Basic Math and Pre-Algebra (Cliffs Study Solver) PDF
Preview Basic Math and Pre-Algebra (Cliffs Study Solver)
01 537644 FM.qxd 5/20/03 9:02 AM Page i CliffsStudySolver™ Basic Math and Pre-Algebra By Jonathan White Contributing Authors Teri Stimmel Scott Searcy 02 537644 Pretest.qxd 5/20/03 9:14 AM Page 26 01 537644 FM.qxd 5/20/03 9:02 AM Page i CliffsStudySolver™ Basic Math and Pre-Algebra By Jonathan White Contributing Authors Teri Stimmel Scott Searcy 01 537644 FM.qxd 5/20/03 9:02 AM Page ii Published by: Wiley Publishing, Inc. 909 Third Avenue New York, NY 10022 www.wiley.com Copyright © 2003 Wiley Publishing, Inc. New York, New York Published by Wiley Publishing, Inc., New York, NY Published simultaneously in Canada Cataloging-in-Publication information is available from the Library of Congress ISBN: 0-7645-3764-4 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 1B/QW/QW/QT/IN No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form orby any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee tothe Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8700. Requests to the Publisher for permission should be addressed to the Legal Department, Wiley Publishing, Inc., 10475 Crosspoint Blvd., Indianapolis, IN 46256, 317-572-3447, fax 317-572-4447, or e-mail [email protected] LIMIT OF LIABILITY/DISCLAIMER OF WARRANTY: THE PUBLISHER AND AUTHOR HAVE USED THEIR BEST EFFORTS IN PREPARING THIS BOOK. THE PUBLISHER AND AUTHOR 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. THERE ARE NO WARRANTIES WHICH EXTEND BEYOND THE DESCRIPTIONS CONTAINED IN THIS PARAGRAPH. NO WARRANTY MAY BE CREATED OR EXTENDED BY SALES REPRE- SENTATIVES OR WRITTEN SALES MATERIALS. THE ACCURACY AND COMPLETENESS OF THE INFORMA- TION PROVIDED HEREIN AND THE OPINIONS STATED HEREIN ARE NOT GUARANTEED OR WARRANTED TO PRODUCE ANY PARTICULAR RESULTS, AND THE ADVICE AND STRATEGIES CONTAINED HEREIN MAY NOT BE SUITABLE FOR EVERY INDIVIDUAL. NEITHER THE PUBLISHER NOR AUTHOR SHALL BE LIABLE FOR ANY LOSS OF PROFIT OR ANY OTHER COMMERCIAL DAMAGES, INCLUDING BUT NOT LIMITED TO SPECIAL, INCIDENTAL, CONSEQUENTIAL, OR OTHER DAMAGES. Trademarks: Wiley, the Wiley Publishing logo, Cliffs, CliffsStudySolver, CliffsNotes, CliffsAP, CliffsComplete, CliffsTestPrep, CliffsQuickReview, CliffsNote-a-Day, and all related trademarks, logos and trade dress are trademarks or registered trademarks of Wiley Publishing, Inc., in the United States and other countries andmay not be used without written permission.All other trademarks are the property of their respective owners. Wiley Publishing, Inc., is not associated with any product or vendor mentioned in this book. For general information on our other products and services or to obtain technical support, please contact our Customer Care Department within the U.S. at 800-762-2974, outside the U.S. at 317-572-3993, or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Note: If you purchased this book without a cover, you should be aware that this book is stolen property. Itwas reported as “unsold and destroyed” to the publisher, and neither the author nor the publisher has received any payment for this “stripped book.” is a trademark of Wiley Publishing, Inc. 01 537644 FM.qxd 5/20/03 9:02 AM Page iii About the Authors Jonathan J. White is Assistant Professor of Mathematics at Coe College in Cedar Rapids, Iowa. Scott Searcy, a high school teacher in Iowa, holds a Bachelor of Arts degree in Math and General Science. Teri Stimmel graduated from Coe College with a Bachelor of Arts degree in Mathematical Science and Secondary Education. 