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More About This Textbook
Overview
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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
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 SystemLength
8.3 The Metric SystemCapacity and Weight (Mass)
Summary Exercises on U.S. and Metric Measurement Units
8.4 Problem Solving with Metric Measurements
8.5 MetricU.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 EquationWriting 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^{®}