22$ students ⓒ $d$ dollars for $9$ minutes

Answer

ⓐ 689 mi/h hours

ⓑ y parents/22 students

Try It 5.136 §5.6 source ↗

Translate the word phrase into an algebraic expression.

ⓐ $m$ miles per $9$ hours ⓑ $x$ students to $8$ buses ⓒ $y$ dollars for $40$ hours

Answer

ⓐ m mi/9 h

ⓑ x students/8 buses

5.6-403 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$20$ to $36$

Answer

\frac{5}{9}

5.6-405 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$42$ to $48$

Answer

\frac{7}{8}

5.6-407 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$49$ to $21$

Answer

\frac{7}{3}

5.6-409 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$84$ to $36$

Answer

\frac{7}{3}

5.6-411 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$0.56$ to $2.8$

Answer

\frac{1}{5}

5.6-413 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$1 \frac{2}{3}$ to $2 \frac{5}{6}$

Answer

\frac{10}{17}

5.6-415 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$4 \frac{1}{6}$ to $3 \frac{1}{3}$

Answer

\frac{5}{4}

5.6-417 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$$18$ to $$63$

Answer

\frac{2}{7}

5.6-419 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$$1.21$ to $$0.44$

Answer

\frac{11}{4}

5.6-421 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$28$ ounces to $84$ ounces

Answer

\frac{1}{3}

5.6-423 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$12$ feet to $46$ feet

Answer

\frac{6}{23}

5.6-425 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$246$ milligrams to $45$ milligrams

Answer

\frac{82}{15}

5.6-427 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

total cholesterol of $175$ to HDL cholesterol of $45$

Answer

\frac{35}{9}

5.6-429 §5.6 source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction.

$27$ inches to $1$ foot

Answer

\frac{9}{4}

5.6-431 §5.6 source ↗

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.

$140$ calories per $12$ ounces

Answer

\frac{35 calories}{3 ounces}

5.6-433 §5.6 source ↗

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.

$8.2$ pounds per $3$ square inches

Answer

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

5.6-435 §5.6 source ↗

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.

$488$ miles in $7$ hours

Answer

\frac{488 miles}{7 hours}

5.6-437 §5.6 source ↗

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction.

$$595$ for $40$ hours

Answer

\frac{$119}{8 hours}

5.6-439 §5.6 source ↗

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

$140$ calories per $12$ ounces

Answer

11.67 calories/ounce

5.6-441 §5.6 source ↗

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

$8.2$ pounds per $3$ square inches

Answer

2.73 lbs./sq. in.

5.6-443 §5.6 source ↗

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

$488$ miles in $7$ hours

Answer

69.71 mph

5.6-445 §5.6 source ↗

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

$$595$ for $40$ hours

Answer

$14.88/hour

5.6-447 §5.6 source ↗

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

$576$ miles on $18$ gallons of gas

Answer

32 mpg

5.6-449 §5.6 source ↗

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

$43$ pounds in $16$ weeks

Answer

2.69 lbs./week

5.6-451 §5.6 source ↗

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

$46$ beats in $0.5$ minute

Answer

92 beats/minute

5.6-453 §5.6 source ↗

Find Unit Rates

In the following exercises, find the unit rate. Round to two decimal places, if necessary.

The bindery at a printing plant assembles $96,000$ magazines in $12$ hours. How many magazines are assembled in one hour?

Answer

8,000

5.6-455 §5.6 source ↗

Find Unit Price

In the following exercises, find the unit price. Round to the nearest cent.

Soap bars at $8$ for $$8.69$

Answer

$1.09/bar

5.6-457 §5.6 source ↗

Find Unit Price

In the following exercises, find the unit price. Round to the nearest cent.

Women’s sports socks at $6$ pairs for $$7.99$

Answer

$1.33/pair

5.6-459 §5.6 source ↗

Find Unit Price

In the following exercises, find the unit price. Round to the nearest cent.

Snack packs of cookies at $12$ for $$5.79$

Answer

$0.48/pack

5.6-461 §5.6 source ↗

Find Unit Price

In the following exercises, find the unit price. Round to the nearest cent.

