Basic Math, Introductory & Intermediate Algebra

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. Measurement

7.1 Problem Solving with U.S. Measurement Units

7.2 The Metric System – Length

7.3 The Metric System – Capacity and Weight (Mass)

7.4 Problem Solving with Metric Measurement

7.5 Metric—U.S. Measurement Conversions and Temperature

 

8. Geometry

8.1 Basic Geometric Terms

8.2 Angles and Their Relationships

8.3 Rectangles and Squares

8.4 Parallelograms and Trapezoids

8.5 Triangles

8.6 Circles

8.7 Volume

8.8 Pythagorean Theorem

8.9 Similar Triangles

 

9. Introduction to Basic Algebra

9.1 Signed Numbers

9.2 Adding and Subtracting Signed Numbers

9.3 Multiplying and Dividing Signed Numbers

9.4 Order of Operations

9.5 Evaluating Expressions and Formulas

9.6 Solving Equations

9.7 Solving Equations with Several Steps

9.8 Using Equations to Solve Application Problems

 

10. Statistics

10.1 Circle Graphs

10.2 Bar Graphs and Line Graphs

10.3 Frequency Distributions and Histograms

10.4 Mean, Median, and Mode

 

11. The Real Number System

11.1 Exponents, Order of Operations, and Inequality

11.2 Variables, Expressions, and Equations

11.3 Real Numbers and the Number Line

11.4 Adding Real Numbers

11.5 Subtracting Real Numbers

11.6 Multiplying and Dividing Real Numbers

11.7 Properties of Real Numbers

11.8 Simplifying Expressions

 

12. Equations, Inequalities, and Applications

12.1 The Addition Property of Equality

12.2 The Multiplication Property of Equality

12.3 More on Solving Linear Equations

12.4 An Introduction to Applications of Linear Equations

12.5 Formulas and Additional Applications from Geometry

12.6 Ratio, Proportion, and Percent

12.7 Solving Linear Inequalities

 

13. Graphs of Linear Equations and Inequalities in Two Variables; Functions

13.1 Linear Equations in Two Variables; The Rectangular Coordinate System

13.2 Graphing Linear Equations in Two Variables

13.3 The Slope of a Line

13.4 Writing and Graphing Equations of Lines

13.5 Graphing Linear Inequalities in Two Variables

13.6 Introduction to Relations and Functions

13.7 Function Notation and Linear Functions

 

14. Systems of Linear Equations and Inequalities

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 Elimination

14.4 Applications of Linear Systems

14.5 Solving Systems of Linear Inequalities

 

15. Exponents and Polynomials

15.1 Adding and Subtracting Polynomials

15.2 The Product Rule and Power Rules for Exponents

15.3 Multiplying Polynomials

15.4 Special Products

15.5 Integer Exponents and the Quotient Rule

15.6 Dividing a Polynomial by a Monomial

15.7 Dividing a Polynomial by a Polynomial

15.8 An Application of Exponents: Scientific Notation

 

16. Factoring and Applications

16.1 Factors; The Greatest Common Factor

16.2 Factoring Trinomials

16.3 Factoring Trinomials by Grouping

16.4 Factoring Trinomials by Using the FOIL Method

16.5 Special Factoring Techniques

16.6 A General Approach to Factoring

16.7 Solving Quadratic Equations by Factoring

16.8 Applications of Quadratic Equations

 

17. Rational Expressions and Functions

17.1 Rational Expressions and Functions; Multiplying and Dividing

17.2 Adding and Subtracting Rational Expressions

17.3 Complex Fractions

17.4 Equations with Rational Expressions and Graphs

17.5 Applications of Rational Expressions

17.6 Variation

 

18. Equations, Inequalities, and Systems Revisited

18.1 Review of Solving Linear Equations and Inequalities

18.2 Set Operations and Compound Inequalities

18.3 Absolute Value Equations and Inequalities

18.4 Review of Systems of Linear Equations in Two Variables

18.5 Systems of Linear Equations in Three Variables; Applications

 

19. Roots, Radicals, and Root Functions

19.1 Radical Expressions and Graphs

19.2 Rational Exponents

19.3 Simplifying Radical Expressions

19.4 Adding and Subtracting Radical Expressions

19.5 Multiplying and Dividing Radical Expressions

19.6 Solving Equations with Radicals

19.7 Complex Numbers

 

20. Quadratic Equations, Inequalities, and Functions

20.1 Solving Quadratic Equations by the Square Root Property

20.2 Solving Quadratic Equations by Completing the Square

20.3 Solving Quadratic Equations by the Quadratic Formula

20.4 Equations Quadratic in Form

20.5 Formulas and Applications

20.6 Graphs of Quadratic Functions

20.7 More about Parabolas and Their Applications

20.8 Polynomial and Rational Inequalities

 

21. Inverse, Exponential, and Logarithmic Functions

21.1 Operations on Functions and Composition

21.2 Inverse Functions

21.3 Exponential Functions

21.4 Logarithmic Functions

21.5 Properties of Logarithms

21.6 Common and Natural Logarithms

21.7 Exponential and Logarithmic Equations and Their Applications

 

22. Nonlinear Functions, Conic Sections, and Nonlinear Systems

22.1 Additional Graphs of Functions; Operations and Composition

22.2 The Circle and the Ellipse

22.3 The Hyperbola and Other Functions Defined by Radicals

22.4 Nonlinear Systems of Equations

22.5 Second-Degree Inequalities and Systems of Inequalities

 

Appendix A. Inductive and Deductive Reasoning

Appendix B. Solving Systems of Linear Equations by Matrix Methods

Appendix C. Synthetic Division