Table Of ContentMATHEMATICS AND PROBLEM
SOLVING FOR FIRE SERVICE
PERSONNEL MANAGEMENT
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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
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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.
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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