CD-RW discs at $25$ for $$14.99$

Answer

$0.60/disc

5.6-463 §5.6 source ↗

Find Unit Price

In the following exercises, find the unit price. Round to the nearest cent.

The grocery store has a special on macaroni and cheese. The price is $$3.87$ for $3$ boxes. How much does each box cost?

Answer

$1.29/box

5.6-465 §5.6 source ↗

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

Mouthwash, $50.7-ounce$ size for $$6.99$ or $33.8-ounce$ size for $$4.79$

Answer

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.

5.6-467 §5.6 source ↗

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

Breakfast cereal, $18$ ounces for $$3.99$ or $14$ ounces for $$3.29$

Answer

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.

5.6-469 §5.6 source ↗

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

Ketchup, $40-ounce$ regular bottle for $$2.99$ or $64-ounce$ squeeze bottle for $$4.39$

Answer

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

5.6-471 §5.6 source ↗

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places.

Cheese $$6.49$ for $1$ lb. block or $$3.39$ for $\frac{1}{2}$ lb. block

Answer

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

5.6-473 §5.6 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

$793$ miles per $p$ hours

Answer

\frac{793 miles}{p hours}

5.6-475 §5.6 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

$$3$ for $0.5$ lbs.

Answer

\frac{$3}{0.5 lbs .}

5.6-477 §5.6 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

$105$ calories in $x$ ounces

Answer

\frac{105 calories}{x ounces}

5.6-479 §5.6 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

the ratio of $y$ and $5 x$

Answer

\frac{y}{5 x}

5.6-481 §5.6 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

One elementary school in Ohio has $684$ students and $45$ teachers. Write the student-to-teacher ratio as a unit rate.

Answer

15.2 students per teacher

5.6-483 §5.6 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

A popular fast food burger weighs $7.5$ ounces and contains $540$ calories, $29$ grams of fat, $43$ grams of carbohydrates, and $25$ grams of protein. Find the unit rate of ⓐ calories per ounce ⓑ grams of fat per ounce ⓒ grams of carbohydrates per ounce ⓓ grams of protein per ounce. Round to two decimal places.

Answer

ⓐ 72 calories/ounce

ⓑ 3.87 grams of fat/ounce

ⓓ 3.33 grams protein/ounce

5.6-485 §5.6 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

Would you prefer the ratio of your income to your friend’s income to be $3/1$ or $1/3 ?$ Explain your reasoning.

Answer

Answers will vary.

5.6-487 §5.6 source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

Kathryn ate a $4-ounce$ cup of frozen yogurt and then went for a swim. The frozen yogurt had $115$ calories. Swimming burns $422$ calories per hour. For how many minutes should Kathryn swim to burn off the calories in the frozen yogurt? Explain your reasoning.

Answer

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

Be Prepared 5.19 §5.7 source ↗

Simplify:

{(−9)}^{2} .

If you missed this problem, review Example 3.52.

Example 3.52 in the book ↗

Answer

81

Be Prepared 5.20 §5.7 source ↗

Round

3.846

to the nearest hundredth.
If you missed this problem, review Example 5.9.

Example 5.9 in the book ↗

Answer

3.85

Be Prepared 5.21 §5.7 source ↗

Evaluate

12 d

for

d = 80 .

If you missed this problem, review Example 2.14.

Example 2.14 in the book ↗

Answer

960

Try It 5.137 §5.7 source ↗

Simplify: ⓐ

\sqrt{36}

ⓑ

\sqrt{169} .

Answer

ⓐ 6

ⓑ 13

Try It 5.138 §5.7 source ↗

Simplify: ⓐ

\sqrt{16}

ⓑ

\sqrt{196} .

Answer

ⓐ 4

ⓑ 14

Try It 5.139 §5.7 source ↗

Simplify: ⓐ

- \sqrt{4}

ⓑ

- \sqrt{225} .

Answer

ⓐ −2

ⓑ −15

Try It 5.140 §5.7 source ↗

Simplify: ⓐ

- \sqrt{81}

ⓑ

- \sqrt{64} .

Answer

ⓐ −9

ⓑ −8

Try It 5.141 §5.7 source ↗

Simplify: ⓐ

\sqrt{−196}

ⓑ

- \sqrt{81} .

