Prealgebra 2e

# Review Exercises

Prealgebra 2eReview Exercises

### Review Exercises

##### Decimals

Name Decimals

In the following exercises, name each decimal.

534.

$0.80.8$

535.

$0.3750.375$

536.

$0.0070.007$

537.

$5.245.24$

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.

$0.430.43$

547.

$0.8250.825$

548.

$9.79.7$

549.

$3.643.64$

Locate Decimals on the Number Line

550.

$0.60.6$

$−0.9−0.9$

$2.22.2$

$−1.3−1.3$

Order Decimals

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

551.

$0.6___0.80.6___0.8$

552.

$0.2___0.150.2___0.15$

553.

$0.803____0.830.803____0.83$

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.

$12.52912.529$

556.

$4.84474.8447$

557.

$5.8975.897$

##### Decimal Operations

In the following exercises, add or subtract.

558.

$5.75+8.465.75+8.46$

559.

$32.89−8.2232.89−8.22$

560.

$24−19.3124−19.31$

561.

$10.2+14.63110.2+14.631$

562.

$−6.4+(−2.9)−6.4+(−2.9)$

563.

$1.83−4.21.83−4.2$

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.

$0.48÷60.48÷6$

569.

$4.32÷244.32÷24$

570.

$6.29÷126.29÷12$

571.

$(−0.8)÷(−0.2)(−0.8)÷(−0.2)$

572.

$1.65÷0.151.65÷0.15$

573.

$9÷0.0459÷0.045$

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.

$3535$

579.

$7878$

580.

$−1920−1920$

581.

$−214−214$

582.

$1313$

583.

$611611$

Order Decimals and Fractions

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

584.

$12___0.212___0.2$

585.

$35___0.35___0.$

586.

$−78___−0.84−78___−0.84$

587.

$−512___−0.42−512___−0.42$

588.

$0.625___13200.625___1320$

589.

$0.33___5160.33___516$

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

590.

$23,1720,0.6523,1720,0.65$

591.

$79,0.75,111579,0.75,1115$

Simplify Expressions Using the Order of Operations

In the following exercises, simplify

592.

$4(10.3−5.8)4(10.3−5.8)$

593.

$34(15.44−7.4)34(15.44−7.4)$

594.

$30÷(0.45+0.15)30÷(0.45+0.15)$

595.

$1.6+381.6+38$

596.

$52(0.5)+(0.4)252(0.5)+(0.4)2$

597.

$−25·910+0.14−25·910+0.14$

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.

$radius=733mradius=733m$

601.

$diameter=11 cmdiameter=11 cm$

##### 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.

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

604.

$u2.5=−12.5u2.5=−12.5$
$u=−5u=−5$$u=−31.25u=−31.25$

605.

$0.45v=−40.50.45v=−40.5$
$v=−18.225v=−18.225$$v=−90v=−90$

Solve Equations with Decimals

In the following exercises, solve.

606.

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

607.

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

608.

$a+2.26=−1.1a+2.26=−1.1$

609.

$p−4.3=−1.65p−4.3=−1.65$

610.

$x−0.24=−8.6x−0.24=−8.6$

611.

$j−7.42=−3.7j−7.42=−3.7$

612.

$0.6p=13.20.6p=13.2$

613.

$−8.6x=34.4−8.6x=34.4$

614.

$−22.32=−2.4z−22.32=−2.4z$

615.

$a0.3=−24a0.3=−24$

616.

$p−7=−4.2p−7=−4.2$

617.

$s−2.5=−10s−2.5=−10$

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.

$2,4,1,0,1,and12,4,1,0,1,and1$

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.

$134to158134to158$

639.

$213to514213to514$

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.

$6464$

661.

$144144$

662.

$−25−25$

663.

$−81−81$

664.

$−9−9$

665.

$−36−36$

666.

$64+22564+225$

667.

$64+22564+225$

Estimate Square Roots

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

668.

$2828$

669.

$155155$

Approximate Square Roots

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

670.

$1515$

671.

$5757$

Simplify Variable Expressions with Square Roots

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

672.

$q2q2$

673.

$64b264b2$

674.

$−121a2−121a2$

675.

$225m2n2225m2n2$

676.

$−100q2−100q2$

677.

$49y249y2$

678.

$4a2b24a2b2$

679.

$121c2d2121c2d2$

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?