# Prealgebra and Introductory Algebra

**by**Martin-Gay, Elayn

### 9780321644909

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## Summary

## Author Biography

An award-winning instructor and best-selling author, **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 developed an acclaimed series of lecture videos to support developmental mathematics students in their quest for success. These highly successful videos originally served as the foundation material for her texts. Today, the videos are specific to each book in the Martin-Gay series. Elayn also pioneered the **Chapter Test Prep Video** to help students as they prepare for a test–their most “teachable moment!”

Elayn’s experience has made her aware of how busy instructors are and what a difference quality support makes. For this reason, she created the **Instructor-to-Instructor** video series. These videos provide instructors with suggestions for presenting specific math topics and concepts in basic mathematics, prealgebra, beginning algebra, and intermediate algebra. Seasoned instructors can use them as a source for alternate approaches in the classroom. New or adjunct faculty may find the videos useful for review.

Her textbooks and acclaimed video program support Elayn's passion of helping

**every**student to succeed.

## Table of Contents

**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 Form* x* ^{2}+ *bx *+ *c*

11.3 Factoring Trinomials of the Form *ax* ^{2} + *bx *+ *c*

11.4 Factoring Trinomials of the Form* ax* ^{2} + *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