Contents

Review Exercises

Decimals

Name Decimals

In the following exercises, name each decimal.

534.

$0.8 0.8$

535.

$0.375 0.375$

536.

$0.007 0.007$

537.

$5.24 5.24$

538.

$−12.5632 −12.5632$

539.

$−4.09 −4.09$

Write Decimals

In the following exercises, write as a decimal.

540.

three tenths

541.

nine hundredths

542.

twenty-seven hundredths

543.

ten and thirty-five thousandths

544.

negative twenty and three tenths

545.

negative five hundredths

Convert Decimals to Fractions or Mixed Numbers

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

546.

$0.43 0.43$

547.

$0.825 0.825$

548.

$9.7 9.7$

549.

$3.64 3.64$

Locate Decimals on the Number Line

550.

ⓐ $0.6$

ⓑ $−0.9$

ⓓ $−1.3$

Order Decimals

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

551.

$0.6___0.8 0.6___0.8$

552.

$0.2___0.15 0.2___0.15$

553.

$0.803____0.83 0.803____0.83$

554.

$−0.56____−0.562 −0.56____−0.562$

Round Decimals

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

555.

$12.529 12.529$

556.

$4.8447 4.8447$

557.

$5.897 5.897$

Decimal Operations

Add and Subtract Decimals

In the following exercises, add or subtract.

558.

$5.75 + 8.46 5.75 + 8.46$

559.

$32.89 - 8.22 32.89 - 8.22$

560.

$24 - 19.31 24 - 19.31$

561.

$10.2 + 14.631 10.2 + 14.631$

562.

$−6.4 + (−2.9) −6.4 + (−2.9)$

563.

$1.83 - 4.2 1.83 - 4.2$

Multiply Decimals

In the following exercises, multiply.

564.

$(0.3) (0.7) (0.3) (0.7)$

565.

$(−6.4) (0.25) (−6.4) (0.25)$

566.

$(−3.35) (−12.7) (−3.35) (−12.7)$

567.

$(15.4) (1000) (15.4) (1000)$

Divide Decimals

In the following exercises, divide.

568.

$0.48 \div 6 0.48 \div 6$

569.

$4.32 \div 24 4.32 \div 24$

570.

$$6.29 \div 12 $6.29 \div 12$

571.

$(−0.8) \div (−0.2) (−0.8) \div (−0.2)$

572.

$1.65 \div 0.15 1.65 \div 0.15$

573.

$9 \div 0.045 9 \div 0.045$

Use Decimals in Money Applications

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

574.

Miranda got $$40 $40$ from her ATM. She spent $$9.32 $9.32$ on lunch and $$16.99 $16.99$ on a book. How much money did she have left? Round to the nearest cent if necessary.

575.

Jessie put $88$ gallons of gas in her car. One gallon of gas costs $$3.528. $3.528.$ How much did Jessie owe for all the gas?

576.

A pack of $1616$ water bottles cost $$6.72. $6.72.$ How much did each bottle cost?

577.

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

Decimals and Fractions

Convert Fractions to Decimals

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

578.

$\frac{3}{5} \frac{3}{5}$

579.

$\frac{7}{8} \frac{7}{8}$

580.

$- \frac{19}{20} - \frac{19}{20}$

581.

$- \frac{21}{4} - \frac{21}{4}$

582.

$\frac{1}{3} \frac{1}{3}$

583.

$\frac{6}{11} \frac{6}{11}$

Order Decimals and Fractions

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

584.

$\frac{1}{2}___0.2 \frac{1}{2}___0.2$

585.

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

586.

$- \frac{7}{8}___−0.84 - \frac{7}{8}___−0.84$

587.

$- \frac{5}{12}___−0.42 - \frac{5}{12}___−0.42$

588.

$0.625___\frac{13}{20} 0.625___\frac{13}{20}$

589.

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

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

590.

$\frac{2}{3}, \frac{17}{20}, 0.65 \frac{2}{3}, \frac{17}{20}, 0.65$

591.