Answer

ⓐ not a real number

ⓑ −9

Try It 5.142 §5.7 source ↗

Simplify: ⓐ

\sqrt{−49}

ⓑ

- \sqrt{121} .

Answer

ⓐ not a real number

ⓑ −11

Try It 5.143 §5.7 source ↗

Simplify: ⓐ

\sqrt{9} + \sqrt{16}

ⓑ

\sqrt{9 + 16} .

Answer

ⓐ 7

ⓑ 5

Try It 5.144 §5.7 source ↗

Simplify: ⓐ

\sqrt{64 + 225}

ⓑ

\sqrt{64} + \sqrt{225} .

Answer

ⓐ 17

ⓑ 23

Try It 5.145 §5.7 source ↗

Estimate

\sqrt{38}

between two consecutive whole numbers.

Answer

6 <

\sqrt{38} <

7

Try It 5.146 §5.7 source ↗

Estimate

\sqrt{84}

between two consecutive whole numbers.

Answer

9 <

\sqrt{84} <

10

Try It 5.147 §5.7 source ↗

Round

\sqrt{11}

to two decimal places.

Answer

≈ 3.32

Try It 5.148 §5.7 source ↗

Round

\sqrt{13}

to two decimal places.

Answer

≈ 3.61

Try It 5.149 §5.7 source ↗

Simplify:

\sqrt{y^{2}} .

Answer

Try It 5.150 §5.7 source ↗

Simplify:

\sqrt{m^{2}} .

Answer

Try It 5.151 §5.7 source ↗

Simplify:

\sqrt{64 x^{2}} .

Answer

Try It 5.152 §5.7 source ↗

Simplify:

\sqrt{169 y^{2}} .

Answer

13y

Try It 5.153 §5.7 source ↗

Simplify:

- \sqrt{121 y^{2}} .

Answer

−11y

Try It 5.154 §5.7 source ↗

Simplify:

- \sqrt{100 p^{2}} .

Answer

−10p

Try It 5.155 §5.7 source ↗

Simplify:

\sqrt{100 a^{2} b^{2}} .

Answer

10ab

Try It 5.156 §5.7 source ↗

Simplify:

\sqrt{225 m^{2} n^{2}} .

Answer

15mn

Try It 5.157 §5.7 source ↗

Katie wants to plant a square lawn in her front yard. She has enough sod to cover an area of

370

square feet. To the nearest tenth of a foot, how long can a side of her square lawn be?

Answer

19.2 feet

Try It 5.158 §5.7 source ↗

Sergio wants to make a square mosaic as an inlay for a table he is building. He has enough tile to cover an area of

2704

square centimeters. How long can a side of his mosaic be?

Answer

52 centimeters

Try It 5.159 §5.7 source ↗

A helicopter drops a rescue package from a height of

1296

feet. How many seconds does it take for the package to reach the ground?

Answer

9 seconds

Try It 5.160 §5.7 source ↗

A window washer drops a squeegee from a platform

196

feet above the sidewalk. How many seconds does it take for the squeegee to reach the sidewalk?

Answer

3.5 seconds

Try It 5.161 §5.7 source ↗

An accident investigator measured the skid marks of a car and found their length was

76

feet. To the nearest tenth, what was the speed of the car before the brakes were applied?

Answer

42.7 mph

Try It 5.162 §5.7 source ↗

The skid marks of a vehicle involved in an accident were

122

feet long. To the nearest tenth, how fast had the vehicle been going before the brakes were applied?

Answer

54.1 mph

5.7-489 §5.7 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{36}$

Answer

5.7-491 §5.7 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{64}$

Answer

5.7-493 §5.7 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$- \sqrt{4}$

Answer

−2

5.7-495 §5.7 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$- \sqrt{1}$

Answer

−1

5.7-497 §5.7 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{−121}$

Answer

not a real number

5.7-499 §5.7 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{−9}$

Answer

not a real number

5.7-501 §5.7 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{9 + 16}$

Answer

5.7-503 §5.7 source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{9} + \sqrt{16}$

Answer

5.7-505 §5.7 source ↗

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

$\sqrt{70}$

Answer

8 <

\sqrt{70} <

9

5.7-507 §5.7 source ↗

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

$\sqrt{200}$

Answer

14 <

\sqrt{200} <

15

5.7-509 §5.7 source ↗

Approximate Square Roots with a Calculator

In the following exercises, use a calculator to approximate each square root and round to two decimal places.

