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Meet the Author
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 bestselling 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.
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
Preface.
Whole Numbers Computation: Diagnostic Test.
1. Introduction to Algebra: Integers.
Place Value.
Introduction to Signed Numbers.
Adding Integers.
Study Tips: Using Your Textbook.
Subtracting Integers.
Rounding and Estimating.
Study Tips: Keys to Remembering What You Study.
Multiplying Integers.
Dividing Integers.
Numbers in the Real World: Wedding Expenses.
Exponents and Order of Operations.
2. Understanding Variables and Solving Equations.
Introduction to Variables.
Simplifying Expressions.
Numbers in the Real World: Expressions.
Solving Equations Using Addition.
Study Tips: Preparing for a Test.
Solving Equations Using Division.
Solving Equations with Several Steps.
3. Solving Application Problems.
Problem Solving: Perimeter.
Problem Solving: Area.
Application Problems with One Unknown Quantity.
Numbers in the Real World: Formulas.
Application Problems with Two Unknown Quantities.
Study Tips: Taking a Test
4. Rational Numbers: Positive and Negative Fractions.
Introduction to Positive and Negative Fractions.
Numbers in the Real World: Quilt Patterns.
Writing Fractions in Lowest Terms.
Multiplying and Dividing Signed Fractions.
Adding and Subtracting Signed Fractions.
Numbers in the Real World: Music.
Problem Solving: Mixed Numbers and Estimating.
Numbers in the Real World: Sharing Hotel Expenses.
Exponents, Order of Operations, and Complex Fractions.
Numbers in the RealWorld: Recipes.
Problem Solving: Equations Containing Fractions.
Geometry Applications: Area and Volume.
Numbers in the Real World: Stock Market.
5. Positive and Negative Decimal Numbers.
Reading and Writing Decimal Numbers.
Rounding Decimal Numbers.
Adding and Subtracting Decimal Numbers.
Multiplying Decimal Numbers.
Dividing Decimal Numbers.
Fractions and Decimals.
Introduction to Statistics: Mean, Median, Mode, and Variability.
Geometry Applications: Pythagorean Theorem.
Problem Solving: Equations Containing Decimals.
Numbers in the Real World: Lawn Fertilizer.
Geometry Applications: Circles, Cylinders, and Surface Area.
6. Ratio, Proportion, and Line/Angle/Triangle Relationships.
Ratios.
Rates.
Proportions.
Problem Solving: Proportions.
Geometry: Lines and Angles.
Geometry Applications: Congruent and Similar Triangles.
7. Percent.
The Basics of Percent.
The Percent Proportion.
The Percent Equation.
Problem Solving with Percent.
Numbers in the Real World: Feeding Hummingbirds.
Consumer Applications: Sales Tax, Tips, and Discounts.
Problem Solving: Simple and Compound Interest.
Numbers in the Real World: Making Your Investments Grow.
8. Measurement.
The English System.
Numbers in the Real World: Growing Sunflowers.
The Metric SystemLength.
Numbers in the Real World: Measuring Up.
The Metric SystemCapacity and Mass (Weight).
Problem Solving: Metric Measurement.
MetricEnglish Conversions and Temperature Formulas.
9. Graphs.
Reading and Interpreting Tables and Pictographs.
Reading and Constructing Circle Graphs.
Bar Graphs and Line Graphs.
Numbers in the Real World: Grocery Shopping.
The Rectangular Coordinate System.
10. Real Numbers, Equations, and Inequalities.
Real Numbers and Expressions.
More on Solving Linear Equations.
Formulas and Solving for a Specified Variable.
Solving Inequalities.
11. Exponents and Polynomials.
The Product Rule and Power Rules for Exponents.
Numbers in the Real World: Do You Have the Knack for Percent?
Integer Exponents and the Quotient Rule.
An Application of Exponents: Scientific Notation.
Addition and Subtraction of Polynomials.
Multiplication of Polynomials.
Products of Binomials.
Division of a Polynomial by a Monomial.
The Quotient of Two Polynomials.
12. Factoring.
Factors; The Greatest Common Factor.
Numbers in the Real World: Number Patterns in our World.
Factoring Trinomials.
Numbers in the Real World: Using Number Properties in Identification.
More on Factoring Trinomials.
Numbers in the Real World: The Influence of Spanish Coinage on Stock Prices.
Special Factorizations.
Summarizing Exercises by Factoring.
Solving Quadratic Equations by Factoring.
Numbers in the Real World: Using Computers to Break Codes.
Applications of Quadratic Equations.
13. Rational Expressions.
The Fundamental Property of Rational Expressions.
Numbers in the Real World: The Dangers of Ultraviolet Rays.
Multiplication and Division of Rational Expressions.
Least Common Denominators.
Numbers in the Real World: Statistics Require Careful Interpretation.
Addition and Subtraction of Rational Expressions.
Numbers in the Real World: Number Magic.
Complex Fractions.
Equations Involving Rational Expressions.
Numbers in the Real World: Geometry in Our World.
Summary Exercises on Rational Expressions.
Applications of Rational Expressions.
Numbers in the Real World: Big Numbers in Our World (and Others)...And Just How Big Is a Googol?
14. Linear Equations and Inequalities in Two Variables.
Introduction to Graphing Linear Equations.
Graphing Linear Equations in Two Variables.
Numbers in the Real World: Some Facts and Figures on Children's Allowances.
The Slope of a Line.
Equations of a Line.
Graphing Linear Inequalities in Two Variables.
Graphing Direct and Inverse Variation.
15. Linear Systems of Equations and Inequalities.
Solving Systems of Linear Equations by Graphing.
Solving Systems of Linear Equations by Addition.
Solving Systems of Linear Equations by Substitution.
Application of Linear Systems.
Solving Systems of Linear Inequalities.
16. Roots and Radicals.
Finding Roots.
Multiplication and Division of Radicals.
Addition and Subtraction of Radicals.
Rationalizing the Denominator.
Simplifying Radical Expressions.
Equations with Radicals.
Numbers in the Real World: Are You a Good "Guesstimator" ?
17. Quadratic Equations.
Solving Quadratic Equations by the Square Root Property.
Numbers in the Real World: A Mathematical Model of the Spread of AIDS.
Solving Quadratic Equations by Completing the Square.
Solving Quadratic Equations by the Quadratic Formula.
Summary Exercises on Quadratic Equations.
Using Function Notation for Quadratic Equations.
Graphing Quadratic Equations and Inequalities.
R. Whole Numbers Review.
Addition of Whole Numbers.
Subtraction of Whole Numbers.
Multiplication of Whole Numbers.
Division of Whole Numbers.
Long Division.
Appendix A: Scientific Calculators
Appendix B: Inductive and Deductive Reasoning.
Numbers in the Real World: Lifetime Earnings.
Answers to Selected Exercises
Index.
TASP Index.
Index of Applications.