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

Simplify Expressions Using the Order of Operations

In the following exercises, simplify

592.

$4 (10.3 - 5.8) 4 (10.3 - 5.8)$

593.

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

594.

$30 \div (0.45 + 0.15) 30 \div (0.45 + 0.15)$

595.

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

596.

$52 (0.5) + {(0.4)}^{2} 52 (0.5) + {(0.4)}^{2}$

597.

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

Find the Circumference and Area of Circles

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

598.

$radius = 6 in. radius = 6 in.$

599.

$radius = 3.5 ft. radius = 3.5 ft.$

600.

$radius = \frac{7}{33} m radius = \frac{7}{33}$

601.

$diameter = 11 cm diameter = 11 cm$

Solve Equations with Decimals

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.

602.

$x - 0.4 = 2.1 x - 0.4 = 2.1$
ⓐ $x = 1.7$ ⓑ $x = 2.5$

603.

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

604.

$\frac{u}{2.5} = −12.5 \frac{u}{2.5} = −12.5$
ⓐ $u = −5$ ⓑ $u = −31.25$

605.

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

Solve Equations with Decimals

In the following exercises, solve.

606.

$m + 3.8 = 7.5 m + 3.8 = 7.5$

607.

$h + 5.91 = 2.4 h + 5.91 = 2.4$

608.

$a + 2.26 = −1.1 a + 2.26 = −1.1$

609.

$p - 4.3 = −1.65 p - 4.3 = −1.65$

610.

$x - 0.24 = −8.6 x - 0.24 = −8.6$

611.

$j - 7.42 = −3.7 j - 7.42 = −3.7$

612.

$0.6 p = 13.2 0.6 p = 13.2$

613.

$−8.6 x = 34.4 −8.6 x = 34.4$

614.

$−22.32 = −2.4 z −22.32 = −2.4 z$

615.

$\frac{a}{0.3} = −24 \frac{a}{0.3} = −24$

616.

$\frac{p}{−7} = −4.2 \frac{p}{−7} = −4.2$

617.

$\frac{s}{−2.5} = −10 \frac{s}{−2.5} = −10$

Translate to an Equation and Solve

In the following exercises, translate and solve.

618.

The difference of $n n$ and $15.2 15.2$ is $4.4 . 4.4 .$

619.

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

620.

The quotient of $y y$ and $−1.8 −1.8$ is $−9 . −9 .$

621.

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

Averages and Probability

Find the Mean of a Set of Numbers

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

622.

$2, 4, 1, 0, 1, and 1 2, 4, 1, 0, 1,$

623.

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

624.

Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited $3, 0, 8, 1, and 8 3, 0, 8, 1,$ minutes. Find the mean

625.

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

Find the Median of a Set of Numbers

In the following exercises, find the median.

626.

$4141$ , $4545$ , $3232$ , $6060$ , $5858$

627.

$2525$ , $2323$ , $2424$ , $2626$ , $2929$ , $1919$ , $1818$ , $3232$

628.

The ages of the eight men in Jerry’s model train club are $52, 63, 45, 51, 55, 75, 60, and 59 . 52, 63, 45, 51, 55, 75, 60,$ Find the median age.

629.

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

Find the Mode of a Set of Numbers

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

630.

$66$ , $44$ , $4, 5 4, 5$ , $6, 6 6, 6$ , $44$ , $44$ , $44$ , $33$ , $55$

631.

The number of siblings of a group of students: $22$ , $00$ , $33$ , $22$ , $44$ , $11$ , $66$ , $55$ , $44$ , $11$ , $22$ , $33$

Use the Basic Definition of Probability

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

632.

The Sustainability Club sells $200200$ tickets to a raffle, and Albert buys one ticket. One ticket will be selected at random to win the grand prize. Find the probability Albert will win the grand prize. Express your answer as a fraction and as a decimal.

633.

