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Algebra for Dummies
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Introduction
About this Book
Conventions used in this book
What you're not to read
Foolish Assumptions
How This Book Is Organized
Part I: Starting Off with the Basics
Part II: Figuring Out Factoring
Part III: Working Equations
Part IV: Applying Algebra
Part V: The Part of Tens
Icons Used in This Book
Where to Go from Here .
Part I: Starting Off with the Basics
Chapter 1: Assembling Your Tools
Beginning with the Basics: Numbers
Really real numbers
Counting on natural numbers
Wholly whole numbers
Integrating integers
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Being reasonable: Rational numbers
Restraining irrational numbers
Picking out primes and composites
Speaking in Algebra
Taking Aim at Algebra Operations
Deciphering the symbols
Grouping
Defining relationships
Taking on algebraic tasks
Chapter 2: Assigning Signs: Positive and Negative Numbers
Showing Some Signs
Picking out positive numbers
Making the most of negative numbers
Comparing positives and negatives
Zeroing in on zero
Going In for Operations
Breaking into binary operations
Introducing non-binary operations
Operating with Signed Numbers
Adding like to like: Same-signed numbers
Adding different signs
Subtracting signed numbers
Multiplying and dividing signed numbers
Working with Nothing: Zero and Signed Numbers
Associating and Commuting with Expressions
Reordering operations: The commutative property
Associating expressions: The associative property
Chapter 3: Figuring Out Fractions and Dealing with Decimals
Pulling Numbers Apart and Piecing Them Back Together
Making your bow to proper fractions
Getting to know improper fractions
Mixing it up with mixed numbers
Following the Sterling Low-Fraction Diet
Inviting the loneliest number on
Figuring out equivalent fractions
Realizing why smaller or fewer is better
Preparing Fractions for Interactions
Finding common denominators
Working with improper fractions
Taking Fractions to Task
Adding and subtracting fractions
Multiplying fractions
Dividing fractions
Dealing with Decimals
Changing fractions to decimals
Changing decimals to fractions
Chapter 4: Exploring Exponents and Raising Radicals
Multiplying the Same Thing Over and Over and Over
Powering up exponential notation
Comparing with exponents
Taking notes on scientific notation
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
Gathering Terms with Grouping Symbols
Checking Your Answers
Making sense or cents or scents
Plugging in to get a charge of your answer
Curbing a Variable’s Versatility
Representing numbers with letters
Attaching factors and coefficients
Interpreting the operations
Doing the Math
Adding and subtracting variables
Adding and subtracting with powers
Multiplying and Dividing Variables
Multiplying variables
Dividing variables
Doing it all
Part II: Figuring Out Factoring
Chapter 6: Working with Numbers in Their Prime
Beginning with the Basics
Composing Composite Numbers
Writing Prime Factorizations
Dividing while standing on your head
Getting to the root of primes with a tree
Wrapping your head around the rules of divisibility
Getting Down to the Prime Factor
Taking primes into account .
Pulling out factors and leaving the rest
Chapter 7: Sharing the Fun: Distribution
Giving One to Each
Distributing first
Adding first
Distributing Signs
Distributing positives
Distributing negatives
Reversing the roles in distributing
Mixing It Up with Numbers and Variables
Negative exponents yielding fractional answers
Working with fractional powers
Distributing More Than One Term
Distributing binomials
Distributing trinomials
Multiplying a polynomial times another polynomial .
Making Special Distributions
Recognizing the perfectly squared binomial
Spotting the sum and difference of the same two terms
Working out the difference and sum of two cubes
Chapter 8: Getting to First Base with Factoring
Factoring
Factoring out numbers
Factoring out variables
Unlocking combinations of numbers and variables
Changing factoring into a division problem
Grouping Terms
Chapter 9: Getting the Second Degree
The Standard Quadratic Expression
Reining in Big and Tiny Numbers
FOILing
FOILing basics
FOILed again, and again
Applying FOIL to a special product
UnFOILing
Unwrapping the FOILing package
Coming to the end of the FOIL roll
Making Factoring Choices
Combining unFOIL and the greatest common factor
Grouping and unFOILing in the same package
Chapter 10: Factoring Special Cases
Befitting Binomials
Factoring the difference of two perfect squares
Factoring the difference of perfect cubes
Factoring the sum of perfect cubes
Tinkering with Multiple Factoring Methods
Starting with binomials
Ending with binomials
Knowing When to Quit .
Incorporating the Remainder Theorem
Synthesizing with synthetic division
Choosing numbers for synthetic division
Part III: Working Equations
Chapter 11: Establishing Ground Rules for Solving Equations
Creating the Correct Setup for Solving Equations
Keeping Equations Balanced
Balancing with binary operations
Squaring both sides and suffering the consequences
Taking a root of both sides
Undoing an operation with its opposite
Solving with Reciprocals
Making a List and Checking It Twice
Doing a reality check
Thinking like a car mechanic when checking your work
Finding a Purpose
Chapter 12: Solving Linear Equations
Playing by the Rules
Solving Equations with Two Terms
Devising a method using division
Making the most of multiplication
Reciprocating the invitation .
