Developmental Mathematics

Elayn Martin-Gay has taught mathematics at the University of New Orleans for more than 25 years. Her numerous teaching awards include the local University Alumni Association’s Award for Excellence in Teaching, and Outstanding Developmental Educator at University of New Orleans, presented by the Louisiana Association of Developmental Educators. Prior to writing textbooks, Elayn Martin-Gay developed an acclaimed series of lecture videos to support developmental mathematics students. These highly successful videos originally served as the foundation materials for her texts. Today, the videos are specific to each book in her series. She has also created Chapter Test Prep Videos to help students during their most “teachable moment”–as they prepare for a test–along with Instructor-to-Instructor videos that provide teaching tips, hints, and suggestions for every developmental mathematics course, including basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Elayn is the author of 12 published textbooks and numerous multimedia interactive products, all specializing in developmental mathematics courses. She has participated as an author across a broad range of educational materials: textbooks, videos, tutorial software, and courseware. This offers an opportunity for multiple combinations for an integrated teaching and learning package, offering great consistency for the student.

Contents

Preface

Applications Index

1. The Whole Numbers

1.1 Study Skill Tips for Success in Mathematics

1.2 Place Value, Names for Numbers, and Reading Tables

1.3 Adding Whole Numbers and Perimeter

1.4 Subtracting Whole Numbers

1.5 Rounding and Estimating

1.6 Multiplying Whole Numbers and Area

1.7 Dividing Whole Numbers

Integrated Review–Operations on Whole Numbers

1.8 An Introduction to Problem Solving

1.9 Exponents, Square Roots, and Order of Operations

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

2. Multiplying and Dividing Fractions

2.1 Introduction to Fractions and Mixed Numbers

2.2 Factors and Prime Factorization

2.3 Simplest Form of a Fraction

Integrated Review–Summary on Fractions, Mixed Numbers, and Factors

2.4 Multiplying Fractions and Mixed Numbers

2.5 Dividing Fractions and Mixed Numbers

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

3. Adding and Subtracting Fractions

3.1 Adding and Subtracting Like Fractions

3.2 Least Common Multiple

3.3 Adding and Subtracting Unlike Fractions

Integrated Review–Operations on Fractions and Mixed Numbers

3.4 Adding and Subtracting Mixed Numbers

3.5 Order, Exponents, and the Order of Operations

3.6 Fractions and Problem Solving

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

4. Decimals

4.1 Introduction to Decimals

4.2 Order and Rounding

4.3 Adding and Subtracting Decimals

4.4 Multiplying Decimals and Circumference of a Circle

Integrated Review–Operations on Decimals

4.5 Dividing Decimals and Order of Operations

4.6 Fractions and Decimals

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

5. Ratio, Proportion, and Percent

5.1 Ratio and Proportion

5.2 Introduction to Percent

5.3 Percents and Fractions

5.4 Solving Percent Problems Using Equations

5.5 Solving Percent Problems Using Proportions

Integrated Review–Ratio, Proportion, and Percent

5.6 Applications of Percent

5.7 Percent and Problem Solving: Sales Tax, Commission, and Discount

5.8 Percent and Problem Solving: Interest

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

6. Geometry

6.1 Lines and Angles

6.2 Plane Figures and Solids

6.3 Perimeter

6.4 Area

6.5 Volume

Integrated Review–Geometry Concepts

6.6 Square Roots and the Pythagorean Theorem

6.7 Congruent and Similar Triangles

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

7. Statistics and Probability

7.1 Reading Pictographs, Bar Graphs, Histograms, and Line Graphs

7.2 Reading Circle Graphs

Integrated Review–Reading Graphs

7.3 Mean, Median, and Mode

7.4 Counting and Introduction to Probability

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

8. Real Numbers and Introduction to Algebra

8.1 Symbols and Sets of Numbers

8.2 Exponents, Order of Operations, and Variable Expressions

8.3 Adding Real Numbers

8.4 Subtracting Real Numbers

Integrated Review–Operations on Real Numbers

