Algebra I For Dummies^®

by Mary Jane Sterling

• ISBN13: 9780764553257
• ISBN10: 0764553259
• Format: Paperback
• Copyright: 2001-09-01
• Publisher: For Dummies

Summary

One of the most commonly asked questions in a mathematics classroom is, "Will I ever use this stuff in real life?" Some teachers can give a good, convincing answer; others hem and haw and stare at the floor. The real response to the question should be, "Yes, you will, because algebra gives you power" - the power to help your children with their math homework, the power to manage your finances, the power to be successful in your career (especially if you have to manage the company budget). The list goes on.Algebra is a system of mathematical symbols and rules that are universally understood, no matter what the spoken language. Algebra provides a clear, methodical process that can be followed from beginning to end to solve complex problems. There's no doubt that algebra can be easy to some while extremely challenging to others. For those of you who are challenged by working with numbers, Algebra For Dummies can provide the help you need.This easy-to-understand reference not only explains algebra in terms you can understand, but it also gives you the necessary tools to solve complex problems. But rest assured, this book is not about memorizing a bunch of meaningless steps; you find out the whys behind algebra to increase your understanding of how algebra works.In Algebra For Dummies, you'll discover the following topics and more: All about numbers - rational and irrational, variables, and positive and negative Figuring out fractions and decimals Explaining exponents and radicals Solving linear and quadratic equations Understanding formulas and solving story problems Having fun with graphs Top Ten lists on common algebraic errors, factoring tips, and divisibility rules.No matter if you're 16 years old or 60 years old; no matter if you're learning algebra for the first time or need a quick refresher course; no matter if you're cramming for an algebra test, helping your kid with his or her homework, or coming up with next year's company budget, Algebra For Dummies can give you the tools you need to succeed.

Author Biography

Mary Jane Sterling has been an educator since graduating from college. Teaching at the junior high, high school, and college levels, she has had the full span of experiences and opportunities while working in education. She has been teaching at Bradley University in Peoria, Illinois, for the past twenty years.

Table of Contents

Introduction.

About This Book.

What Not to Read.

Foolish Assumptions.

How This Book Is Organized.

Where to Go from Here.

Part I: Starting Off with the Basics.

Chapter 1: Assembling Your Tools.

Beginning with the Basics: Numbers.

Varying Variables.

Speaking in Algebra.

Taking Aim at Algebra Operations.

Playing by the Rules.

Chapter 2: Assigning Signs: Positive and Negative Numbers.

Showing Some Signs.

Going In for Operations.

Operating with Signed Numbers.

Working with Nothing: Zero and Signed Numbers.

Associating and Commuting with Expressions.

Chapter 3: Figuring Out Fractions and Dealing with Decimals.

Pulling Numbers Apart and Piecing Them Back Together.

Following the Sterling Low-Fraction Diet.

Fitting Fractions Together.

Putting Fractions to Task.

Dealing with Decimals.

Chapter 4: Exploring Exponents and Raising Radicals.

Multiplying the Same Thing Over and Over and . . . .

Exploring Exponential Expressions.

Multiplying Exponents.

Dividing and Conquering.

Testing the Power of Zero.

Working with Negative Exponents.

Powers of Powers.

Squaring Up to Square Roots.

Chapter 5: Doing Operations in Order and Checking Your Answers.

Ordering Operations.

Checking Your Answers.

Writing Understandable Answers.

Chapter 6: Prepping for Operations.

Realizing Some Restrictions.

Representing Numbers with Letters.

Doing the Math.

Multiplying and Dividing Variables.

Doing It All.

Part II: Figuring Out Factoring.

Chapter 7: Working with Numbers in Their Prime.

Beginning with the Basics.

Composing Composite Numbers.

Writing Prime Factorizations.

Getting Down to the Prime Factor.

Chapter 8: Sharing the Fun: Distributing.

Giving One to Each.

Distributing Signs.

