Basic Math and Pre-Algebra For Dummies(2nd) 无水印原版pdf.pdf

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Cover

Contents at a Glance

Table of Contents

Introduction

About This Book

Foolish Assumptions

Icons Used in This Book

Beyond the Book

Where to Go from Here

Part I: Getting Started with Basic Math and Pre-Algebra

1: Playing the Numbers Game

Inventing Numbers

Understanding Number Sequences

Looking at the Number Line

Four Important Sets of Numbers

2: It's All in the Fingers: Numbers and Digits

Knowing Your Place Value

Close Enough for Rock 'n' Roll: Rounding and Estimating

3: The Big Four: Addition, Subtraction, Multiplication, and Division

Adding Things Up

Take It Away: Subtracting

Multiplying

Doing Division Lickety-Split

Part II: Getting a Handle on Whole Numbers

4: Putting the Big Four Operations to Work

Knowing Properties of the Big Four Operations

Doing Big Four Operations with Negative Numbers

Understanding Units

Understanding Inequalities

Moving beyond the Big Four: Exponents, Square Roots, and Absolute Value

5: A Question of Values: Evaluating Arithmetic Expressions

Seeking Equality for All: Equations

Introducing Order of Operations

6: Say What? Turning Words into Numbers

Dispelling Two Myths about Word Problems

Solving Basic Word Problems

Solving More-Complex Word Problems

7: Divisibility

Knowing the Divisibility Tricks

Identifying Prime and Composite Numbers

8: Fabulous Factors and Marvelous Multiples

Knowing Six Ways to Say the Same Thing

Connecting Factors and Multiples

Finding Fabulous Factors

Making Marvelous Multiples

Part III: Parts of the Whole: Fractions, Decimals, and Percents

9: Fooling with Fractions

Slicing a Cake into Fractions

Knowing the Fraction Facts of Life

Increasing and Reducing Terms of Fractions

Converting between Improper Fractions and Mixed Numbers

Understanding Cross-multiplication

Making Sense of Ratios and Proportions

10: Parting Ways: Fractions and the Big Four Operations

Multiplying and Dividing Fractions

All Together Now: Adding Fractions

Taking It Away: Subtracting Fractions

Working Properly with Mixed Numbers

11: Dallying with Decimals

Understanding Basic Decimal Stuff

Performing the Big Four with Decimals

Converting between Decimals and Fractions

12: Playing with Percents

Making Sense of Percents

Dealing with Percents Greater than 100%

Converting to and from Percents, Decimals, and Fractions

Solving Percent Problems

Putting All the Percent Problems Together

13: Word Problems with Fractions, Decimals, and Percents

Adding and Subtracting Parts of the Whole in Word Problems

Problems about Multiplying Fractions

Multiplying Decimals and Percents in Word Problems

Handling Percent Increases and Decreases in Word Problems

Part IV: Picturing and Measuring — Graphs, Measures, Stats, and Sets

14: A Perfect Ten: Condensing Numbers with Scientific Notation

First Things First: Using Powers of Ten as Exponents

Working with Scientific Notation

15: How Much Have You Got? Weights and Measures

Examining Differences between the English and Metric Systems

Estimating and Converting between the English and Metric Systems

16: Picture This: Basic Geometry

Getting on the Plane: Points, Lines, Angles, and Shapes

Closed Encounters: Shaping Up Your Understanding of 2-D Shapes

Taking a Trip to Another Dimension: Solid Geometry

Measuring Shapes: Perimeter, Area, Surface Area, and Volume

17: Seeing Is Believing: Graphing as a Visual Tool

Looking at Three Important Graph Styles

Using the xy-Graph

18: Solving Geometry and Measurement Word Problems

The Chain Gang: Solving Measurement Problems with Conversion Chains

Solving Geometry Word Problems

19: Figuring Your Chances: Statistics and Probability

Gathering Data Mathematically: Basic Statistics

Looking at Likelihoods: Basic Probability

20: Setting Things Up with Basic Set Theory

Understanding Sets

Performing Operations on Sets

Part V: The X-Files: Introduction to Algebra

21: Enter Mr. X: Algebra and Algebraic Expressions

Seeing How X Marks the Spot

Expressing Yourself with Algebraic Expressions

Simplifying Algebraic Expressions

22: Unmasking Mr. X: Algebraic Equations

Understanding Algebraic Equations

The Balancing Act: Solving for x

Rearranging Equations and Isolating x

23: Putting Mr. X to Work: Algebra Word Problems

Solving Algebra Word Problems in Five Steps

Choosing Your Variable Wisely

Solving More-Complex Algebraic Problems

Part VI: The Part of Tens

24: Ten Little Math Demons That Trip People Up

Knowing the Multiplication Table

Adding and Subtracting Negative Numbers

Multiplying and Dividing Negative Numbers

Knowing the Difference between Factors and Multiples

Reducing Fractions to Lowest Terms

Adding and Subtracting Fractions

Multiplying and Dividing Fractions

Identifying Algebra's Main Goal: Find x

Knowing Algebra's Main Rule: Keep the Equation in Balance

Seeing Algebra's Main Strategy: Isolate x

25: Ten Important Number Sets to Know