$\sqrt{19}$

Answer

4.36

5.7-511 §5.7 source ↗

Approximate Square Roots with a Calculator

In the following exercises, use a calculator to approximate each square root and round to two decimal places.

$\sqrt{53}$

Answer

7.28

5.7-513 §5.7 source ↗

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{y^{2}}$

Answer

5.7-515 §5.7 source ↗

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{49 x^{2}}$

Answer

5.7-517 §5.7 source ↗

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$- \sqrt{64 a^{2}}$

Answer

−8a

5.7-519 §5.7 source ↗

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{144 x^{2} y^{2}}$

Answer

12xy

5.7-521 §5.7 source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of $75$ square feet. How long can a side of his garden be?

Answer

8.7 feet

5.7-523 §5.7 source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Gravity An airplane dropped a flare from a height of $1,024$ feet above a lake. How many seconds did it take for the flare to reach the water?

Answer

8 seconds

5.7-525 §5.7 source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, $4,000$ feet above the Colorado River. How many seconds did it take for the hammer to reach the river?

Answer

15.8 seconds

5.7-527 §5.7 source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Accident investigation The skid marks from a car involved in an accident measured $216$ feet. What was the speed of the car before the brakes were applied?

Answer

72 mph

5.7-529 §5.7 source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was $117$ feet. What was the speed of the vehicle before the brakes were applied?

Answer

53.0 mph

5.7-531 §5.7 source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Decorating Morris wants to have a square mosaic inlaid in his new patio. His budget allows for $2,025$ tiles. Each tile is square with an area of one square inch. How long can a side of the mosaic be?

Answer

45 inches

5.7-533 §5.7 source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

What is the difference between $9^{2}$ and $\sqrt{9} ?$

Answer

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.

5.R-535 §5.R source ↗

Name Decimals

In the following exercises, name each decimal.

$0.375$

Answer

three hundred seventy-five thousandths

5.R-537 §5.R source ↗

Name Decimals

In the following exercises, name each decimal.

$5.24$

Answer

five and twenty-four hundredths

5.R-539 §5.R source ↗

Name Decimals

In the following exercises, name each decimal.

$−4.09$

Answer

negative four and nine hundredths

5.R-541 §5.R source ↗

Write Decimals

In the following exercises, write as a decimal.

nine hundredths

Answer

0.09

5.R-543 §5.R source ↗

Write Decimals

In the following exercises, write as a decimal.

ten and thirty-five thousandths

Answer

10.035

5.R-545 §5.R source ↗

Write Decimals

In the following exercises, write as a decimal.

negative five hundredths

Answer

−0.05

5.R-547 §5.R source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

$0.825$

Answer

\frac{33}{40}

5.R-549 §5.R source ↗

Convert Decimals to Fractions or Mixed Numbers

In the following exercises, convert each decimal to a fraction. Simplify the answer if possible.

$3.64$

Answer

3 \frac{16}{25}

5.R-551 §5.R source ↗

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$

$0.6___0.8$

Answer

5.R-553 §5.R source ↗

Order Decimals

In the following exercises, order each of the following pairs of numbers, using $<$ or $>.$

$0.803____0.83$

Answer

5.R-555 §5.R source ↗

Round Decimals

$12.529$

Answer

ⓐ 12.53

ⓑ 12.5

5.R-557 §5.R source ↗

Round Decimals

$5.897$

Answer

ⓐ 5.90

ⓑ 5.9

ⓒ 6

5.R-559 §5.R source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$32.89 - 8.22$

Answer

24.67

5.R-561 §5.R source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$10.2 + 14.631$

Answer

24.831

5.R-563 §5.R source ↗

Add and Subtract Decimals

In the following exercises, add or subtract.

$1.83 - 4.2$

Answer

−2.37

5.R-565 §5.R source ↗

Multiply Decimals

In the following exercises, multiply.

$(−6.4) (0.25)$

Answer

−1.6

5.R-567 §5.R source ↗

Multiply Decimals

In the following exercises, multiply.

