Developmental Mathematics

Marge Lial (late) became interested in math at an early age-it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology; trips to various digs and ruin sites produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. We dedicate the new editions of the paperback developmental math series to Marge in honor of her contributions to the field in which she helped thousands of students succeed. When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons. A native Midwesterner, Terry McGinnis received her Bachelor's of Science in Elementary Education with a concentration in Mathematics from Iowa State University. She has taught elementary and middle school mathematics, and developed and implemented the curriculum used with her students. Terry has been involved in college mathematics publishing for over 20 years, working with a variety of authors on textbooks in developmental mathematics and precalculus. After working behind the scenes on many of the Lial/Hornsby textbooks and supplements for over 10 years, Terry joined Margaret Lial and John Hornsby in 2002 as coauthor of their developmental mathematics series that includes Introductory Algebra, Intermediate Algebra, and Introductory and Intermediate Algebra. When not working, Terry enjoys spinning at a local health club, walking, and reading fiction. She is the devoted mother of two sons, Andrew and Tyler. Diana Hestwood lives in Minnesota and has taught at Metropolitan Community College in Minneapolis for two decades. She has done research on the student brain and is an expert on study skills. She is the author of Lial/Hestwood's Prealgebra and coauthor of Lial/Salzman/Hestwood's Basic Math and Lial/Hestwood/Hornsby/McGinnis's Prealgebra and Introductory Algebra. Stan Salzman is a long time resident of Sacramento, California. Stan has taught at American River College for many years, where he was a member of the business department. He is the author of Business Math and Essential Math, published by Pearson Education, Inc., and is coauthor of Basic Math.

1. Whole Numbers

1.1 Reading and Writing Whole Numbers

1.2 Adding Whole Numbers

1.3 Subtracting Whole Numbers

1.4 Multiplying Whole Numbers

1.5 Dividing Whole Numbers

1.6 Long Division

1.7 Rounding Whole Numbers

1.8 Exponents, Roots, and Order of Operations

1.9 Reading Pictographs, Bar Graphs, and Line Graphs

1.10 Solving Application Problems



2. Multiplying and Dividing Fractions

2.1 Basics of Fractions

2.2 Mixed Numbers

2.3 Factors

2.4 Writing a Fraction in Lowest Terms

2.5 Multiplying Fractions

2.6 Applications of Multiplication

2.7 Dividing Fractions

2.8 Multiplying and Dividing Mixed Numbers



3. Adding and Subtracting Fractions

3.1 Adding and Subtracting Like Fractions

3.2 Least Common Multiples

3.3 Adding and Subtracting Unlike Fractions

3.4 Adding and Subtracting Mixed Numbers

3.5 Order Relations and the Order of Operations



4. Decimals

4.1 Reading and Writing Decimal Numbers

4.2 Rounding Decimal Numbers

4.3 Adding and Subtracting Decimal Numbers

4.4 Multiplying Decimal Numbers

4.5 Dividing Decimal Numbers

4.6 Fractions and Decimals



5. Ratio and Proportion

5.1 Ratios

5.2 Rates

5.3 Proportions

5.4 Solving Proportions

5.5 Solving Application Problems with Proportions



6. Percent

6.1 Basics of Percent

6.2 Percents and Fractions

6.3 Using the Percent Proportion and Identifying the Components in a Percent Problem

6.4 Using Proportions to Solve Percent Problems

6.5 Using the Percent Equation

6.6 Solving Application Problems with Percent

6.7 Simple Interest

6.8 Compound Interest



7. Geometry

7.1 Lines and Angles

7.2 Rectangles and Squares

7.3 Parallelograms and Trapezoids

7.4 Triangles

7.5 Circles

7.6 Volume and Surface Area

7.7 Pythagorean Theorem

7.7 Congruent and Similar Triangles



8. Statistics

8.1 Circle Graphs

8.2 Bar Graphs and Line Graphs

8.3 Frequency Distributions and Histograms

8.4 Mean, Median, and Mode



9. The Real Number System

9.1 Exponents, Order of Operations, and Inequality

9.2 Variables, Expressions, and Equations

9.3 Real Numbers and the Number Line

9.4 Adding Real Numbers

9.5 Subtracting Real Numbers

9.6 Multiplying and Dividing Real Numbers

9.7 Properties of Real Numbers

9.8 Simplifying Expressions



10. Equations, Inequalities, and Applications

10.1 The Addition Property of Equality

10.2 The Multiplication Property of Equality

10.3 More on Solving Linear Equations

10.4 An Introduction to Applications of Linear Equations

10.5 Formulas and Additional Applications from Geometry

10.6 Solving Linear Inequalities



11. Graphs of Linear Equations and Inequalities in Two Variables

11.1 Linear Equations in Two Variables; The Rectangular Coordinate System

11.2 Graphing Linear Equations in Two Variables

11.3 The Slope of a Line

11.4 Writing and Graphing Equations of Lines

11.5 Graphing Linear Inequalities in Two Variables



12. Exponents and Polynomials

12.1 Adding and Subtracting Polynomials

12.2 The Product Rule and Power Rules for Exponents

12.3 Multiplying Polynomials

12.4 Special Products

12.5 Integer Exponents and the Quotient Rule

12.6 Dividing a Polynomial by a Monomial

12.7 Dividing a Polynomial by a Polynomial

12.8 An Application of Exponents: Scientific Notation



13. Factoring and Applications

13.1 Factors; The Greatest Common Factor

13.2 Factoring Trinomials

13.3 Factoring Trinomials by Grouping

13.4 Factoring Trinomials by Using the FOIL Method

13.5 Special Factoring Techniques

13.6 A General Approach to Factoring

13.7 Solving Quadratic Equations by Factoring

13.8 Applications of Quadratic Equations



14. Rational Expressions and Applications

14.1 The Fundamental Property of Rational Expressions

14.2 Multiplying and Dividing Rational Expressions

14.3 Least Common Denominators

14.4 Adding and Subtracting Rational Expressions

14.5 Complex Fractions

14.6 Solving Equations with Rational Expressions

14.7 Applications of Rational Expressions

14.8 Variation



15. Systems of Linear Equations and Inequalities

15.1 Solving Systems of Linear Equations by Graphing

15.2 Solving Systems of Linear Equations by Substitution

15.3 Solving Systems of Linear Equations by Elimination

15.4 Applications of Linear Systems

15.5 Solving Systems of Linear Inequalities



16. Roots and Radicals

16.1 Evaluating Roots

16.2 Multiplying, Dividing, and Simplifying Radicals

16.3 Adding and Subtracting Radicals

16.4 Rationalizing the Denominator

16.5 More Simplifying and Operations with Radicals

16.6 Solving Equations with Radicals



17. Quadratic Equations

17.1 Solving Quadratic Equations by the Square Root Property

17.2 Solving Quadratic Equations by Completing the Square

17.3 Solving Quadratic Equations by the Quadratic Formula

17.4 Graphing Quadratic Equations

17.5 Introduction to Functions

Appendix A: Measurement
A.1 Problem Solving with U.S. Measurement Units
A.2 The Metric System-Length
A.3 The Metric System-Capacity and Weight (Mass)
A.4 Metric-U.S. Measurement Conversions and Temperature
Appendix B: Inductive and Deductive Reasoning
Other Appendices:
- Set Operations and Compound Inequalities
- Absolute Value Equations and Inequalities
- Writing Equations of Parallel and Perpendicular Lines
- Rational Exponents
Answers to Selected Exercises
Solutions to Selected Exercises
Index