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Table of Contents
Introduction 1
About This Book 1
Foolish Assumptions 2
Icons Used in This Book 3
Beyond the Book 3
Where to Go from Here 4
Part 1: Getting Started with Basic Math and Pre-algebra 5
Chapter 1: Playing the Numbers Game 7
Inventing Numbers 8
Understanding Number Sequences 8
Evening the odds 9
Counting by threes, fours, fives, and so on 9
Getting square with square numbers 10
Composing yourself with composite numbers 11
Stepping out of the box with prime numbers 12
Multiplying quickly with exponents 13
Looking at the Number Line 14
Adding and subtracting on the number line 14
Getting a handle on nothing, or zero 15
Taking a negative turn: Negative numbers 16
Multiplying the possibilities 17
Dividing things up 17
Discovering the space in between: Fractions 19
Four Important Sets of Numbers 19
Counting on the counting numbers 20
Introducing integers 20
Staying rational 21
Getting real 21
Chapter 2: It’s All in the Fingers: Numbers and Digits 23
Knowing Your Place Value 23
Counting to ten and beyond 24
Telling placeholders from leading zeros 25
Reading long numbers 26
Close Enough for Rock ’n’ Roll: Rounding and Estimating 26
Rounding numbers 26
Estimating value to make problems easier 28
Table of Contents
Chapter 3: The Big Four: Addition, Subtraction, Multiplication, and Division 29
Adding Things Up 30
In line: Adding larger numbers in columns 30
Carry on: Dealing with two-digit answers 31
Take It Away: Subtracting 31
Columns and stacks: Subtracting larger numbers 32
Can you spare a ten? Borrowing to subtract 33
Multiplying 35
Signs of the times 36
Memorizing the multiplication table 37
Double digits: Multiplying larger numbers 40
Doing Division Lickety-Split 42
Making short work of long division 42
Getting leftovers: Division with a remainder 45
Part 2: Getting a Handle on Whole Numbers 47
Chapter 4: Putting the Big Four Operations to Work 49
Knowing Properties of the Big Four Operations 50
Inverse operations 50
Commutative operations 51
Associative operations 52
Distribution to lighten the load 53
Doing Big Four Operations with Negative Numbers 53
Addition and subtraction with negative numbers 54
Multiplication and division with negative numbers 56
Understanding Units 57
Adding and subtracting units 57
Multiplying and dividing units 57
Understanding Inequalities 58
Doesn’t equal (≠) 58
Less than (<) and greater than (>) 59
Less than or equal to (≤) and greater than or equal to (≥) 59
Approximately equals (≈) 60
Moving Beyond the Big Four: Exponents, Square Roots, and Absolute Value 60
Understanding exponents 60
Discovering your roots 61
Figuring out absolute value 62
Chapter 5: A Question of Values: Evaluating Arithmetic Expressions 63
Seeking Equality for All: Equations 64
Basic Math & Pre-Algebra For Dummies, 2nd Edition
Hey, it’s just an expression 64
Evaluating the situation 65
Putting the Three E’s together 66
Introducing Order of Operations 66
Applying order of operations to Big Four expressions 67
Using order of operations in expressions with exponents 70
Understanding order of precedence in expressions
with parentheses 71
Chapter 6: Say What? Turning Words into Numbers 75
Dispelling Two Myths about Word Problems 76
Word problems aren’t always hard 76
Word problems are useful 76
Solving Basic Word Problems 77
Turning word problems into word equations 77
Plugging in numbers for words 80
Solving More-Complex Word Problems 82
When numbers get serious 82
Too much information 83
Putting it all together 85
Chapter 7: Divisibility 87
Knowing the Divisibility Tricks 87
Counting everyone in: Numbers you can divide everything by 88
In the end: Looking at the final digits 88
Add it up: Checking divisibility by adding up digits 90
Ups and downs: Divisibility by 11 91
Identifying Prime and Composite Numbers 92
Chapter 8: Fabulous Factors and Marvelous Multiples 95
Knowing Six Ways to Say the Same Thing 96
Connecting Factors and Multiples 97
Finding Fabulous Factors 97
Deciding when one number is a factor of another 97
Understanding factor pairs 98
Generating a number’s factors 98
Identifying prime factors 100
Finding the greatest common factor (GCF) 105
Making Marvelous Multiples 105
Generating multiples 105
Finding the least common multiple (LCM) 106