Mixing It Up with Numbers and Variables.

Distributing More than One Term.

Making Special Distributions.

Chapter 9: Factoring in the First Degree.

Factoring.

Grouping Terms.

Chapter 10: Getting the Second Degree.

The Standard Quadratic Expression.

Reining in Big Numbers.

FOILing.

UnFOILing.

Factoring Several Expressions.

Chapter 11: Factoring Special Cases.

Befitting Binomials.

Tinkering with Trinomials and More.

Knowing When to Quit.

Part III: Working Equations.

Chapter 12: Lining Up for Linear Equations.

Solving with Division.

Solving with Multiplication.

Solving with Reciprocals.

Setting Up Equations.

Chapter 13: Solving Linear Equations.

Keeping Equations Balanced.

Playing by the Rules.

Balancing Fractions.

Solving for Variables.

Getting Impossible Answers.

Chapter 14: Taking a Crack at Quadratic Equations.

Squaring Up to Quadratics.

Rooting Out Another Result from Quadratic Equations.

Factoring for a Solution.

Solving Quadratics with Three Terms.

Applying Quadratic Solutions.

Figuring Out the Quadratic Formula.

Chapter 15: Distinguishing Equations with Distinctive Powers.

Queuing Up to Cubic Equations.

Working Quadratic-Like Equations.

Rooting Out Radicals.

Dividing Synthetically.

Chapter 16: Fixing Inequalities.

Operating on Inequalities.

Solving Linear Inequalities.

Working with More Than Two Expressions.

Solving Quadratic Inequalities.

Working with Absolute Value Inequalities.

Part IV: Applying Algebra.

Chapter 17: Making Formulas Behave.

Measuring Up.

Spreading Out: Area Formulas.

Pumping Up with Volume Formulas.

Going the Distance with Distance Formulas.

Calculating Interest and Percent.

Working Out the Combinations and Permutations.

Formulating Your Own Formulas.

Chapter 18: Sorting Out Story Problems.

Setting Up to Solve Story Problems.

Working Around Perimeter, Area, and Volume.

Making Up Mixtures.

Going the Distance.

Righting Right Triangles.

Going 'Round in Circles.

Chapter 19: Going Visual: Graphing.

Graphing is Good.

Grappling with Graphs.

Actually Graphing Points.

Graphing a Line.

Investigating Intercepts.

Sighting the Slope.

Marking Parallel and Perpendicular Lines.

Intersecting Lines.

Curling Up with Parabolas.

Part V: The Part of Tens.

Chapter 20: The Ten Most Common Errors.

Missing Middle Term.

Distributing.

Breaking Up Fractions.

Breaking Up Radicals.

Order of Operations.

Fractional Exponents.

Multiplying Bases Together.

A Power to a Power.

Reducing.

Negative Exponents.

Chapter 21: Ten Ways to Factor a Polynomial.

Two Terms with a GCF.

The Difference of Two Squares.

The Difference of Two Cubes.

The Sum of Two Cubes.

Three Terms with a GCF.

Three Terms with unFOIL.

Changing to Quadratic-Like.

Four or More Terms with a GCF.

Four or More Terms with Equal Grouping.

Four or More Terms with Unequal Grouping.

Chapter 22: Ten Divisibility Rules.

Divisibility by 2.

Divisibility by 3.

Divisibility by 4.

Divisibility by 5.

Divisibility by 6.

Divisibility by 8.

Divisibility by 9.

Divisibility by 10.

Divisibility by 11.

Divisibility by 12.

Chapter 23: Ten Tips for Dealing with Story Problems.

Draw a Picture.

Make a List.

Assign Variables to Represent Numbers.

Translate Conjunctions and Verbs.

Look at the Last Sentence.

Find a Formula.

Simplify by Substituting.

Solve an Equation.

Check for Sense.

Check for Accuracy.

Glossary.

Index.

Book Registration Information.