$(15.4) (1000)$

Answer

15,400

5.R-569 §5.R source ↗

Divide Decimals

In the following exercises, divide.

$4.32 \div 24$

Answer

0.18

5.R-571 §5.R source ↗

Divide Decimals

In the following exercises, divide.

$(−0.8) \div (−0.2)$

Answer

5.R-573 §5.R source ↗

Divide Decimals

In the following exercises, divide.

$9 \div 0.045$

Answer

200

5.R-575 §5.R source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Jessie put $8$ gallons of gas in her car. One gallon of gas costs $$3.528.$ How much did Jessie owe for all the gas?

Answer

$28.22

5.R-577 §5.R source ↗

Use Decimals in Money Applications

In the following exercises, use the strategy for applications to solve.

Alice bought a roll of paper towels that cost $$2.49.$ She had a coupon for $$0.35$ off, and the store doubled the coupon. How much did Alice pay for the paper towels?

Answer

$1.79

5.R-579 §5.R source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{7}{8}$

Answer

0.875

5.R-581 §5.R source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$- \frac{21}{4}$

Answer

−5.25

5.R-583 §5.R source ↗

Convert Fractions to Decimals

In the following exercises, convert each fraction to a decimal.

$\frac{6}{11}$

Answer

0 . \overset{—}{54}

5.R-585 §5.R source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$\frac{3}{5}___0 .$

Answer

5.R-587 §5.R source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$-$ $\frac{5}{12}___−0.42$

Answer

5.R-589 §5.R source ↗

Order Decimals and Fractions

In the following exercises, order each pair of numbers, using $<$ or $>.$

$0.33___\frac{5}{16}$

Answer

5.R-591 §5.R source ↗

In the following exercises, write each set of numbers in order from least to greatest.

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

Answer

\frac{11}{15},

0.75,

\frac{7}{9}

5.R-593 §5.R source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify

$\frac{3}{4} (15.44 - 7.4)$

Answer

6.03

5.R-595 §5.R source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify

$1.6 + \frac{3}{8}$

Answer

1.975

5.R-597 §5.R source ↗

Simplify Expressions Using the Order of Operations

In the following exercises, simplify

$-$ $\frac{2}{5} \cdot \frac{9}{10} +$ $0.14$

Answer

−0.22

5.R-599 §5.R source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle.

$radius =$ $3.5 ft.$

Answer

ⓐ 21.98 ft.

ⓑ 38.465 sq.ft.

5.R-601 §5.R source ↗

Find the Circumference and Area of Circles

In the following exercises, approximate the ⓐ circumference and ⓑ area of each circle.

$diameter =$ $11 cm$

Answer

ⓐ 34.54 cm

ⓑ 94.985 sq.cm

5.R-603 §5.R source ↗

Determine Whether a Decimal is a Solution of an Equation

In the following exercises, determine whether the each number is a solution of the given equation.

$y + 3.2 = −1.5$
ⓐ $y = 1.7$ ⓑ $y = −4.7$

Answer

ⓐ no

ⓑ yes

5.R-605 §5.R source ↗

Determine Whether a Decimal is a Solution of an Equation

In the following exercises, determine whether the each number is a solution of the given equation.

$0.45 v = −40.5$
ⓐ $v = −18.225$ ⓑ $v = −90$

Answer

ⓐ no

ⓑ yes

5.R-607 §5.R source ↗

Solve Equations with Decimals

In the following exercises, solve.

$h + 5.91 = 2.4$

Answer

h = −3.51

5.R-609 §5.R source ↗

Solve Equations with Decimals

In the following exercises, solve.

$p - 4.3 = −1.65$

Answer

p = 2.65

5.R-611 §5.R source ↗

Solve Equations with Decimals

In the following exercises, solve.

$j - 7.42 = −3.7$

Answer

j = 3.72

5.R-613 §5.R source ↗

Solve Equations with Decimals

In the following exercises, solve.

$−8.6 x = 34.4$

Answer

x = −4

5.R-615 §5.R source ↗

Solve Equations with Decimals

In the following exercises, solve.

$\frac{a}{0.3} = −24$

Answer

a = −7.2

5.R-617 §5.R source ↗

Solve Equations with Decimals

In the following exercises, solve.

