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Prealgebra

Review Exercises

PrealgebraReview Exercises
  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

Visualize Fractions

In the following exercises, name the fraction of each figure that is shaded.

574.
A circle is shown. It is divided into 8 equal pieces. 5 pieces are shaded.
575.
A square is shown. It is divided into 9 equal pieces. 5 pieces are shaded.

In the following exercises, name the improper fractions. Then write each improper fraction as a mixed number.

576.
Two squares are shown. Both are divided into four equal pieces. The square on the left has all 4 pieces shaded. The square on the right has one piece shaded.
577.
Two circles are shown. Both are divided into two equal pieces. The circle on the left has both pieces shaded. The circle on the right has one piece shaded.

In the following exercises, convert the improper fraction to a mixed number.

578.

58155815

579.

63116311

In the following exercises, convert the mixed number to an improper fraction.

580.

12141214

581.

945945

582.

Find three fractions equivalent to 25.25. Show your work, using figures or algebra.

583.

Find three fractions equivalent to 43.43. Show your work, using figures or algebra.

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

584.

58,43,334,458,43,334,4

585.

14,14,113,−113,72,7214,14,113,−113,72,72

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

586.

−1___25−1___25

587.

−212___−3−212___−3

Multiply and Divide Fractions

In the following exercises, simplify.

588.

63846384

589.

9012090120

590.

14a14b14a14b

591.

8x8y8x8y

In the following exercises, multiply.

592.

25·81325·813

593.

13·12713·127

594.

29·(4532)29·(4532)

595.

6m·4116m·411

596.

14(−32)14(−32)

597.

315·178315·178

In the following exercises, find the reciprocal.

598.

2929

599.

154154

600.

33

601.

1414

602.

Fill in the chart.

Opposite Absolute Value Reciprocal
513513
310310
9494
−12−12

In the following exercises, divide.

603.

23÷1623÷16

604.

(3x5)÷(2y3)(3x5)÷(2y3)

605.

45÷345÷3

606.

8÷2238÷223

607.

823÷1112823÷1112

Multiply and Divide Mixed Numbers and Complex Fractions

In the following exercises, perform the indicated operation.

608.

315·178315·178

609.

−5712·4411−5712·4411

610.

8÷2238÷223

611.

823÷1112823÷1112

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

612.

the quotient of 88 and yy

613.

the quotient of VV and the difference of hh and 66

In the following exercises, simplify the complex fraction

614.

58455845

615.

89−489−4

616.

n438n438

617.

−156112−156112

In the following exercises, simplify.

618.

5+1655+165

619.

8·4523·128·4523·12

620.

8·7+5(810)9·36·48·7+5(810)9·36·4

Add and Subtract Fractions with Common Denominators

In the following exercises, add.

621.

38+2838+28

622.

45+1545+15

623.

25+1525+15

624.

1532+9321532+932

625.

x10+710x10+710

In the following exercises, subtract.

626.

811611811611

627.

11125121112512

628.

45y545y5

629.

31307303130730

630.

32(32)32(32)

631.

1115515(215)1115515(215)

Add and Subtract Fractions with Different Denominators

In the following exercises, find the least common denominator.

632.

13and11213and112

633.

13and4513and45

634.

815and1120815and1120

635.

34,16,and51034,16,and510

In the following exercises, change to equivalent fractions using the given LCD.

636.

13and15,LCD=1513and15,LCD=15

637.

38and56,LCD=2438and56,LCD=24

638.

916and512,LCD=48916and512,LCD=48

639.

13,34and45,LCD=6013,34and45,LCD=60

In the following exercises, perform the indicated operations and simplify.

640.

15+2315+23

641.

111223111223

642.

9103491034

643.

1136112011361120

644.

2225+9402225+940

645.

y1013y1013

646.

25+(59)25+(59)

647.

411÷27d411÷27d

648.

25+(3n8)(29n)25+(3n8)(29n)

649.

(23)2(58)2(23)2(58)2

650.

(1112+38)÷(56110)(1112+38)÷(56110)

In the following exercises, evaluate.

651.

y45y45 when

  1. y=45y=45
  2. y=14y=14
652.

6mn26mn2 when m=34andn=13m=34andn=13

Add and Subtract Mixed Numbers

In the following exercises, perform the indicated operation.

653.

413+913413+913

654.

625+735625+735

655.

5811+24115811+2411

656.

358+378358+378

657.

91320411209132041120

658.

2310191023101910

659.

211121712211121712

660.

8611291186112911

Solve Equations with Fractions

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

661.

x12=16:x12=16:

  1. x=1x=1
  2. x=23x=23
  3. x=13x=13
662.

y+35=59:y+35=59:

  1. y=12y=12
  2. y=5245y=5245
  3. y=245y=245

In the following exercises, solve the equation.

663.

n+911=411n+911=411

664.

x16=76x16=76

665.

h(78)=25h(78)=25

666.

x5=−10x5=−10

667.

z=23z=23

In the following exercises, translate and solve.

668.

The sum of two-thirds and nn is 35.35.

669.

The difference of qq and one-tenth is 12.12.

670.

The quotient of pp and −4−4 is −8.−8.

671.

Three-eighths of yy is 24.24.

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