Prealgebra & Introductory Algebra

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.

1. The Whole Numbers

1.1 Tips for Success in Mathematics

1.2 Place Value, Names for Numbers, and Reading Tables

1.3 Adding and Subtracting Whole Numbers, and Perimeter

1.4 Rounding and Estimating

1.5 Multiplying Whole Numbers and Area

1.6 Dividing Whole Numbers

Integrated Review–Operations on Whole Numbers

1.7 Exponents and Order of Operations

1.8 Introduction to Variables, Algebraic Expressions, and Equations

           

2. Integers and Introduction to Solving Equations

2.1 Introduction to Integers

2.2 Adding Integers

2.3 Subtracting Integers

2.4 Multiplying and Dividing Integers

Integrated Review–Integers

2.5 Order of Operations

2.6 Solving Equations: The Addition and Multiplication Properties

 

3. Solving Equations and Problem Solving

3.1 Simplifying Algebraic Expressions

3.2 Solving Equations: Review of the Addition and Multiplication Properties

Integrated Review–Expressions and Equations

3.3 Solving Linear Equations in One Variable

3.4 Linear Equations in One Variable and Problem Solving

 

4. Fractions and Mixed Numbers

4.1 Introduction to Fractions and Mixed Numbers

4.2 Factors and Simplest Form

4.3 Multiplying and Dividing Fractions

4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent Fractions

4.5 Adding and Subtracting Unlike Fractions

Integrated Review–Summary on Fractions and Operations on Fractions

4.6 Complex Fractions and Review of Order of Operations

4.7 Operations on Mixed Numbers

4.8 Solving Equations Containing Fractions

 

5. Decimals

5.1 Introduction to Decimals

5.2 Adding and Subtracting Decimals

5.3 Multiplying Decimals and Circumference of a Circle

5.4 Dividing Decimals

Integrated Review–Operations on Decimals

5.5 Fractions, Decimals, and Order of Operations

5.6 Solving Equations Containing Decimals

5.7 Decimal Applications: Mean, Median, and Mode

 

6. Ratio, Proportion, and Percent

6.1 Ratio and Proportion

6.2 Percents, Decimals, and Fractions

6.3 Solving Percent Problems with Equations

6.4 Solving Percent Problems with Proportions

Integrated Review–Ratio, Proportion, and Percent

6.5 Applications of Percent

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

6.7 Percent and Problem Solving: Interest

 

7. Graphs and Triangle Applications

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

7.2 Reading and Drawing Circle Graphs

Integrated Review–Reading Graphs

7.3 Square Roots and the Pythagorean Theorem

7.4 Congruent and Similar Triangles

7.5 Counting and Introduction to Probability

 

8. Geometry and Measurement

8.1 Lines and Angles

8.2 Perimeter

8.3 Area, Volume, and Surface Area

Integrated Review–Geometry Concepts

8.4 Linear Measurement

8.5 Weight and Mass

8.6 Capacity

8.7 Temperature and Conversions Between the U.S. and Metric Systems

 

9. Equations, Inequalities, and Problem Solving

9.1 Symbols and Sets of Numbers

9.2 Properties of Real Numbers

9.3 Further Solving Linear Equations

Integrated Review–Real Numbers and Solving

Linear Equations

9.4 Further Problem Solving

9.5 Formulas and Problem Solving

9.6 Linear Inequalities and Problem Solving

 

10. Exponents and Polynomials

10.1 Exponents

10.2 Negative Exponents and Scientific Notation

10.3 Introduction to Polynomials

10.4 Adding and Subtracting Polynomials

10.5 Multiplying Polynomials

10.6 Special Products

Integrated Review–Exponents and Operations on Polynomials

10.7 Dividing Polynomials

 

11. Factoring Polynomials

11.1 The Greatest Common Factor

11.2 Factoring Trinomials of the Formx2+ bx + c

11.3 Factoring Trinomials of the Form ax2 + bx + c

11.4 Factoring Trinomials of the Formax2 + bx +c by Grouping

11.5 Factoring Perfect Square Trinomials and the Difference of Two Squares

Integrated Review–Choosing a Factoring Strategy

11.6 Solving Quadratic Equations by Factoring

11.7 Quadratic Equations and Problem Solving

 

12. Rational Expressions

12.1 Simplifying Rational Expressions

12.2 Multiplying and Dividing Rational Expressions

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

12.4 Adding and Subtracting Rational Expressions with Different Denominators

12.5 Solving Equations Containing Rational Expressions

Integrated Review–Summary on Rational Expressions

12.6 Rational Equations and Problem Solving

12.7 Simplifying Complex Fractions

 

13. Graphing Equations and Inequalities

13.1 The Rectangular Coordinate System

13.2 Graphing Linear Equations

13.3 Intercepts

13.4 Slope and Rate of Change

13.5 Equations of Lines

Integrated Review–Summary on Linear Equations

13.6 Introduction to Functions

13.7 Graphing Linear Inequalities in Two Variables

13.8 Direct and Inverse Variation

 

14. Systems of Equations

14.1 Solving Systems of Linear Equations by Graphing

14.2 Solving Systems of Linear Equations by Substitution

14.3 Solving Systems of Linear Equations by Addition

Integrated Review–Summary on Solving Systems of Equations

14.4 Systems of Linear Equations and Problem Solving

 

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

 

16. Quadratic Equations

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 of Solving Quadratic Equations

16.4 Graphing Quadratic Equations in Two Variables

 

Appendices

Appendix A. Tables

1. Geometric Figures

2. Percents, Decimals, and Fraction Equivalents

3. Finding Common Percents of a Number

4. Squares and Square Roots

Appendix B. Factoring Sums and Differences of Cubes

Appendix C. Mixture and Uniform Motion Problem Solving

Appendix D. Systems of Linear Inequalities

Appendix E. Geometric Formulas

 

Student Resources

Study Skills Builders

Bigger Picture—Study Guide Outline

Practice Final Exam

Answers to Selected Exercises