Extending the Number of Terms to Three
Eliminating the extra constant term
Vanquishing the extra variable term
Simplifying to Keep It Simple
Nesting isn’t for the birds
Distributing first
Multiplying or dividing before distributing .
Featuring Fractions
Promoting practical proportions
Transforming fractional equations into proportions
Solving for Variables in Formulas.
Chapter 13: Taking a Crack at Quadratic Equations
Squaring Up to Quadratics
Rooting Out Results from Quadratic Equations
Factoring for a Solution
Zeroing in on the multiplication property of zero
Assigning the greatest common factor and multiplication
property of zero to solving quadratics
Solving Quadratics with Three Terms
Applying Quadratic Solutions
Figuring Out the Quadratic Formula
Imagining the Worst with Imaginary Numbers
Chapter 14: Distinguishing Equations with Distinctive Powers
Queuing Up to Cubic Equations
Solving perfectly cubed equations
Working with the not-so-perfectly cubed
Going for the greatest common factor
Grouping cubes .
Solving cubics with integers
Working Quadratic-Like Equations
Rooting Out Radicals.
Powering up both sides
Squaring both sides twice
Solving Synthetically
Chapter 15: Rectifying Inequalities
Translating between Inequality and Interval Notation
Intervening with interval notation .
Grappling with graphing inequalities
Operating on Inequalities
Adding and subtracting inequalities
Multiplying and dividing inequalities
Solving Linear Inequalities .
Working with More Than Two Expressions
Solving Quadratic and Rational Inequalities
Working without zeros
Dealing with more than two factors
Figuring out fractional inequalities
Working with Absolute-Value Inequalities
Working absolute-value equations
Working absolute-value inequalities
Part IV: Applying Algebra
Chapter 16: Taking Measure with Formulas
Measuring Up .
Finding out how long: Units of length
Putting the Pythagorean theorem to work
Working around the perimeter
Spreading Out: Area Formulas .
Laying out rectangles and squares
Tuning in triangles
Going around in circles
Pumping Up with Volume Formulas
Prying into prisms and boxes
Cycling cylinders.
Scaling a pyramid
Pointing to cones
Rolling along with spheres
Chapter 17: Formulating for Profit and Pleasure
Going the Distance with Distance Formulas
Calculating Interest and Percent
Compounding interest formulas
Gauging taxes and discounts
Working Out the Combinations and Permutations
Counting down to factorials
Counting on combinations
Ordering up permutations
Chapter 18: Sorting Out Story Problems
Setting Up to Solve Story Problems
Working around Perimeter, Area, and Volume
Parading out perimeter and arranging area
Adjusting the area
Pumping up the volume
Making Up Mixtures
Mixing up solutions
Tossing in some solid mixtures
Investigating investments and interest
Going for the green: Money
Going the Distance .
Figuring distance plus distance
Figuring distance and fuel.
Going ’Round in Circles
Chapter 19: Going Visual: Graphing
Graphing Is Good
Grappling with Graphs
Making a point
Ordering pairs, or coordinating coordinates
Actually Graphing Points
Graphing Formulas and Equations
Lining up a linear equation
Going around in circles with a circular graph
Throwing an object into the air
Curling Up with Parabolas .
Trying out the basic parabola
Putting the vertex on an axis
Sliding and multiplying
Chapter 20: Lining Up Graphs of Lines
Graphing a Line
Graphing the equation of a line.
Investigating Intercepts
Sighting the Slope
Formulating slope
Combining slope and intercept
Getting to the slope-intercept form
Graphing with slope-intercept
Marking Parallel and Perpendicular Lines
Intersecting Lines
Graphing for intersections
Substituting to find intersections
Part V: The Part of Tens
Chapter 21: The Ten Best Ways to Avoid Pitfalls
Keeping Track of the Middle Term
Distributing: One for You and One for Me.
Breaking Up Fractions (Breaking Up Is Hard to Do)
Renovating Radicals
Order of Operations
Fractional Exponents
Multiplying Bases Together
A Power to a Power
Reducing for a Better Fit
Negative Exponents
Chapter 22: The Ten Most Famous Equations
Albert Einstein’s Theory of Relativity ..
The Pythagorean Theorem
The Value of e
Diameter and Circumference Related with Pi .
Isaac Newton’s Formula for the Force of Gravity
Euler’s Identity
Fermat’s Last Theorem .
Monthly Loan Payments
The Absolute-Value Inequality ...
The Quadratic Formula .
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