8.5 Multiplying and Dividing Real Numbers

8.6 Properties of Real Numbers

8.7 Simplifying Expressions

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

9. Equations, Inequalities, and Problem Solving

9.1 The Addition Property of Equality

9.2 The Multiplication Property of Equality

9.3 Further Solving Linear Equations

Integrated Review–Solving Linear Equations

9.4 Further Problem Solving

9.5 Formulas and Problem Solving

9.6 Percent and Mixture Problem Solving

9.7 Linear Inequalities and Problem Solving

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

10. Graphing Equations and Inequalities

10.1 The Rectangular Coordinate System

10.2 Graphing Linear Equations

10.3 Intercepts

10.4 Slope and Rate of Change

10.5 Equations of Lines

Integrated Review–Summary on Linear Equations

10.6 Introduction to Functions

10.7 Graphing Linear Inequalities in Two Variables

10.8 Direct and Inverse Variation

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

11. Systems of Equations

11.1 Solving Systems of Linear Equations by Graphing

11.2 Solving Systems of Linear Equations by Substitution

11.3 Solving Systems of Linear Equations by Addition

Integrated Review–Summary on Solving Systems of Equations

11.4 Systems of Linear Equations and Problem Solving

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

12. Exponents and Polynomials

12.1 Exponents

12.2 Negative Exponents and Scientific Notation

12.3 Introduction to Polynomials

12.4 Adding and Subtracting Polynomials

12.5 Multiplying Polynomials

12.6 Special Products

Integrated Review–Exponents and Operations on Polynomials

12.7 Dividing Polynomials

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

13. Factoring Polynomials

13.1 The Greatest Common Factor and Factoring by Grouping

13.2 Factoring Trinomials of the Form x2 + bx + c

13.3 Factoring Trinomials of the Form ax2 + bx + c

13.4 Factoring Trinomials of the Form ax2 + bx + c by Grouping

13.5 Factoring Perfect Square Trinomials and the Difference of Two Squares

Integrated Review–Choosing a Factoring Strategy

13.6 Solving Quadratic Equations by Factoring

13.7 Quadratic Equations and Problem Solving

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

14. Rational Expressions

14.1 Simplifying Rational Expressions

14.2 Multiplying and Dividing Rational Expressions

14.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator

14.4 Adding and Subtracting Rational Expressions with Different Denominators

14.5 Solving Equations Containing Rational Expressions

Integrated Review–Summary on Rational Expressions

14.6 Rational Equations and Problem Solving

14.7 Simplifying Complex Fractions

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

15. Roots and Radicals

15.1 Introduction to Radicals

15.2 Simplifying Radicals

15.3 Adding and Subtracting Radicals

15.4 Multiplying and Dividing Radicals

Integrated Review–Simplifying Radicals

15.5 Solving Equations Containing Radicals

15.6 Radical Equations and Problem Solving

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

16. Quadratic Equations and Nonlinear Graphs

16.1 Solving Quadratic Equations by the Square Root Property

16.2 Solving Quadratic Equations by Completing the Square

16.3 Solving Quadratic Equations by the Quadratic Formula

Integrated Review–Summary on Solving Quadratic Equations

16.4 Graphing Quadratic Equations in Two Variables

16.5 Interval Notation, Finding Domains and Ranges from Graphs, and Graphing Piecewise-Defined Functions

Group Activity

Vocabulary Check

Chapter Highlights

Chapter Review

Chapter Test

Cumulative Review

Appendices

Appendix A: Further Algebraic Topics

A.1 Factoring Sums and Differences of Cubes

A.2 Sets and Compound Inequalities

A.3 Absolute Value Equations and Inequalities

A.4 The Distance and Midpoint Formulas

A.5 Writing Equations of Parallel and Perpendicular Lines

A.6 Nonlinear Inequalities in One Variable

A.7 Rational Exponents

A.8 Systems of Linear Inequalities

Appendix B: Tables

B.1 Table of Squares and Square Roots

B.2 Table of Percents, Decimals, and Fraction Equivalents

B.3 Compound Interest

Student Resources

Study Skills Builders

Bigger Picture–Study Guide Outline

Practice Final Exam

Answers to Selected Exercises

Video Answer Section

Subject Index

Photo Credits