Counting on Counting (or Natural) Numbers

Identifying Integers

Knowing the Rationale behind Rational Numbers

Making Sense of Irrational Numbers

Absorbing Algebraic Numbers

Moving through Transcendental Numbers

Getting Grounded in Real Numbers

Trying to Imagine Imaginary Numbers

Grasping the Complexity of Complex Numbers

Going beyond the Infinite with Transfinite Numbers

Index

About the Author

Basic Math & Pre-Algebra 2nd Edition by Mark Zegarelli

Basic Math & Pre-Algebra For Dummies®, 2nd Edition Published by: John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com Copyright © 2014 by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as per- mitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written per- mission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions. Trademarks: Wiley, For Dummies, the Dummies Man logo, Dummies.com, Making Everything Easier, and related trade dress are trademarks or registered trademarks of John Wiley & Sons, Inc., and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc., is not associated with any product or vendor mentioned in this book. LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: WHILE THE PUBLISHER AND AUTHOR HAVE USED THEIR BEST EFFORTS IN PREPARING THIS BOOK, THEY MAKE NO REPRESENTATIONS OR WARRANTIES WITH RESPECT TO THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS BOOK AND SPECIFICALLY DISCLAIM ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES REPRESENTATIVES OR WRITTEN SALES MATERIALS. THE ADVISE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR YOUR SITUATION. YOU SHOULD CONSULT WITH A PROFESSIONAL WHERE APPROPRIATE. NEITHER THE PUBLISHER NOR THE AUTHOR SHALL BE LIABLE FOR DAMAGES ARISING HEREFROM. For general information on our other products and services, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002. For technical support, please visit www.wiley.com/techsupport. Wiley publishes in a variety of print and electronic formats and by print-on-demand. Some material included with standard print versions of this book may not be included in e-books or in print-on-demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley prod- ucts, visit www.wiley.com. Library of Congress Control Number: 2013952434 ISBN 978-1-118-79198-1 (pbk); ISBN 978-1-118-79199-8 (ebk); ISBN 978-1-118-79205-6 (ebk) Manufactured in the United States of America 10 9 8 7 6 5 4 3 2 1

Contents at a Glance Introduction ................................................................ 1 Part I: Getting Started with Basic Math and Pre-Algebra ................................................................. 5 Chapter 1: Playing the Numbers Game ........................................................................... 7 Chapter 2: It’s All in the Fingers: Numbers and Digits ................................................ 25 Chapter 3: The Big Four: Addition, Subtraction, Multiplication, and Division ........ 31 Part II: Getting a Handle on Whole Numbers ............... 49 Chapter 4: Putting the Big Four Operations to Work .................................................. 51 Chapter 5: A Question of Values: Evaluating Arithmetic Expressions ...................... 67 Chapter 6: Say What? Turning Words into Numbers .................................................. 79 Chapter 7: Divisibility ...................................................................................................... 91 Chapter 8: Fabulous Factors and Marvelous Multiples .............................................. 99 Part III: Parts of the Whole: Fractions, Decimals, and Percents ........................................................... 113 Chapter 9: Fooling with Fractions ................................................................................ 115 Chapter 10: Parting Ways: Fractions and the Big Four Operations ......................... 131 Chapter 11: Dallying with Decimals ............................................................................. 157 Chapter 12: Playing with Percents ............................................................................... 181 Chapter 13: Word Problems with Fractions, Decimals, and Percents .................... 193 Part IV: Picturing and Measuring — Graphs, Measures, Stats, and Sets ......................................... 205 Chapter 14: A Perfect Ten: Condensing Numbers with Scientific Notation ........... 207 Chapter 15: How Much Have You Got? Weights and Measures ............................... 215 Chapter 16: Picture This: Basic Geometry .................................................................. 227 Chapter 17: Seeing Is Believing: Graphing as a Visual Tool...................................... 249 Chapter 18: Solving Geometry and Measurement Word Problems ......................... 257 Chapter 19: Figuring Your Chances: Statistics and Probability ............................... 269 Chapter 20: Setting Things Up with Basic Set Theory .............................................. 281