$\frac{s}{−2.5} = −10$

Answer

s = 25

5.R-619 §5.R source ↗

Translate to an Equation and Solve

In the following exercises, translate and solve.

The product of $−5.9$ and $x$ is $−3.54 .$

Answer

−5.9x = −3.54; x = 0.6

5.R-621 §5.R source ↗

Translate to an Equation and Solve

In the following exercises, translate and solve.

The sum of $m$ and $(−4.03)$ is $6.8 .$

Answer

m + (−4.03) = 6.8; m = 10.83

5.R-623 §5.R source ↗

Find the Mean of a Set of Numbers

In the following exercises, find the mean of the numbers.

$$270$ , $$310.50$ , $$243.75$ , and $$252.15$

Answer

$269.10

5.R-625 §5.R source ↗

Find the Mean of a Set of Numbers

In the following exercises, find the mean of the numbers.

In the last three months, Raul’s water bills were $$31.45,$ $$48.76,$ $and $42.60 .$ Find the mean.

Answer

$40.94

5.R-627 §5.R source ↗

Find the Median of a Set of Numbers

In the following exercises, find the median.

$25$ , $23$ , $24$ , $26$ , $29$ , $19$ , $18$ , $32$

Answer

24.5

5.R-629 §5.R source ↗

Find the Median of a Set of Numbers

In the following exercises, find the median.

The number of clients at Miranda’s beauty salon each weekday last week were $18,$ $7,$ $12,$ $16,$ $and 20 .$ Find the median number of clients.

Answer

16 clients

5.R-631 §5.R source ↗

Find the Mode of a Set of Numbers

In the following exercises, identify the mode of the numbers.

The number of siblings of a group of students: $2$ , $0$ , $3$ , $2$ , $4$ , $1$ , $6$ , $5$ , $4$ , $1$ , $2$ , $3$

Answer

5.R-633 §5.R source ↗

Use the Basic Definition of Probability

In the following exercises, solve. (Round decimals to three places.)

Luc has to read $3$ novels and $12$ short stories for his literature class. The professor will choose one reading at random for the final exam. Find the probability that the professor will choose a novel for the final exam. Express your answer as a fraction and as a decimal.

Answer

\frac{1}{5}; 0.2

5.R-635 §5.R source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

$56$ to $32$

Answer

\frac{7}{4}

5.R-637 §5.R source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

$1.2$ to $1.8$

Answer

\frac{2}{3}

5.R-639 §5.R source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

$2 \frac{1}{3} to 5 \frac{1}{4}$

Answer

\frac{4}{9}

5.R-641 §5.R source ↗

Write a Ratio as a Fraction

In the following exercises, write each ratio as a fraction. Simplify the answer if possible.

$28$ inches to $3$ feet

Answer

\frac{7}{9}

5.R-643 §5.R source ↗

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

$90$ pounds per $7.5$ square inches

Answer

\frac{12 pounds}{1 square inch}

5.R-645 §5.R source ↗

Write a Rate as a Fraction

In the following exercises, write each rate as a fraction. Simplify the answer if possible.

$$612.50$ for $35$ hours

Answer

\frac{$35}{2 hours}

5.R-647 §5.R source ↗

Find Unit Rates

In the following exercises, find the unit rate.

$90$ pounds per $7.5$ square inches

Answer

12 pounds/sq.in.

5.R-649 §5.R source ↗

Find Unit Rates

In the following exercises, find the unit rate.

$$612.50$ for $35$ hours

Answer

$17.50/hour

5.R-651 §5.R source ↗

Find Unit Price

In the following exercises, find the unit price.

Highlighters: $6$ for $$2.52$

Answer

$0.42

5.R-653 §5.R source ↗

Find Unit Price

In the following exercises, find the unit price.

Anna bought a pack of $8$ kitchen towels for $$13.20 .$ How much did each towel cost? Round to the nearest cent if necessary.

Answer

$1.65

5.R-655 §5.R source ↗

In the following exercises, find each unit price and then determine the better buy.