01 537644 FM.qxd 5/20/03 9:02 AM Page iv Publisher’s Acknowledgments Editorial Composition Project Editor: Kelly D. Dobbs Project Coordinator: Ryan Steffen Acquisitions Editor: Greg Tubach Indexer: Steve Rath Technical Editor: Jonathan Lee Proofreader: Linda Quigley Editorial Assistant: April Yoder Wiley Publishing, Inc., Composition Services 01 537644 FM.qxd 5/20/03 9:02 AM Page v Table of Contents Pretest 1 Problems 1 Answers 20 Chapter 1: The Basics 27 Collections of Numbers 27 Ways to Show Multiplication and Division 27 Multiplying and Dividing Using Zero 28 Symbols and Terminology 28 Some Fundamental Properties 29 Some Properties (Axioms) of Addition 29 Some Properties (Axioms) of Multiplication 30 A Property of Two Operations 30 Grouping Symbols and Order of Operations 31 Order of Operations 32 Chapter Problems and Solutions 34 Problems 34 Answers and Solutions 35 Supplemental Chapter Problems 36 Problems 36 Answers 37 Chapter 2: Whole Numbers 39 Place Value 39 Computation 41 Adding and Subtracting 41 Multiplying 43 Dividing 45 Rounding Off 49 Estimating 49 Estimating Sums and Differences 50 Estimating Products and Quotients 51 Divisibility Rules 52 Factoring 54 Prime Numbers 56 Composite Numbers 57 Factor Trees 58 01 537644 FM.qxd 5/20/03 9:02 AM Page vi vi CliffsStudySolver Basic Math and Pre-Algebra Chapter Problems and Solutions 59 Problems 59 Answers and Solutions 61 Supplemental Chapter Problems 63 Problems 63 Answers 64 Chapter 3: Fractions 67 Equivalent Fractions 67 Reducing Fractions 68 Enlarging Denominators 69 Mixed Numbers 70 Adding and Subtracting Fractions 72 Adding and Subtracting Mixed Numbers 75 Adding Mixed Numbers 75 Subtracting Mixed Numbers 76 Multiplying Fractions and Mixed Numbers 78 Multiplying Fractions 78 Multiplying Mixed Numbers 79 Dividing Fractions and Mixed Numbers 81 Dividing Fractions 81 Dividing Mixed Numbers 81 Compound Fractions 83 Chapter Problems and Solutions 84 Problems 84 Answers and Solutions 85 Supplemental Chapter Problems 87 Problems 87 Answers 88 Chapter 4: Decimals 91 Place Value 91 Comparing Decimals 92 Decimal Computation 93 Adding Decimals 94 Subtracting Decimals 95 Multiplying Decimals 97 Dividing Decimals 100 Estimating 105 01 537644 FM.qxd 5/20/03 9:02 AM Page vii Table of Contents vii Changing between Fractions and Decimals 106 Changing Fractions to Decimals 106 Changing Decimals to Fractions 109 Chapter Problems and Solutions 111 Problems 111 Answers and Solutions 112 Supplemental Chapter Problems 115 Problems 115 Solutions 116 Chapter 5: Percents 119 Changing Percents, Decimals, and Fractions 119 Changing Decimals to Percents 119 Changing Percents to Decimals 120 Changing Fractions to Percents 121 Changing Percents to Fractions 122 Applications of Percents 123 Finding Percents of a Number 123 Finding What Percent One Number Is of Another Number 125 Finding a Number When a Percent of It Is Known 127 The Proportion Method 130 Finding Percent Increase or Percent Decrease 132 Chapter Problems and Solutions 134 Problems 134 Answers and Solutions 135 Supplemental Chapter Problems 138 Problems 138 Answers 140 Chapter 6: Integers and Rationals 143 Integers 143 Number Lines 143 Adding Integers 143 Subtracting Integers 145 Minus Preceding Grouping Symbols 147 Multiplying and Dividing Integers 148 Absolute Value 150 Rational Numbers 152 Negative Fractions 152 Adding Positive and Negative Fractions 152 01 537644 FM.qxd 5/20/03 9:02 AM Page viii viii CliffsStudySolver Basic Math and Pre-Algebra Adding Positive and Negative Mixed Numbers 154 Subtracting Positive and Negative Fractions 156 Subtracting Positive and Negative Mixed Numbers 157 Multiplying Positive and Negative Fractions 158 Multiplying Positive and Negative Mixed Numbers 159 Dividing Positive and Negative Fractions 160 Dividing Positive and Negative Mixed Numbers 161 Chapter Problems and Solutions 163 Problems 163 Answers and Solutions 164 Supplemental Chapter Problems 166 Answers 167 Chapter 7: Powers, Exponents, and Roots 169 Powers and Exponents 169 Exponents 169 Negative Exponents 170 Squares and Cubes 171 Operations with Powers and Exponents 172 More Operations with Powers and Exponents 174 Square Roots and Cube Roots 176 Square Roots 176 Cube Roots 177 Simplifying Square Roots 178 Chapter Problems and Solutions 180 Problems 180 Answers and Solutions 180 Supplemental Chapter Problems and Answers 181 Problems 181 Answers 182 Chapter 8: Powers of Ten and Scientific Notation 185 Powers of Ten 185 Multiplying Powers of Ten 185 Dividing Powers of Ten 186 Scientific Notation 187 Multiplying in Scientific Notation 188 Dividing in Scientific Notation 190 Other Operations in Scientific Notation 191
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