Easy Algebra Step-by-Step, Second Edition

by William Clark, Sandra Luna McCune

Overview

The Quick and Effective Way to Learn Algebra

The fastest way to learn algebra is to build a solid foundation in the basics. Inside this book you won’t find a lot of endless drills. Instead, you get an original, step-by-step approach to learning algebra. In your first steps, you are introduced to essential concepts—allowing you to grasp the subject almost immediately. You will gradually progress to more challenging skills. Along the way, the authors show you how to solve practical problems using clear, step-by-step instructions. Exercises for each section, with detailed, worked-out solutions, will let you check your progress. In no time at all, you will have acquired the knowledge and skills you need to solve algebraic problems with confidence.

Easy Step-by-Step Algebra features:

• A unique building-block approach to mastering algebra

• Down-to-earth explanations of important rules and concepts

• Sample problems that are carefully explained—step by step

• Insights on how to avoid common mistakes

• Exercises to practice what you’ve learned and measure your progress

• Brand-new chapters—Signal Words and Phrases and Word Problems—that will round out your new set of math skills

Product Details

ISBN-13:	9781260025927
Publisher:	McGraw-Hill Professional Publishing
Publication date:	12/04/2017
Pages:	304
Sales rank:	1,039,066
Product dimensions:	7.30(w) x 9.10(h) x 0.80(d)

About the Author

Sandra Luna McCune, PhD, is a former Regents Professor who taught as a mathematics specialist at Stephen F. Austin State University. She is currently an in-demand consultant on math and statistics.

William D. Clark, PhD, is a professor of mathematics at Stephen F. Austin State University.

Table of Contents

Preface ix

1 Numbers of Algebra 1

Natural Numbers, Whole Numbers, and Integers 1

Rational, Irrational, and Real Numbers 4

Properties of the Real Numbers 8

2 Computation with Real Numbers 14

Comparing Numbers and Absolute Value 14

Addition and Subtraction of Signed Numbers 17

Multiplication and Division of Signed Numbers 26

3 Roots and Radicals 32

Squares, Square Roots, and Perfect Squares 32

Cube Roots and nth Roots 36

Simplifying Radicals 39

4 Exponentiation 44

Exponents 44

Natural Number Exponents 45

Zero and Negative Integer Exponents 48

Unit Fraction and Rational Exponents 53

5 Order of Operations 58

Grouping Symbols 58

PEMDAS 60

6 Algebraic Expressions 64

Algebraic Terminology 64

Evaluating Algebraic Expressions 66

Dealing with Parentheses 70

7 Rules for Exponents 74

Product Rule 74

Quotient Rule 75

Rules for Powers 77

Rules for Exponents Summary 79

8 Adding and Subtracting Polynomials 83

Terms and Monomials 83

Polynomials 85

Like Terms 87

Addition and Subtraction of Monomials 88

Combining Like Terms 89

Addition and Subtraction of Polynomials 90

9 Multiplying Polynomials 94

Multiplying Monomials 94

Multiplying Polynomials by Monomials 96

Multiplying Binomials 98

The FOIL Method 99

Multiplying Polynomials 101

Special Products 103

10 Simplifying Polynomial Expressions 104

Identifying Polynomial Expressions 104

Simplifying Polynomial Expressions 106

11 Dividing Polynomials 110

Dividing a Polynomial by a Monomial 110

Dividing a Polynomial by a Polynomial 113

12 Factoring Polynomials 119

Factoring and Its Objectives 119

Greatest Common Factor 120

GCF with a Negative Coefficient 123

A Quantity as a Common Factor 125

Factoring Four Terms 126

Factoring Quadratic Trinomials 127

Factoring Perfect Trinomial Squares 133

Factoring Binomials 134

Guidelines for Factoring 137

13 Rational Expressions 139

Reducing Algebraic Fractions to Lowest Terms 139

Multiplying Algebraic Fractions 143

Dividing Algebraic Fractions 145

Adding (or Subtracting) Algebraic Fractions, Like Denominators 146

Adding (or Subtracting) Algebraic Fractions, Unlike Denominators 148

Simplifying Complex Fractions 151

14 Solving Linear Equations and Inequalities 154

Solving One-Variable Linear Equations 154

Solving Two-Variable Linear Equations for a Specific Variable 159

Solving One-Variable Linear Inequalities 160

15 Solving Quadratic Equations 163

Solving Quadratic Equations of the Form ax² + c = 0 163

Solving Quadratic Equations by Factoring 165

Solving Quadratic Equations by Completing the Square 166

Solving Quadratic Equations by Using the Quadratic Formula 167

16 The Cartesian Coordinate Plane 171

Definitions for the Plane 171

Ordered Pairs in the Plane 171

Quadrants of the Plane 174

Finding the Distance Between Two Points in the Plane 176

Finding the Midpoint Between Two Points in the Plane 177

Finding the Slope of a Line Through Two Points in the Plane 178

Slopes of Parallel and Perpendicular Lines 181

17 Graphing Linear Equations 184

Properties of a Line 184

Graphing a Linear Equation That Is in Standard Form 184

Graphing a Linear Equation That Is in Slope-y-Intercept Form 186

18 The Equation of a Line 189

Determining the Equation of a Line Given the Slope and y-Intercept 189

Determining the Equation of a Line Given the Slope and One Point on the Line 190

Determining the Equation of a Line Given Two Distinct Points on the Line 192

19 Basic Function Concepts 195

Representations of a Function 195

Terminology of Functions 197

Some Common Functions 201

20 Systems of Equations 205

Solutions to a System of Equations 205

Solving a System of Equations by Substitution 206

Solving a System of Equations by Elimination 208

Solving a System of Equations by Graphing 210

21 Signal Words and Phrases 213

Common Signal Words and Phrases for Addition 213

Common Signal Words and Phrases for Subtraction 215

Common Signal Words and Phrases for Multiplication 217

Common Signal Words and Phrases for Division 219

Common Signal Words and Phrases for Equality 221

22 Word Problems 225

Algebraic Problem-Solving Process 225

Be Careful with Units 227

Age Relationships 227

Consecutive Numbers 229

Ratios 231

Mixtures 232

Coins 235

Rate-Time-Distance 237

Work 238

Percentage 240

Simple Interest 243

Number Relationships 244

Geometric Shapes 246

Appendix: Measurement Units and Conversions 249

Answer Key 251

Index 283