Table of Contents
Part 3: Parts of the Whole: Fractions, Decimals, and Percents 109
Chapter 9: Fooling with Fractions 111
Slicing a Cake into Fractions 112
Knowing the Fraction Facts of Life 114
Telling the numerator from the denominator 114
Flipping for reciprocals 114
Using ones and zeros 115
Mixing things up 115
Knowing proper from improper 115
Increasing and Reducing Terms of Fractions 116
Increasing the terms of fractions 117
Reducing fractions to lowest terms 118
Converting between Improper Fractions and Mixed Numbers 120
Knowing the parts of a mixed number 121
Converting a mixed number to an improper fraction 121
Converting an improper fraction to a mixed number 122
Understanding Cross-multiplication 122
Making Sense of Ratios and Proportions 123
Chapter 10: Parting Ways: Fractions and the Big Four Operations 125
Multiplying and Dividing Fractions 126
Multiplying numerators and denominators straight across 126
Doing a flip to divide fractions 127
All Together Now: Adding Fractions 129
Finding the sum of fractions with the same denominator 129
Adding fractions with different denominators 130
Taking It Away: Subtracting Fractions 137
Subtracting fractions with the same denominator 137
Subtracting fractions with different denominators 138
Working Properly with Mixed Numbers 140
Multiplying and dividing mixed numbers 141
Adding and subtracting mixed numbers 142
Chapter 11: Dallying with Decimals 149
Understanding Basic Decimal Stuff 150
Counting dollars and decimals 150
Identifying the place value of decimals 152
Knowing the decimal facts of life 153
Basic Math & Pre-Algebra For Dummies, 2nd Edition
Performing the Big Four with Decimals 157
Adding decimals 158
Subtracting decimals 159
Multiplying decimals 160
Dividing decimals 161
Converting between Decimals and Fractions 165
Making simple conversions 165
Changing decimals to fractions 165
Changing fractions to decimals 167
Chapter 12: Playing with Percents 171
Making Sense of Percents 171
Dealing with Percents Greater than 100% 172
Converting to and from Percents, Decimals, and Fractions 173
Going from percents to decimals 173
Changing decimals into percents 174
Switching from percents to fractions 174
Turning fractions into percents 175
Solving Percent Problems 175
Figuring out simple percent problems 176
Turning the problem around 177
Deciphering more-difficult percent problems 178
Putting All the Percent Problems Together 178
Identifying the three types of percent problems 179
Solving percent problems with equations 180
Chapter 13: Word Problems with Fractions, Decimals, and Percents 183
Adding and Subtracting Parts of the Whole in Word Problems 184
Sharing a pizza: Fractions 184
Buying by the pound: Decimals 185
Splitting the vote: Percents 185
Problems about Multiplying Fractions 186
Renegade grocery shopping: Buying less than they tell you to 186
Easy as pie: Working out what’s left on your plate 187
Multiplying Decimals and Percents in Word Problems 188
To the end: Figuring out how much money is left 188
Finding out how much you started with 189
Handling Percent Increases and Decreases in Word Problems 191
Raking in the dough: Finding salary increases 191
Earning interest on top of interest 192
Getting a deal: Calculating discounts 193
Table of Contents
Part 4: Picturing and Measuring — Graphs, Measures, Stats, and Sets 195
Chapter 14: A Perfect Ten: Condensing Numbers with Scientific Notation 197
First Things First: Using Powers of Ten as Exponents 198
Counting zeros and writing exponents 198
Adding exponents to multiply 200
Working with Scientific Notation 200
Writing in scientific notation 201
Seeing why scientific notation works 202
Understanding order of magnitude 203
Multiplying with scientific notation 203
Chapter 15: How Much Have You Got? Weights and
Measures 205
Examining Differences between the English and Metric Systems 206
Looking at the English system 206
Looking at the metric system 208
Estimating and Converting between the English and Metric Systems 210
Estimating in the metric system 211
Converting units of measurement 213
Chapter 16: Picture This: Basic Geometry 217
Getting on the Plane: Points, Lines, Angles, and Shapes 218
Making some points 218
Knowing your lines 218
Figuring the angles 219
