Basic Math and Pre-Algebra (Cliffs Study Solver)

335 Pages·2003·1.52 MB·English

by  Jonathan J. White

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 [phone],
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