Basic Math and Pre-Algebra For Dummies, 2nd Edition

Table of contents

1. 1. Introduction
      1. About This Book
      2. Foolish Assumptions
      3. Icons Used in This Book
      4. Beyond the Book
      5. Where to Go from Here
   2. Part I: Getting Started with Basic Math and Pre-Algebra
      1. Chapter 1: Arming Yourself with the Basics of Basic Math
         1. Inventing Numbers
         2. Understanding Number Sequences
            1. Evening the odds
            2. Counting by threes, fours, fives, and so on
            3. Getting square with square numbers
            4. Composing yourself with composite numbers
            5. Stepping out of the box with prime numbers
            6. Multiplying quickly with exponents
         3. Looking at the Number Line
            1. Adding and subtracting on the number line
            2. Getting a handle on nothing, or zero
            3. Taking a negative turn: Negative numbers
            4. Multiplying the possibilities
            5. Dividing things up
            6. Discovering the space in between: Fractions
         4. Four Important Sets of Numbers
            1. Counting on the counting numbers
            2. Introducing integers
            3. Staying rational
            4. Getting real
      2. Chapter 2: Arming Yourself with the Basics of Basic Math
         1. Knowing Your Place Value
            1. Counting to ten and beyond
            2. Telling placeholders from leading zeros
            3. Reading long numbers
         2. Close Enough for Rock ’n’ Roll: Rounding and Estimating
            1. Rounding numbers
            2. Estimating value to make problems easier
      3. Chapter 3: Arming Yourself with the Basics of Basic Math
         1. Adding Things Up
            1. In line: Adding larger numbers in columns
            2. Carry on: Dealing with two-digit answers
         2. Take It Away: Subtracting
            1. Columns and stacks: Subtracting larger numbers
            2. Can you spare a ten? Borrowing to subtract
         3. Multiplying
            1. Signs of the times
            2. Memorizing the multiplication table
            3. Double digits: Multiplying larger numbers
         4. Doing Division Lickety-Split
            1. Making short work of long division
            2. Getting leftovers: Division with a remainder
   3. Part II: Getting a Handle on Whole Numbers
      1. Chapter 4: Getting a Handle on Whole Numbers
         1. Knowing Properties of the Big Four Operations
            1. Inverse operations
            2. Commutative operations
            3. Associative operations
            4. Distribution to lighten the load
         2. Doing Big Four Operations with Negative Numbers
            1. Addition and subtraction with negative numbers
            2. Multiplication and division with negative numbers
         3. Understanding Units
            1. Adding and subtracting units
            2. Multiplying and dividing units
         4. Understanding Inequalities
            1. Doesn't equal (≠)
            2. Less than (<) and greater than (>)
            3. Less than or equal to (≤) and greater than or equal to (≥)
            4. Approximately equals (≈)
         5. Moving Beyond the Big Four: Exponents, Square Roots, and Absolute Value
            1. Understanding exponents
            2. Discovering your roots
            3. Figuring out absolute value
      2. Chapter 5: Getting a Handle on Whole Numbers
         1. Seeking Equality for All: Equations
            1. Hey, it's just an expression
            2. Evaluating the situation
            3. Putting the Three E's together
         2. Introducing Order of Operations
            1. Applying order of operations to Big Four expressions
            2. Using order of operations in expressions with exponents
            3. Understanding order of precedence in expressions with parentheses
      3. Chapter 6: Getting a Handle on Whole Numbers
         1. Dispelling Two Myths about Word Problems
            1. Word problems aren't always hard
            2. Word problems are useful
         2. Solving Basic Word Problems
            1. Turning word problems into word equations
            2. Plugging in numbers for words
         3. Solving More-Complex Word Problems
            1. When numbers get serious
            2. Too much information
            3. Putting it all together
      4. Chapter 7: Getting a Handle on Whole Numbers
         1. Knowing the Divisibility Tricks
            1. Counting everyone in: Numbers you can divide everything by
            2. In the end: Looking at the final digits
            3. Add it up: Checking divisibility by adding up digits
            4. Ups and downs: Divisibility by 11
         2. Identifying Prime and Composite Numbers
      5. Chapter 8: Getting a Handle on Whole Numbers
         1. Knowing Six Ways to Say the Same Thing
         2. Connecting Factors and Multiples
         3. Finding Fabulous Factors
            1. Deciding when one number is a factor of another
            2. Understanding factor pairs
            3. Generating a number's factors
            4. Identifying prime factors
            5. Finding the greatest common factor (GCF)
