Master Math: Basic M a t h and Pre-Algebra BY Debra Ross CAREER PRESS 3 Tice Road P.O. Box 687 Franklin Lakes, NJ 074 17 1 -800-CAREER- 1 201-848-0310 (NJ and outside US.) FAX: 20 1-848- 1727 Copyright 0 1996 by Debra Anne Ross All rights reserved under the Pan-American and International Copyright Conventions. This book may not be reproduced, in whole or in part, in any form or by any means electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system now known or hereafter invented, without written permission from the publisher, The Career Press. MASTER mTH: BASICM ATH AND PRE-ALGEBRA Cover design by The Visual Group Printed in the U.S.A. by Book-mart Press To order this title, please call toll-free 1-800-CAREER-1( NJ and Canada: 201-848-0310)t o order using VISA or Mastercard, or for further information on books from Career Press. Library of Congress Cataloging-in-Publication Data Ross, Debra h e , 1 958 Master math : basic math and pre-algebra / by Debra Anne Ross. p. cm. Includes index. ISBN 1-56414-214-0 (pbk.) 1. Mathematics. I. Title. QA39.2.R6547 1996 5 13.2-dc20 96-22992 CIP Acknowle-ents I am indebted to Dr. Melanie McNeil, Professor of Chemical Engineering at San Jose State University, for reviewing this text for accuracy. This page intentionally left blank Introduction 1 Chapter 1 Numbers and Their Operations 5 1.1. Digits and the base ten system 6 1.2. Whole numbers 7 1.3. Addition of whole numbers 7 1.4. Subtraction of whole numbers 15 1.5. Multiplication of whole numbers 22 1.6. Division of whole numbers 35 1.7. Divisibility, remainders, factors and multiples 43 1.8. Integers 45 1.9. Even and odd integers 46 1.10. Zero 47 1.11. Addition and subtraction of negative and positive integers 48 1.12. Multiplication and division of negative and positive integers 51 1.13. The real number line 52 1.14. Absolute value 53 1.15. Prime numbers 54 1.16. Rational vs. irrational numbers 54 1.17. Complex numbers 55 1.18. Rounding, truncating and estimating numbers 59 1.19. Inequalities, >, <, 2, 62 1.20. Factorial 66 Chapter 2 Fractions 67 2.1. Definitions 67 2.2. Multiplying fractions 68 2.3. Adding and subtracting fractions with common denominators 69 2.4. Adding and subtracting fractions with different denominators 70 2.5. Dividing fractions 76 2.6. Reducing fractions 77 2.7. Complex fractions, mixed numbers and improper fractions 78 2.8. Adding and subtracting mixed numbers 82 2.9. Comparing fractions: Which is larger or smaller? 83 Chapter 3 Decimals 87 3.1. Definitions 87 3.2. Adding and subtracting decimals 90 3.3. Multiplying decimals 93 3.4. Dividing decimals 95 3.5. Rounding decimals 97 3.6. Comparing the size of decimals 98 3.7. Decimals and money 99 Chapter 4 Percentages 101 4.1. Definitions 101 4.2. Figuring out the percents of numbers 102 4.3 Adding, subtracting, multiplying and dividing percents 105 4.4. Percent increase and decrease (percent change) 107 4.5. Simple and compound interest 109 Chapter 5 Converting Percentages, Fractions and Decimals 111 5.1. Converting fractions to percents 111 5.2. Converting percents to fractions 112 5.3. Converting fractions to decimals 113 5.4. Converting decimals to fractions 113 5.5. Converting percents to decimals 115 5.6. Converting decimals to percents 117 Chapter 6 Ratios, Proportions and Variation 118 6.1. Definitions 118 6.2. Comparing ratios to fractions and percents 120 6.3. Variation and proportion 121 Chapter 7 Powers and Exponents 123 7.1. Definition of the exponent or power 123 7.2. Negative exponents 124 7.3. Multiplying exponents with the same base 125 7.4. Multiplying exponents with different bases 126 7.5. Dividing exponents with the same base 126 7.6. Dividing exponents with different bases 128 7.7. Raising a power of a base to a power 128 7.8. Distributing exponents into parenthesis 129 7.9. Addition of exponents 130 7.10. Subtraction of exponents 131 7.11. Exponents involving fractions 131 Chapter 8 Logarithms 133 8.1. Definition of the logarithm 133 8.2. Common (base ten) and natural logarithm 135 8.3. Solving equations with logarithms or exponents 136 8.4. Exponential form and logarithmic form 138 8.5. Laws of logarithms: addition, subtraction, multiplication, division, power and radical 139 8.6. Examples: the Richter scale, pH and radiometric dating 140 Chapter 9 Roots and Radicals 145 146 9.1. Definitions 147 9.2. The square root 149 9.3. Estimating square roots 152 9.4. The cubed root 9.5. The fourth and fifth roots 153 9.6. Simplifying radicals by factoring 154 9.7. Multiplying radicals 155 9.8. Dividing radicals 155 9.9. Radicals involving fractions 156 9.10. Rationalizing the denominator 156 9.11. Addition of radicals 157 9.12. Subtraction of radicals 158 Chapter 10 Important Statistical Quantities 159 10.1. Average (arithmetic mean) 159 10.2. Median 161 10.3. Mode 163 10.4. Probability 164 10.5. Standard deviation, variance, histograms and distributions 164 Index 170 Appendix Tables of Contents of Second and Third Books in the Master Math Series 173