Prealgebra

# Review Exercises

PrealgebraReview 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.

$0.6 0.6$

$−0.9 −0.9$

$2.2 2.2$

$−1.3 −1.3$

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

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.

$0.48 ÷ 6 0.48 ÷ 6$

569.

$4.32 ÷ 24 4.32 ÷ 24$

570.

$6.29 ÷ 12 6.29 ÷ 12$

571.

$( −0.8 ) ÷ ( −0.2 ) ( −0.8 ) ÷ ( −0.2 )$

572.

$1.65 ÷ 0.15 1.65 ÷ 0.15$

573.

$9 ÷ 0.045 9 ÷ 0.045$

Use Decimals in Money Applications

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

574.

Miranda got $4040$ from her ATM. She spent $9.329.32$ on lunch and $16.9916.99$ 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 $0.350.35$ 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.

$3 5 3 5$

579.

$7 8 7 8$

580.

$− 19 20 − 19 20$

581.

$− 21 4 − 21 4$

582.

$1 3 1 3$

583.

$6 11 6 11$

Order Decimals and Fractions

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

584.

$1 2 ___ 0.2 1 2 ___ 0.2$

585.

$3 5 ___ 0 . 3 5 ___ 0 .$

586.

$− 7 8 ___ −0.84 − 7 8 ___ −0.84$

587.

$− 5 12 ___ −0.42 − 5 12 ___ −0.42$

588.

$0.625 ___ 13 20 0.625 ___ 13 20$

589.

$0.33 ___ 5 16 0.33 ___ 5 16$

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

590.

$2 3 , 17 20 , 0.65 2 3 , 17 20 , 0.65$

591.

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

Simplify Expressions Using the Order of Operations

In the following exercises, simplify

592.

$4 ( 10.3 − 5.8 ) 4 ( 10.3 − 5.8 )$

593.

$3 4 ( 15.44 − 7.4 ) 3 4 ( 15.44 − 7.4 )$

594.

$30 ÷ ( 0.45 + 0.15 ) 30 ÷ ( 0.45 + 0.15 )$

595.

$1.6 + 3 8 1.6 + 3 8$

596.

$52 ( 0.5 ) + ( 0.4 ) 2 52 ( 0.5 ) + ( 0.4 ) 2$

597.

$− 2 5 · 9 10 + 0.14 − 2 5 · 9 10 + 0.14$

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.

$radius = 7 33 m radius = 7 33 m$

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.

$x−0.4=2.1x−0.4=2.1$
$x=1.7x=1.7$ $x=2.5x=2.5$

603.

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

604.

$u 2.5 = −12.5 u 2.5 = −12.5$
$u = −5 u = −5$ $u = −31.25 u = −31.25$

605.

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

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.

$a 0.3 = −24 a 0.3 = −24$

616.

$p −7 = −4.2 p −7 = −4.2$

617.

$s −2.5 = −10 s −2.5 = −10$

Translate to an Equation and Solve

In the following exercises, translate and solve.

618.

The difference of $nn$ and $15.215.2$ is $4.4.4.4.$

619.

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

620.

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

621.

The sum of $mm$ 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.

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

623.

$270270$, $310.50310.50$, $243.75243.75$, and$252.15252.15$

624.

Each workday last week, Yoshie kept track of the number of minutes she had to wait for the bus. She waited $3,0,8,1,and83,0,8,1,and8$ minutes. Find the mean

625.

In the last three months, Raul’s water bills were $31.45,48.76,and42.60.31.45,48.76,and42.60.$ 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 $52,63,45,51,55,75,60,and59.52,63,45,51,55,75,60,and59.$ Find the median age.

629.

The number of clients at Miranda’s beauty salon each weekday last week were $18,7,12,16,and20.18,7,12,16,and20.$ 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.

$66$, $44$, $4,54,5$, $6,66,6$, $44$, $44$, $44$, $33$, $55$

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.

$3.53.5$ to $0.50.5$

637.

$1.21.2$ to $1.81.8$

638.

$1 3 4 to 1 5 8 1 3 4 to 1 5 8$

639.

$2 1 3 to 5 1 4 2 1 3 to 5 1 4$

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 $7.57.5$ square inches

644.

$126126$ miles in $44$ hours

645.

$612.50612.50$ for $3535$ hours

Find Unit Rates

In the following exercises, find the unit rate.

646.

$180180$ calories per $88$ ounces

647.

$9090$ pounds per $7.57.5$ square inches

648.

$126126$ miles in $44$ hours

649.

$612.50612.50$ for $3535$ hours

Find Unit Price

In the following exercises, find the unit price.

650.

t-shirts: $33$ for $8.978.97$

651.

Highlighters: $66$ for $2.522.52$

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 $4.294.29$ or $2222$ ounces for $7.29?7.29?$

655.

Vitamins: $6060$ tablets for $6.496.49$ 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 $hhourshhours$

657.

$aa$ adults to $4545$ children

658.

the ratio of $4y4y$ and the difference of $xx$ and $1010$

659.

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

## Simplify and Use Square Roots

Simplify Expressions with Square Roots

In the following exercises, simplify.

660.

$64 64$

661.

$144 144$

662.

$− 25 − 25$

663.

$− 81 − 81$

664.

$−9 −9$

665.

$−36 −36$

666.

$64 + 225 64 + 225$

667.

$64 + 225 64 + 225$

Estimate Square Roots

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

668.

$28 28$

669.

$155 155$

Approximate Square Roots

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

670.

$15 15$

671.

$57 57$

Simplify Variable Expressions with Square Roots

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

672.

$q 2 q 2$

673.

$64 b 2 64 b 2$

674.

$− 121 a 2 − 121 a 2$

675.

$225 m 2 n 2 225 m 2 n 2$

676.

$− 100 q 2 − 100 q 2$

677.

$49 y 2 49 y 2$

678.

$4 a 2 b 2 4 a 2 b 2$

679.

$121 c 2 d 2 121 c 2 d 2$

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?

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