         4. Making Marvelous Multiples
            1. Generating multiples
            2. Finding the least common multiple (LCM)
   4. Part III: Parts of the Whole: Fractions, Decimals, and Percents
      1. Chapter 9: Fooling with Fractions
         1. Slicing a Cake into Fractions
         2. Knowing the Fraction Facts of Life
            1. Telling the numerator from the denominator
            2. Flipping for reciprocals
            3. Using ones and zeros
            4. Mixing things up
            5. Knowing proper from improper
         3. Increasing and Reducing Terms of Fractions
            1. Increasing the terms of fractions
            2. Reducing fractions to lowest terms
         4. Converting between Improper Fractions and Mixed Numbers
            1. Knowing the parts of a mixed number
            2. Converting a mixed number to an improper fraction
            3. Converting an improper fraction to a mixed number
         5. Understanding Cross-multiplication
         6. Making Sense of Ratios and Proportions
      2. Chapter 10: Par ting Ways: Fractions and the Big Four Operations
         1. Multiplying and Dividing Fractions
            1. Multiplying numerators and denominators straight across
            2. Doing a flip to divide fractions
         2. All Together Now: Adding Fractions
            1. Finding the sum of fractions with the same denominator
            2. Adding fractions with different denominators
         3. Taking It Away: Subtracting Fractions
            1. Subtracting fractions with the same denominator
            2. Subtracting fractions with different denominators
         4. Working Properly with Mixed Numbers
            1. Multiplying and dividing mixed numbers
            2. Adding and subtracting mixed numbers
      3. Chapter 11: Dallying with Decimals
         1. Understanding Basic Decimal Stuff
            1. Counting dollars and decimals
            2. Identifying the place value of decimals
            3. Knowing the decimal facts of life
         2. Performing the Big Four with Decimals
            1. Adding decimals
            2. Subtracting decimals
            3. Multiplying decimals
            4. Dividing decimals
         3. Converting between Decimals and Fractions
            1. Making simple conversions
            2. Changing decimals to fractions
            3. Changing fractions to decimals
      4. Chapter 12: Playing with Percents
         1. Making Sense of Percents
         2. Dealing with Percents Greater than 100%
         3. Converting to and from Percents, Decimals, and Fractions
            1. Going from percents to decimals
            2. Changing decimals into percents
            3. Switching from percents to fractions
            4. Turning fractions into percents
         4. Solving Percent Problems
            1. Figuring out simple percent problems
            2. Turning the problem around
            3. Deciphering more-difficult percent problems
         5. Putting All the Percent Problems Together
            1. Identifying the three types of percent problems
            2. Solving percent problems with equations
      5. Chapter 13: Word Problems with Fractions, Decimals, and Percents
         1. Adding and Subtracting Parts of the Whole in Word Problems
            1. Sharing a pizza: Fractions
            2. Buying by the pound: Decimals
            3. Splitting the vote: Percents
         2. Problems about Multiplying Fractions
            1. Renegade grocery shopping: Buying less than they tell you to
            2. Easy as pie: Working out what's left on your plate
         3. Multiplying Decimals and Percents in Word Problems
            1. To the end: Figuring out how much money is left
            2. Finding out how much you started with
         4. Handling Percent Increases and Decreases in Word Problems
            1. Raking in the dough: Finding salary increases
            2. Earning interest on top of interest
            3. Getting a deal: Calculating discounts
   5. Part IV: Picturing and Measuring — Graphs, Measures, Stats, and Sets
      1. Chapter 14: A Perfect Ten: Condensing Numbers with Scientific Notation
         1. First Things First: Using Powers of Ten as Exponents
            1. Counting zeros and writing exponents
            2. Adding exponents to multiply
         2. Working with Scientific Notation
            1. Writing in scientific notation
            2. Seeing why scientific notation works
            3. Understanding order of magnitude
            4. Multiplying with scientific notation
      2. Chapter 15: Picturing and Measuring — Graphs, Measures, Stats, and Sets
         1. Examining Differences between the English and Metric Systems
            1. Looking at the English system
            2. Looking at the metric system
         2. Estimating and Converting between the English and Metric Systems
            1. Estimating in the metric system
            2. Converting units of measurement
      3. Chapter 16: Picturing and Measuring — Graphs, Measures, Stats, and Sets
         1. Getting on the Plane: Points, Lines, Angles, and Shapes
            1. Making some points
