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Prealgebra and Introductory Algebra,9780321859228
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Prealgebra and Introductory Algebra

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The Lial Series has helped thousands of students succeed in developmental mathematics by providing the best learning and teaching support to students and instructors.

Author Biography

Marge Lial 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.

Table of Contents

1. Introduction to Algebra: Integers

Study Skills: Your Brain Can Learn Mathematics

1.1 Place Value

            Study Skills: Using Your Textbook

1.2 Introduction to Integers

            Study Skills: Homework: How, Why, and When

1.3 Adding Integers

1.4 Subtracting Integers

1.5 Problem Solving: Rounding and Estimating

1.6 Multiplying Integers

1.7 Dividing Integers

            Summary Exercises on Operations with Integers

Study Skills: Taking Lecture Notes

1.8 Exponents and Order of Operations

            Study Skills: Reviewing a Chapter

            Study Skills: Managing Your Time


2. Understanding Variables and Solving Equations

2.1 Introduction to Variables

            Study Skills: Using Study Cards

2.2 Simplifying Expressions

            Study Skills: Using Study Cards Revisited

Summary Exercises on Variables and Expressions

2.3 Solving Equations Using Addition

2.4 Solving Equations Using Division

2.5 Solving Equations with Several Steps

            Study Skills: Tips for Taking Math Tests


3. Solving Application Problems

3.1 Problem Solving: Perimeter

3.2 Problem Solving: Area

            Summary Exercises on Perimeter and Area

3.3 Solving Application Problems with One Unknown Quantity

3.4 Solving Application Problems with Two Unknown Quantities

            Study Skills: Tips for Improving Test Scores

            Math in the Media: Formulas: Predicting a Young Child's Vocabulary


4. Rational Numbers: Positive and Negative Fractions

4.1 Introduction to Signed Fractions

4.2 Writing Fractions in Lowest Terms

4.3 Multiplying and Dividing Signed Fractions

4.4 Adding and Subtracting Signed Fractions

            Study Skills: Making a Mind Map

4.5 Problem Solving: Mixed Numbers and Estimating

            Summary Exercises on Fractions

4.6 Exponents, Order of Operations, and Complex Fractions

4.7 Problem Solving: Equations Containing Fractions

4.8 Geometry Applications: Area and Volume

            Study Skills: Analyzing Your Test Results


5. Rational Numbers: Positive and Negative Decimals

5.1 Reading and Writing Decimal Numbers

5.2 Rounding Decimal Numbers

5.3 Adding and Subtracting Signed Decimal Numbers

5.4 Multiplying Signed Decimal Numbers

5.5 Dividing Signed Decimal Numbers

            Summary Exercises on Decimals

5.6 Fractions and Decimals

5.7 Problem Solving with Statistics: Mean, Median, and Mode

5.8 Geometry Applications: Pythagorean Theorem and Square Roots

5.9 Problem Solving: Equations Containing Decimals

5.10 Geometry Applications: Circles, Cylinders, and Surface Area


6. Ratio, Proportion, and Line/Angle/Triangle Relationships

6.1 Ratios

6.2 Rates

6.3 Proportions

            Summary Exercises on Ratios, Rates, and Proportions

6.4 Problem Solving with Proportions

6.5 Geometry: Lines and Angles

6.6 Geometry Applications: Congruent and Similar Triangles


7. Percent

7.1 The Basics of Percent

7.2 The Percent Proportion

7.3 The Percent Equation

Summary Exercises on Percent

7.4 Problem Solving with Percent

7.5 Consumer Applications: Sales Tax, Tips, Discounts, and Simple Interest

Study Skills: Preparing for Your Final Exam


8. Measurement

8.1 Problem Solving with U.S. Measurement Units

8.2 The Metric System-Length

8.3 The Metric System-Capacity and Weight (Mass)

            Summary Exercises on U.S. and Metric Measurement Units

8.4 Problem Solving with Metric Measurements

8.5 Metric-U.S. Measurement Conversions and Temperature


9. Graphs

9.1 Problem Solving with Tables and Pictographs

9.2 Reading and Constructing Circle Graphs

9.3 Bar Graphs and Line Graphs

9.4 The Rectangular Coordinate System

9.5 Introduction to Graphing Linear Equations


10. Real Numbers, Equations, and Inequalities

10.1 Real Numbers and Expressions

10.2 More on Solving Linear Equations

10.3 Formulas and Solving for a Specified Variable

10.4 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

Summary Exercises: Applying Graphing and Equation-Writing Techniques for Lines

11.5 Graphing Linear Inequalities in Two Variables


12. Systems of Equations and Inequalities

12.1 Solving Systems of Linear Equations by Graphing

12.2 Solving Systems of Linear Equations by Substitution

12.3 Solving Systems of Linear Equations by Elimination

Summary Exercises: Applying Techniques for Solving Systems of Linear Equations

12.4 Application of Linear Systems

12.5 Solving Systems of Linear Inequalities


13. Exponents and Polynomials

13.1 Adding and Subtracting Polynomials

13.2 The Product Rule and Power Rules for Exponents

13.3 Multiplying Polynomials

13.4 Special Products

13.5 Integer Exponents and the Quotient Rule

            Summary Exercises: Applying the Rules for Exponents

13.6 Dividing a Polynomial by a Monomial

13.7 Dividing a Polynomial by a Polynomial

13.8 An Application of Exponents: Scientific Notation


14. Factoring and Applications

14.1 Factors; The Greatest Common Factor

14.2 Factoring Trinomials

14.3 Factoring Trinomials by Grouping

14.4 Factoring Trinomials Using FOIL

14.5 Special Factoring Techniques

            Summary Exercises: Recognizing and Applying Factoring Strategies

14.6 Solving Quadratic Equations by Factoring

14.7 Applications of Quadratic Equations


15. Rational Expressions and Applications

15.1 The Fundamental Property of Rational Expressions

15.2 Multiplying and Dividing Rational Expressions

15.3 Least Common Denominators

15.4 Adding and Subtracting Rational Expressions

15.5 Complex Fractions

15.6 Solving Equations with Rational Expressions

Summary Exercises: Simplifying Rational Expressions vs. Solving Rational Equations

15.7 Applications of Rational Expressions

15.8 Variation


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

            Summary Exercises: Applying 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

            Summary Exercises: Applying Methods for Solving Quadratic Equations

17.4 Graphing Quadratic Equations

17.5 Introduction to Functions


R. Whole Numbers Review

R.1 Adding Whole Numbers

R.2 Subtracting Whole Numbers

R.3 Multiplying Whole Numbers

R.4 Dividing Whole Numbers

R.5 Long Division


Appendix A: Inductive and Deductive Reasoning

Appendix B: Set Operations and Compound Inequalities*

Appendix C: Absolute Value Equations and Inequalities*

Appendix D: Writing Equations of Parallel and Perpendicular Lines*

Appendix E: Factoring Sums and Differences Cubes*

Appendix F: The Distance and Midpoint Formulas*

Appendix G: Rational Exponents*


*Available in MyMathLab®


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