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Prealgebra 2e

Review Exercises

Prealgebra 2eReview Exercises
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  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

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

Add and Subtract Decimals

In the following exercises, add or subtract.

558.

5.75+8.465.75+8.46

559.

32.898.2232.898.22

560.

2419.312419.31

561.

10.2+14.63110.2+14.631

562.

−6.4+(−2.9)−6.4+(−2.9)

563.

1.834.21.834.2

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÷12$6.29÷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 $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.

3535

579.

7878

580.

19201920

581.

214214

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___−0.8478___−0.84

587.

512___−0.42512___−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(10.35.8)4(10.35.8)

593.

34(15.447.4)34(15.447.4)

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+0.1425·910+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.

x0.4=2.1x0.4=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=1.7y=−4.7y=−4.7

604.

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

605.

0.45v=−40.50.45v=−40.5
v=−18.225v=−18.225v=−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.

p4.3=−1.65p4.3=−1.65

610.

x0.24=−8.6x0.24=−8.6

611.

j7.42=−3.7j7.42=−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.

$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,and83,0,8,1,and8 minutes. Find the mean.

625.

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

$612.50$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 7.57.5 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 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.

2525

663.

8181

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.

121a2121a2

675.

225m2n2225m2n2

676.

100q2100q2

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?

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