            2. Knowing your lines
            3. Figuring the angles
            4. Shaping things up
         2. Closed Encounters: Shaping Up Your Understanding of 2-D Shapes
            1. Polygons
            2. Circles
         3. Taking a Trip to Another Dimension: Solid Geometry
            1. The many faces of polyhedrons
            2. 3-D shapes with curves
         4. Measuring Shapes: Perimeter, Area, Surface Area, and Volume
            1. 2-D: Measuring on the flat
            2. Spacing out: Measuring in three dimensions
      4. Chapter 17: Picturing and Measuring — Graphs, Measures, Stats, and Sets
         1. Looking at Three Important Graph Styles
            1. Bar graph
            2. Pie chart
            3. Line graph
         2. Using the xy-Graph
            1. Plotting points on an xy-graph
            2. Drawing lines on an xy-graph
      5. Chapter 18: Picturing and Measuring — Graphs, Measures, Stats, and Sets
         1. The Chain Gang: Solving Measurement Problems with Conversion Chains
            1. Setting up a short chain
            2. Working with more links
            3. Pulling equations out of the text
            4. Rounding off: Going for the short answer
         2. Solving Geometry Word Problems
            1. Working from words and images
            2. Breaking out those sketching skills
      6. Chapter 19: Picturing and Measuring — Graphs, Measures, Stats, and Sets
         1. Gathering Data Mathematically: Basic Statistics
            1. Understanding differences between qualitative and quantitative data
            2. Working with qualitative data
            3. Working with quantitative data
         2. Looking at Likelihoods: Basic Probability
            1. Figuring the probability
            2. Oh, the possibilities! Counting outcomes with multiple coins
      7. Chapter 20: Picturing and Measuring - Graphs, Measures, Stats, and Sets
         1. Understanding Sets
            1. Elementary, my dear: Considering what's inside sets
            2. Sets of numbers
         2. Performing Operations on Sets
            1. Union: Combined elements
            2. Intersection: Elements in common
            3. Relative complement: Subtraction (sorta)
            4. Complement: Feeling left out
   6. Part V: The X-Files: Introduction to Algebra
      1. Chapter 21: The X-Files: Introduction to Algebra
         1. Seeing How X Marks the Spot
         2. Expressing Yourself with Algebraic Expressions
            1. Evaluating algebraic expressions
            2. Coming to algebraic terms
            3. Making the commute: Rearranging your terms
            4. Identifying the coefficient and variable
            5. Identifying like terms
            6. Considering algebraic terms and the Big Four
         3. Simplifying Algebraic Expressions
            1. Combining like terms
            2. Removing parentheses from an algebraic expression
      2. Chapter 22: The X-Files: Introduction to Algebra
         1. Understanding Algebraic Equations
         2. Using x in equations
         3. Choosing among four ways to solve algebraic equations
         4. The Balancing Act: Solving for x
         5. Striking a balance
         6. Using the balance scale to isolate x
         7. Rearranging Equations and Isolating x
            1. Rearranging terms on one side of an equation
            2. Moving terms to the other side of the equals sign
            3. Removing parentheses from equations
            4. Cross-multiplying
      3. Chapter 23: The X-Files: Introduction to Algebra
         1. Solving Algebra Word Problems in Five Steps
            1. Declaring a variable
            2. Setting up the equation
            3. Solving the equation
            4. Answering the question
            5. Checking your work
         2. Choosing Your Variable Wisely
         3. Solving More-Complex Algebraic Problems
            1. Charting four people
            2. Crossing the finish line with five people
   7. Part VI: The Part of Tens
      1. Chapter 24: The Part of Tens
         1. Knowing the Multiplication Table
         2. Adding and Subtracting Negative Numbers
         3. Multiplying and Dividing Negative Numbers
         4. Knowing the Difference between Factors and Multiples
         5. Reducing Fractions to Lowest Terms
         6. Adding and Subtracting Fractions
         7. Multiplying and Dividing Fractions
         8. Identifying Algebra's Main Goal: Find x
         9. Knowing Algebra's Main Rule: Keep the Equation in Balance
         10. Seeing Algebra's Main Strategy: Isolate x
      2. Chapter 25: The Part of Tens
         1. Counting on Counting (or Natural) Numbers
         2. Identifying Integers
         3. Knowing the Rationale behind Rational Numbers
         4. Making Sense of Irrational Numbers
         5. Absorbing Algebraic Numbers
         6. Moving through Transcendental Numbers
         7. Getting Grounded in Real Numbers
         8. Trying to Imagine Imaginary Numbers
         9. Grasping the Complexity of Complex Numbers
         10. Going beyond the Infinite with Transfinite Numbers
   8. About the Author
   9. Cheat Sheet
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