Luc has to read $33$ novels and $1212$ 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.

Ratios and Rate

Write a Ratio as a Fraction

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

634.

$2828$ to $4040$

635.

$5656$ to $3232$

636.

$3.5 3.5$ to $0.5 0.5$

637.

$1.2 1.2$ to $1.8 1.8$

638.

$1 \frac{3}{4} to 1 \frac{5}{8} 1 \frac{3}{4}$

639.

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

640.

$6464$ ounces to $3030$ ounces

641.

$2828$ inches to $33$ feet

Write a Rate as a Fraction

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

642.

$180180$ calories per $88$ ounces

643.

$9090$ pounds per $7.5 7.5$ square inches

644.

$126126$ miles in $44$ hours

645.

$$612.50 $612.50$ for $3535$ hours

Find Unit Rates

In the following exercises, find the unit rate.

646.

$180180$ calories per $88$ ounces

647.

$9090$ pounds per $7.5 7.5$ square inches

648.

$126126$ miles in $44$ hours

649.

$$612.50 $612.50$ for $3535$ hours

Find Unit Price

In the following exercises, find the unit price.

650.

t-shirts: $33$ for $$8.97 $8.97$

651.

Highlighters: $66$ for $$2.52 $2.52$

652.

An office supply store sells a box of pens for $$11 . $11 .$ The box contains $1212$ pens. How much does each pen cost?

653.

Anna bought a pack of $88$ kitchen towels for $$13.20 . $13.20 .$ How much did each towel cost? Round to the nearest cent if necessary.

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

654.

Shampoo: $1212$ ounces for $$4.29 $4.29$ or $2222$ ounces for $$7.29 ? $7.29 ?$

655.

Vitamins: $6060$ tablets for $$6.49 $6.49$ or $100100$ for $$11.99 ? $11.99 ?$

Translate Phrases to Expressions with Fractions

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

656.

$535535$ miles per $h hours h$

657.

$a a$ adults to $4545$ children

658.

the ratio of $4 y 4 y$ and the difference of $x x$ and $1010$

659.

the ratio of $1919$ and the sum of $33$ and $n n$

Simplify and Use Square Roots

Simplify Expressions with Square Roots

In the following exercises, simplify.

660.

$\sqrt{64} \sqrt{64}$

661.

$\sqrt{144} \sqrt{144}$

662.

$- \sqrt{25} - \sqrt{25}$

663.

$- \sqrt{81} - \sqrt{81}$

664.

$\sqrt{−9} \sqrt{−9}$

665.

$\sqrt{−36} \sqrt{−36}$

666.

$\sqrt{64} + \sqrt{225} \sqrt{64} + \sqrt{225}$

667.

$\sqrt{64 + 225} \sqrt{64 + 225}$

Estimate Square Roots

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

668.

$\sqrt{28} \sqrt{28}$

669.

$\sqrt{155} \sqrt{155}$

Approximate Square Roots

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

670.

$\sqrt{15} \sqrt{15}$

671.

$\sqrt{57} \sqrt{57}$

Simplify Variable Expressions with Square Roots

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

672.

$\sqrt{q^{2}} \sqrt{q^{2}}$

673.

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

674.

$- \sqrt{121 a^{2}} - \sqrt{121 a^{2}}$

675.

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

676.

$- \sqrt{100 q^{2}} - \sqrt{100 q^{2}}$

677.

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

678.

$\sqrt{4 a^{2} b^{2}} \sqrt{4 a^{2} b^{2}}$

679.

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

Use Square Roots in Applications

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

680.

Art Diego has $225225$ square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?

681.

Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of $3030$ square feet. How long can a side of the flower garden be?

682.

Gravity A hiker dropped a granola bar from a lookout spot $576576$ feet above a valley. How long did it take the granola bar to reach the valley floor?

683.

Accident investigation The skid marks of a car involved in an accident were $216216$ feet. How fast had the car been going before applying the brakes?