Prealgebra

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. 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.""

Pretest: Whole Numbers Computation

 

1. Introduction to Algebra: Integers

Study Skills Your Brain Can Learn Mathematics

1.1 Place Value

Study Skills Using Your Text

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 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 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 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

 

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 Computation with 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 Computation with Decimal Numbers

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 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 Percent Computation

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 U.S. and Metric Measurement Units

8.4 Problem Solving with Metric Measurement

8.5 Metric—U.S. Measurement Conversions and Temperature

 

9. Graphs and Graphing

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. Exponents and Polynomials

10.1 The Product Rule and Power Rules for Exponents

10.2 Integer Exponents and the Quotient Rule

Summary Exercises Using Exponent Rules

10.3 An Application of Exponents: Scientific Notation

10.4 Adding and Subtracting Polynomials

10.5 Multiplying Polynomials: An Introduction

 

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

8.3 The Metric System–Capacity and Weight (Mass)

Summary Exercises U.S. and Metric Measurement Units

8.4 Problem Solving with Metric Measurement

8.5 Metric—U.S. Measurement Conversions and Temperature

 

Appendix: Inductive and Deductive Reasoning