Vitamins: $60$ tablets for $$6.49$ or $100$ for $$11.99 ?$

Answer

$0.11, $0.12; 60 tablets for $6.49

5.R-657 §5.R source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

$a$ adults to $45$ children

Answer

\frac{a adults}{45 children}

5.R-659 §5.R source ↗

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

the ratio of $19$ and the sum of $3$ and $n$

Answer

\frac{19}{3 + n}

5.R-661 §5.R source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{144}$

Answer

5.R-663 §5.R source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$- \sqrt{81}$

Answer

−9

5.R-665 §5.R source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{−36}$

Answer

not a real number

5.R-667 §5.R source ↗

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{64 + 225}$

Answer

5.R-669 §5.R source ↗

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

$\sqrt{155}$

Answer

12 <

\sqrt{155} <

13

5.R-671 §5.R source ↗

Approximate Square Roots

In the following exercises, approximate each square root and round to two decimal places.

$\sqrt{57}$

Answer

7.55

5.R-673 §5.R source ↗

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{64 b^{2}}$

Answer

5.R-675 §5.R source ↗

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{225 m^{2} n^{2}}$

Answer

15mn

5.R-677 §5.R source ↗

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{49 y^{2}}$

Answer

5.R-679 §5.R source ↗

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{121 c^{2} d^{2}}$

Answer

11cd

5.R-681 §5.R source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of $30$ square feet. How long can a side of the flower garden be?

Answer

5.5 feet

5.R-683 §5.R source ↗

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Accident investigation The skid marks of a car involved in an accident were $216$ feet. How fast had the car been going before applying the brakes?

Answer

72 mph

5.T-685 §5.T source ↗

Write

1.73

as a fraction.

Answer

1 \frac{73}{100}

5.T-687 §5.T source ↗

Round

16.749

Answer

ⓐ 16.7

ⓑ 16.75

5.T-689 §5.T source ↗

In the following exercises, simplify each expression.

$15.4 + 3.02$

Answer

18.42

5.T-691 §5.T source ↗

In the following exercises, simplify each expression.

$(0.64) (0.3)$

Answer

0.192

5.T-693 §5.T source ↗

In the following exercises, simplify each expression.

$0.96 \div (−12)$

Answer

−0.08

5.T-695 §5.T source ↗

In the following exercises, simplify each expression.

$−0.6 \div (−0.3)$

Answer

5.T-697 §5.T source ↗

In the following exercises, simplify each expression.

$24 \div (0.1 + 0.02)$

Answer

200

5.T-699 §5.T source ↗

In the following exercises, simplify each expression.

$1.6 + \frac{3}{8}$

Answer

1.975

5.T-701 §5.T source ↗

In the following exercises, solve.

$m + 3.7 = 2.5$

Answer

−1.2

5.T-703 §5.T source ↗

In the following exercises, solve.

$−6.5 y = −57.2$

Answer

8.8

5.T-705 §5.T source ↗

In the following exercises, solve.

Three friends went out to dinner and agreed to split the bill evenly. The bill was $$79.35 .$ How much should each person pay?

Answer

$26.45

5.T-707 §5.T source ↗

In the following exercises, solve.

The ages, in months, of $10$ children in a preschool class are:
$55$ , $55$ , $50$ , $51$ , $52$ , $50$ , $53$ , $51$ , $55$ , $49$
Find the ⓐ mean ⓑ median ⓒ mode

Answer

ⓐ 52.1

ⓑ 51.5

5.T-709 §5.T source ↗

In the following exercises, solve.

Find each unit price and then the better buy.
Laundry detergent: $64$ ounces for $$10.99$ or $48$ ounces for $$8.49$

Answer

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.

5.T-711 §5.T source ↗

In the following exercises, simplify.

$\sqrt{144 n^{2}}$

Answer

12n

5.T-713 §5.T source ↗

In the following exercises, simplify.

Yanet wants a square patio in her backyard. She has $225$ square feet of tile. How long can a side of the patio be?

Answer

15 feet

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Problems and answers are adapted from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith and Andrea Honeycutt Mathis, OpenStax, and are used under the CC BY-NC-SA 4.0 licence. Access for free at https://openstax.org/books/prealgebra-2e/pages/1-introduction. Illustrations: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license. This adaptation is released under the same licence, is non-commercial, and is neither affiliated with nor endorsed by OpenStax or Rice University.