Part V: The X-Files: Introduction to Algebra ............... 289 Chapter 21: Enter Mr. X: Algebra and Algebraic Expressions .................................. 291 Chapter 22: Unmasking Mr. X: Algebraic Equations .................................................. 309 Chapter 23: Putting Mr. X to Work: Algebra Word Problems ................................... 321 Part VI: The Part of Tens .......................................... 331 Chapter 24: Ten Little Math Demons That Trip People Up ...................................... 333 Chapter 25: Ten Important Number Sets to Know .................................................... 339 Index ...................................................................... 347

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 I: 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 ................................ 10 Stepping out of the box with prime numbers .................................. 12 Multiplying quickly with exponents .................................................. 12 Looking at the Number Line ......................................................................... 13 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 Dividings things up .............................................................................. 18 Discovering the space in between: Fractions................................... 20 Four Important Sets of Numbers ................................................................. 20 Counting on the counting numbers ................................................... 21 Introducing integers ............................................................................ 21 Staying rational .................................................................................... 22 Getting real ........................................................................................... 22 Chapter 2: It’s All in the Fingers: Numbers and Digits . . . . . . . . . . . . . 25 Knowing Your Place Value ........................................................................... 25 Counting to ten and beyond ............................................................... 26 Telling placeholders from leading zeros .......................................... 27 Reading long numbers......................................................................... 28 Close Enough for Rock ’n’ Roll: Rounding and Estimating ....................... 28 Rounding numbers .............................................................................. 28 Estimating value to make problems easier ....................................... 30

vi Basic Math & Pre-Algebra For Dummies, 2nd Edition Chapter 3: The Big Four: Addition, Subtraction, Multiplication, and Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Adding Things Up .......................................................................................... 31 In line: Adding larger numbers in columns ...................................... 32 Carry on: Dealing with two-digit answers ......................................... 32 Take It Away: Subtracting ............................................................................. 33 Columns and stacks: Subtracting larger numbers ........................... 34 Can you spare a ten? Borrowing to subtract .................................... 35 Multiplying ...................................................................................................... 38 Signs of the times ................................................................................. 38 Memorizing the multiplication table ................................................. 39 Double digits: Multiplying larger numbers ....................................... 43 Doing Division Lickety-Split ......................................................................... 44 Making short work of long division ................................................... 45 Getting leftovers: Division with a remainder.................................... 48 Part II: Getting a Handle on Whole Numbers ................ 49 Chapter 4: Putting the Big Four Operations to Work . . . . . . . . . . . . . . . 51 Knowing Properties of the Big Four Operations ........................................ 51 Inverse operations ............................................................................... 52 Commutative operations .................................................................... 53 Associative operations ........................................................................ 54 Distribution to lighten the load .......................................................... 55 Doing Big Four Operations with Negative Numbers ................................. 55 Addition and subtraction with negative numbers ........................... 56 Multiplication and division with negative numbers ........................ 58 Understanding Units ..................................................................................... 59 Adding and subtracting units ............................................................. 59 Multiplying and dividing units ........................................................... 59 Understanding Inequalities .......................................................................... 60 Doesn’t equal (≠) .................................................................................. 60 Less than (<) and greater than (>) ..................................................... 61 Less than or equal to (≤) and greater than or equal to (≥) ............. 61 Approximately equals (≈) ................................................................... 62 Moving beyond the Big Four: Exponents, Square Roots, and Absolute Value ........................................................................................... 62 Understanding exponents ................................................................... 62 Discovering your roots ....................................................................... 64 Figuring out absolute value ................................................................ 64 Chapter 5: A Question of Values: Evaluating Arithmetic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Seeking Equality for All: Equations ............................................................. 67 Hey, it’s just an expression ................................................................. 69 Evaluating the situation ...................................................................... 69 Putting the Three E’s together ........................................................... 69

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