Shaping things up 221
Closed Encounters: Shaping Up Your Understanding
of 2-D Shapes 221
Polygons 222
Circles 224
Taking a Trip to Another Dimension: Solid Geometry 225
The many faces of polyhedrons 225
3-D shapes with curves 226
Measuring Shapes: Perimeter, Area, Surface Area, and Volume 227
2-D: Measuring on the flat 228
Spacing out: Measuring in three dimensions 235
Basic Math & Pre-Algebra For Dummies, 2nd Edition
Chapter 17: Seeing Is Believing: Graphing as a Visual Tool 239
Looking at Three Important Graph Styles 240
Bar graph 240
Pie chart 241
Line graph 242
Using the xy-Graph 243
Plotting points on an xy-graph 244
Drawing lines on an xy-graph 245
Chapter 18: Solving Geometry and Measurement Word Problems 247
The Chain Gang: Solving Measurement Problems with Conversion Chains 248
Setting up a short chain 248
Working with more links 249
Pulling equations out of the text 250
Rounding off: Going for the short answer 251
Solving Geometry Word Problems 253
Working from words and images 253
Breaking out those sketching skills 255
Chapter 19: Figuring Your Chances: Statistics and Probability 259
Gathering Data Mathematically: Basic Statistics 260
Understanding differences between qualitative and quantitative data 260
Working with qualitative data 261
Working with quantitative data 264
Looking at Likelihoods: Basic Probability 266
Figuring the probability 267
Oh, the possibilities! Counting outcomes with multiple coins 268
Chapter 20: Setting Things Up with Basic Set Theory 271
Understanding Sets 272
Elementary, my dear: Considering what’s inside sets 273
Sets of numbers 275
Performing Operations on Sets 275
Union: Combined elements 276
Intersection: Elements in common 276
Relative complement: Subtraction (sorta) 277
Complement: Feeling left out 277
Table of Contents
Part 5: the X-files: Introduction to Algebra 279
Chapter 21: Enter Mr X: Algebra and Algebraic
Expressions 281
Seeing How X Marks the Spot 282
Expressing Yourself with Algebraic Expressions 282
Evaluating algebraic expressions 283
Coming to algebraic terms 285
Making the commute: Rearranging your terms 286
Identifying the coefficient and variable 287
Identifying like terms 288
Considering algebraic terms and the Big Four 289
Simplifying Algebraic Expressions 292
Combining like terms 292
Removing parentheses from an algebraic expression 293
Chapter 22: Unmasking Mr X: Algebraic Equations 299
Understanding Algebraic Equations 300
Using X in Equations 300
Choosing among four ways to solve algebraic equations 301
The Balancing Act: Solving for x 302
Striking a balance 303
Using the Balance Scale to Isolate X 304
Rearranging Equations and Isolating x 305
Rearranging terms on one side of an equation 305
Moving terms to the other side of the equals sign 306
Removing parentheses from equations 307
Cross-multiplying 309
Chapter 23: Putting Mr X to Work: Algebra Word Problems 311
Solving Algebra Word Problems in Five Steps 312
Declaring a variable 312
Setting up the equation 313
Solving the equation 314
Answering the question 314
Checking your work 315
Choosing Your Variable Wisely 315
Solving More-Complex Algebraic Problems 316
Charting four people 316
Crossing the finish line with five people 318
Basic Math & Pre-Algebra For Dummies, 2nd Edition
Part 6: the Part of Tens 321
Chapter 24: Ten Little Math Demons That Trip People Up 323
Knowing the Multiplication Table 324
Adding and Subtracting Negative Numbers 324
Multiplying and Dividing Negative Numbers 325
Knowing the Difference between Factors and Multiples 325
Reducing Fractions to Lowest Terms 326
Adding and Subtracting Fractions 326
Multiplying and Dividing Fractions 327
Identifying Algebra’s Main Goal: Find X 327
Knowing Algebra’s Main Rule: Keep the Equation in Balance 328
Seeing Algebra’s Main Strategy: Isolate x 328
Chapter 25: Ten Important Number Sets to Know 329
Counting on Counting (or Natural) Numbers 330
Identifying Integers 330
Knowing the Rationale behind Rational Numbers 331
Making Sense of Irrational Numbers 331
Absorbing Algebraic Numbers 332
Moving through Transcendental Numbers 333
Getting Grounded in Real Numbers 333
Trying to Imagine Imaginary Numbers 333
Grasping the Complexity of Complex Numbers 334
Going beyond the Infinite with Transfinite Numbers 335
Index 337
