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
Table of Contents:
1 Numbers of Algebra
Natural Numbers, Whole Numbers, and Integers
Rational, Irrational, and Real Numbers
Properties of the Real Numbers
2 Computation with Real Numbers
Comparing Numbers and Absolute Value
Addition and Subtraction of Signed Numbers
Multiplication and Division of Signed Numbers
3 Roots and Radicals
Squares, Square Roots, and Perfect Squares
Cube Roots and nth Roots
Simplifying Radicals
4 Exponentiation
Exponents
Natural Number Exponents
Zero and Negative Integer Exponents
Unit Fraction and Rational Exponents
5 Order of Operations
Grouping Symbols
PEMDAS
6 Algebraic Expressions
Algebraic Terminology
Evaluating Algebraic Expressions
Dealing with Parentheses
7 Rules for Exponents
Product Rule
Quotient Rule
Rules for Powers
Rules for Exponents Summary
8 Adding and Subtracting Polynomials
Terms and Monomials
Polynomials
Like Terms
Addition and Subtraction of Monomials
Combining Like Terms
Addition and Subtraction of Polynomials
9 Multiplying Polynomials
Multiplying Monomials
Multiplying Polynomials by Monomials
Multiplying Binomials
The FOIL Method
Multiplying Polynomials
Special Products
10 Simplifying Polynomial Expressions
Identifying Polynomial Expressions
Simplifying Polynomial Expressions
11 Dividing Polynomials
Dividing a Polynomial by a Monomial
Dividing a Polynomial by a Polynomial
12 Factoring Polynomials
Factoring and Its Objectives
Greatest Common Factor
GCF with a Negative Coefficient
A Quantity as a Common Factor
Factoring Four Terms
Factoring Quadratic Trinomials
Factoring Perfect Trinomial Squares
Factoring Binomials
Guidelines for Factoring
13 Rational Expressions
Reducing Algebraic Fractions to Lowest Terms
Multiplying Algebraic Fractions
Dividing Algebraic Fractions
Adding (or Subtracting) Algebraic Fractions, Like Denominators
Adding (or Subtracting) Algebraic Fractions, Unlike Denominators
Simplifying Complex Fractions
14 Solving Linear Equations and Inequalities
Solving One-Variable Linear Equations
Solving Two-Variable Linear Equations for a Specific Variable
Solving One-Variable Linear Inequalities
15 Solving Quadratic Equations
Solving Quadratic Equations of the Form ax2 + c = 0
Solving Quadratic Equations by Factoring
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by Using the Quadratic Formula
16 The Cartesian Coordinate Plane
Definitions for the Plane
Ordered Pairs in the Plane
Quadrants of the Plane
Finding the Distance Between Two Points in the Plane
Finding the Midpoint Between Two Points in the Plane
Finding the Slope of a Line Through Two Points in the Plane
Slopes of Parallel and Perpendicular Lines
17 Graphing Linear Equations
Properties of a Line
Graphing a Linear Equation That Is in Standard Form
Graphing a Linear Equation That Is in Slope-y-Intercept Form
18 The Equation of a Line
Determining the Equation of a Line Given the Slope and y-Intercept
Determining the Equation of a Line Given the Slope and One Point on the Line
Determining the Equation of a Line Given Two Distinct Points on the Line
19 Basic Function Concepts
Representations of a Function
Terminology of Functions
Some Common Functions
20 Systems of Equations
Solutions to a System of Equations
Solving a System of Equations by Substitution
Solving a System of Equations by Elimination
Solving a System of Equations by Graphing
21 Signal Words and Phrases
Common Signal Words and Phrases for Addition
Common Signal Words and Phrases for Subtraction
Common Signal Words and Phrases for Multiplication
Common Signal Words and Phrases for Division
Common Signal Words and Phrases for Equality
22 Word Problems
Algebraic Problem-Solving Process
Be Careful with Units
Age Relationships
Consecutive Numbers
Ratios
Mixtures
Coins
Rate-Time-Distance
Work
Percentage
Simple Interest
Number Relationships
Geometric Shapes
Appendix: Measurement Units and Conversions
Answer Key
Index
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.
