# Basic Math & Pre-Algebra For Dummies

## 2nd edition

By: Mark Zegarelli

Paperback | 3 June 2016 | Edition Number 2

##### At a Glance

384 Pages

Revised

24 x 19 x 2

### Paperback

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**Basic Math & Pre-Algebra For Dummies, 2nd Edition (9781119293637) was previously published as Basic Math & Pre-Algebra For Dummies, 2nd Edition (9781118791981). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.**

Tips for simplifying tricky basic math and pre-algebra operations

Whether you're a student preparing to take algebra or a parent who wants or needs to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals, and percents, you'll build necessary math skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations.

- Explanations and practical examples that mirror today's teaching methods
- Relevant cultural vernacular and references
*Standard For Dummies*materials that match the current standard and design

*Basic Math & Pre-Algebra For Dummies* takes the intimidation out of tricky operations and helps you get ready for algebra!

**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

ISBN: 9781119293637

ISBN-10: 1119293634

Series: For Dummies

Published: 3rd June 2016

Format: Paperback

Language: English

Number of Pages: 384

Audience: General Adult

Publisher: John Wiley & Sons Inc (US)

Country of Publication: US

Edition Number: 2

Edition Type: Revised

Dimensions (cm): 24 x 19 x 2

Weight (kg): 0.74

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