Prealgebra

John Tobey received his BA in mathematics from Wheaton College in Wheaton, Illinois in 1965, his MA in mathematics education from Harvard University in 1966, and his PhD in mathematics education from Boston University in 1980. He has taught in the mathematics department at the United States Military Academy at West Point and has served as the mathematics Department Chairman at North Shore Community College in Danvers, Massachusetts for five years. John has served as the president of the New England Mathematics Association of Two Year Colleges. He has received the NISOD award for outstanding teaching from the University of Texas at Austin. John is the author of seven mathematics books published by Pearson Education. John has spoken to many mathematics departments and at many professional meetings throughout the country on the topic of developmental mathematics education and distance learning in mathematics. He lives in Massachusetts.   Jeffrey Slater has been a professor at North Shore Community College for thirty-eight years and received the Teacher of the Year in 2002. Jeff travels around the country speaking on student retention and is also a consultant to the Federal Government. He lives in Marblehead, Mass. with his wife Shelley and his yellow lab Gracie.   Jamie Blair has directed the Mathematics Learning Center at Orange Coast College for the past seventeen years. She designed, developed, and implemented the Center, and as a result of this effort has provided technical expertise related to the particulars of the Math Center to numerous other two-year colleges and at many conferences. In 2007 Jamie was appointed to the Team of Basic Skills Specialist by the California State Academic Senate. She is also currently participating on Title 3 committees on her campus. She specializes in teaching students who have never been successful in mathematics. She is an expert in the area of basic skills in relation to the learning needs of students. She lives in California.

How Am I Doing? Guide to Math Success

To the Student

Preface

Acknowledgments

 

1. Whole Numbers and Introduction to Algebra

1.1 Understanding Whole Numbers

1.2 Adding Whole Number Expressions

1.3 Subtracting Whole Number Expressions

1.4 Multiplying Whole Number Expressions

1.5 Dividing Whole Number Expressions

1.6 Exponents and the Order of Operations

            Putting Your Skills to Work: Use Math to Save Money   


            How Am I Doing? Sections 1.1–1.6

1.7 More on Algebraic Expressions

1.8 Introduction to Solving Linear Equations

1.9 Solving Applied Problems Using Several Operations

            Chapter 1 Organizer

            Chapter 1 Review Problems

            How Am I Doing? Chapter 1 Test

 

2. Integers

2.1 Understanding Integers

2.2 Adding Integers

2.3 Subtracting Integers

            Putting Your Skills to Work: Use Math to Save Money   

            How Am I Doing? Sections 2.1–2.3

2.4 Multiplying and Dividing Integers

2.5 The Order of Operations and Applications Involving Integers

2.6 Simplifying and Evaluating Algebraic Expressions

            Chapter 2 Organizer

            Chapter 2 Review Problems

            How Am I Doing? Chapter 2 Test

            Cumulative Test for Chapters 1–2

 

3. Introduction to Equations and Algebraic Expressions

3.1 Solving Equations of the Form x + a = c and x – a = c

3.2 Solving Equations of the Form ax = c

            How Am I Doing? Sections 3.1–3.2

3.3 Equations and Geometric Formulas

           Putting Your Skills to Work: Use Math to Save Money   

3.4 Performing Operations with Exponents

            Chapter 3 Organizer

            Chapter 3 Review Problems

            How Am I Doing? Chapter 3 Test

            Cumulative Test for Chapters 1–3

 

4. Fractions, Ratio, and Proportion

4.1 Factoring Whole Numbers

4.2 Understanding Fractions

4.3 Simplifying Fractional Expressions

            Putting Your Skills to Work: Use Math to Save Money   

            How Am I Doing? Sections 4.1–4.3

4.4 Simplifying Fractional Expressions with Exponents

4.5 Ratios and Rates

4.6 Proportions and Applications

            Chapter 4 Organizer

            Chapter 4 Review Problems

            How Am I Doing? Chapter 4 Test

            Cumulative Test for Chapters 1–4

 

5. Operations on Fractional Expressions

5.1 Multiplying and Dividing Fractional Expressions

5.2 Multiples and Least Common Multiples of Algebraic Expressions

5.3 Adding and Subtracting Fractional Expressions

5.4 Operations with Mixed Numbers

            Putting Your Skills to Work: Use Math to Save Money   

            How Am I Doing? Sections 5.1–5.4

5.5 Order of Operations and Complex Fractions

5.6 Solving Applied Problems Involving Fractions

5.7 Solving Equations of the Form x/a=c           


            Chapter 5 Organizer

            Chapter 5 Review Problems

            How Am I Doing? Chapter 5 Test

            Cumulative Test for Chapters 1–5

 

6. Polynomials

6.1 Adding and Subtracting Polynomials

6.2 Multiplying Polynomials

            How Am I Doing? Sections 6.1–6.2

6.3 Translating from English to Algebra

            Putting Your Skills to Work: Use Math to Save Money   

6.4 Factoring Using the Greatest Common Factor

            Chapter 6 Organizer

            Chapter 6 Review Problems

            How Am I Doing? Chapter 6 Test

            Cumulative Test for Chapters 1–6

 

7. Solving Equations

7.1 Solving Equations Using One Principle of Equality

7.2 Solving Equations Using More Than One Principle of Equality

7.3 Solving Equations with Parentheses

            How Am I Doing? Sections 7.1–7.3

7.4 Solving Equations with Fractions

7.5 Using Equations to Solve Applied Problems

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 7 Organizer

            Chapter 7 Review Problems

            How Am I Doing? Chapter 7 Test

            Cumulative Test for Chapters 1–7

 

8. Decimals and Percents

8.1 Understanding Decimal Fractions

8.2 Adding and Subtracting Decimal Expressions

8.3 Multiplying and Dividing Decimal Expressions

8.4 Solving Equations and Applied Problems Involving Decimals

            How Am I Doing? Sections 8.1–8.4

8.5 Estimating with Percents

8.6 Percents

8.7 Solving Percent Problems Using Equations

8.8 Solving Percent Problems Using Proportions

8.9 Solving Applied Problems Involving Percents

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 8 Organizer

            Chapter 8 Review Problems

            How Am I Doing? Chapter 8 Test

            Cumulative Test for Chapters 1–8

 

9. Graphing and Statistics

9.1 Interpreting and Constructing Graphs

9.2 Mean, Median, and Mode

            How Am I Doing? Sections 9.1–9.2

9.3 The Rectangular Coordinate System

9.4 Linear Equations in Two Variables

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 9 Organizer

            Chapter 9 Review Problems

            How Am I Doing? Chapter 9 Test

            Cumulative Test for Chapters 1–9

 

10. Measurement and Geometric Figures

10.1 Using Unit Fractions with U.S. and Metric Units

10.2 Converting Between the U.S. and Metric Systems

10.3 Angles

            How Am I Doing? Sections 10.1–10.3

10.4 Square Roots and the Pythagorean Theorem

10.5 The Circle

10.6 Volume

10.7 Similar Geometric Figures

            Putting Your Skills to Work: Use Math to Save Money

            Chapter 10 Organizer

            Chapter 10 Review Problems

            How Am I Doing? Chapter 10 Test

 

Practice Final Examination

 

Appendix A. Consumer Finance Applications

Appendix B. Introduction to U.S. and Metric Units of Measurement

Appendix C. Scientific Calculators

Appendix D. Additional Arithmetic Practice

Appendix E. Congruent Triangles

 

Solutions to Practice Problems

Answers to Selected Exercises

Applications Index

Index

Photo Credits