Mathematics and Problem Solving for Fire Service Personnel PDF
Preview Mathematics and Problem Solving for Fire Service Personnel
MATHEMATICS AND PROBLEM SOLVING FOR FIRE SERVICE PERSONNEL MANAGEMENT This page intentionally left blank MATHEMATICS AND PROBLEM SOLVING FOR FIRE SERVICE PERSONNEL MANAGEMENT Eugene F. Mahoney, MS, BS Retired Battalion Chief, LAFD Retired Fire Chief, Arcadia Fire Department Retired Professor of Fire Science Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Publisher:Julie Levin Alexander Marketing Assistant:Judy Noh Editor-in-Chief:Marlene McHugh Pratt Managing Production Editor:Patrick Walsh Senior Acquisitions Editor:Stephen Smith Production Liaison:Frances Russello Senior Managing Editor for Development: Production Editor:Julie Li Lois Berlowitz Senior Media Editor:Amy Peltier Development Editor:Eileen M. Clawson Media Project Manager:Lorena Cerisano Associate Editor:Monica Moosang Creative Director:Jayne Conte Editorial Assistant:Heather Luciano Cover Designer:Lisbeth Axell Director of Marketing:Karen Allman Cover Image Credit:Courtesy of Rick McClure, LAFD Executive Marketing Manager:Katrin Beacom Compositor:Aptara®, Inc. Marketing Specialist:Michael Sirinides Printing and Binding:Edwards Brothers, Inc. Many of the designations by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. Copyright ©2010 by Pearson Education, Inc., Upper Saddle River, New Jersey 07458.Pearson Prentice Hall. All rights reserved. Printed in the United States of America. This publication is protected by Copyright and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department. Library of Congress Cataloging-in-Publication Data Mahoney, Gene Mathematics and problem solving for fire service personnel / Eugene Mahoney. p. cm. ISBN-13: 978-0-13-502825-4 ISBN-10: 0-13-502825-6 1. Mathematics—Problems, exercises, etc. 2. Problem solving—Problems, exercises, etc. 3. Word problems—Problems, exercises, etc. I. Title. QA43.M2285 2010 510.76—dc22 2009014129 10 9 8 7 6 5 4 3 2 1 ISBN-10: 0-13-502825-6 www.bradybooks.com ISBN-13: 978-0-13-502825-4 This book is dedicated to my stepdaughter, Jeri Stapp, who devoted so many hours to mastering the principles established herein. This page intentionally left blank Contents Preface xiii Acknowledgments xv About the Author xvii Introduction xix Chapter 1 Introduction to the World of Numbers 1 Suggestions for Readers 2 The Basic Concept of Numbers 2 Introduction to the Number System 3 An Explanation of Numbers 4 Determining Prime Numbers 5 Divisibility Rules 5 Determining Whether a Number Larger than 100 is a Prime Number 6 Positive and Negative Integers 7 Word Problems 8 Changing Word Problems to Number Problems 9 Sample Word Problems 9 Chapter 2 Solving and Proving Whole Number Addition Problems 13 A Review of the Addition Process 14 Proving Addition Problems 17 Clues to Errors 20 Proving Smaller Addition Problems 21 Introduction to Positive and Negative Integers 22 Adding Positive and Negative Integers 23 Practice Adding Positive and Negative Problems 24 Sample Word Problems 25 vii viii ■ CONTENTS Chapter 3 Working with Whole Number Multiplication Problems 38 A Review of the Multiplication Process 39 The Multiplication Tables 39 A Review of the Times Tables 39 Multiplying by Nine 40 Solving a Multiplication Problem 42 Proving a Multiplication Problem 45 Shortcut Multiplication Procedures 46 Multiplying a Two-Digit Number by Eleven 47 Mentally Multiplying Two ’Teen Numbers 47 Squaring a Number Ending in Five 49 Multiplying a Number by Ten 49 Multiplying a Number by 100 50 Multiplying Positive and Negative Integers 51 Chapter 4 Solving Whole Number Division, Subtraction, and Square Root Problems 59 A Review of the Division Process 60 The Division Process 60 Determining Whether a Division Problem Has Been Solved Correctly 61 Dividing a Four-Digit Dividend by a Two-Digit Divisor 61 Determining Whether the Problem Has Been Solved Correctly 62 Determining Whether a Dividend Can Be Divided Evenly 62 Shortcuts for Division Problems 64 Dividing Positive and Negative Integers 65 A Review of the Subtraction Process 68 Proving a Subtraction Problem 69 Subtracting Negative and Positive Integers 70 A Review of the Square Root Process 77 Solving a Two-Digit Square Root Problem 80 Proving a Square Root Problem 82 Chapter 5 Working with Fractions 87 Introduction to Fractions 88 Types of Common Fractions 88 Related Principles of Whole Numbers 89 Changing a Fraction to an Equivalent Fraction 90 Changing a Fraction to a Higher or Lower Term 90 Converting a Mixed Number to an Improper Fraction 91 Converting an Improper Fraction to a Mixed Number 91 Converting a Decimal to a Fraction 91 Converting Minutes to a Fraction 92 CONTENTS ■ ix Addition of Mixed Numbers 98 Subtraction of Common Fractions 104 Subtracting Mixed Numbers 104 Multiplication of Common Fractions 109 The Multiplication Process 110 Canceling 110 Multiplying Whole Numbers and Common Fractions 112 Multiplying Mixed Numbers, Whole Numbers, and Common Fractions 113 Dividing a Whole Number by a Mixed Number 119 Dividing a Mixed Number by a Mixed Number 119 Chapter 6 Working with Decimals 123 Rounding Numbers 125 Converting a Fraction to a Decimal 126 Converting a Decimal to a Fraction 126 Principles of Adding Decimals 128 Proving Decimal Addition Problems 129 Principles of Subtracting Decimals 134 Principles of Multiplying Decimals 138 The Principles of Dividing Decimals 145 Chapter 7 Solving Combination Problems 151 Basic Sequence for Working Combination Problems 152 Important Information 157 Chapter 8 Understanding Measurements 167 Length Measurements 169 A Word of Caution Regarding Metric Usage 170 Area Measurements 178 Pressure Measurements 182 Volume Measurements 191 Rectangular Containers 192 Cylindrical Containers 193 Weight Measurements 198 Determining the Weight of Water in a Container 199 Fluid Measurements 202 Temperature Measurements 207 Chapter 9 Working with Percent and Percentages 211 Introduction to the Term Ratio 212 Introduction to Percent 212
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