AMERICAN TECHNICAL PUBLISHERS Orland Park, Illinois 60467-5756
Practical Math contains practical applications commonly used in a variety of industries and trades. Specific procedures vary with each task and must be performed by a qualified person. For maximum safety, always refer to specific manufacturer recommendations, insurance regulations, specific job site and plant procedures, applicable federal, state, and local regulations, and any authority having jurisdiction. The material contained herein is intended to be an educational resource for the user. American Technical Publishers, Inc. assumes no responsibility or liability in connection with this material or its use by any individual or organization.
American Technical Publishers, Inc., Editorial Staff Editor in Chief: Jonathan F. Gosse Vice President — Production: Peter A. Zurlis Digital Media Manager: Carl R. Hansen Assistant Production Manager: Nicole D. Bigos Technical Editor: Cathy A. Scruggs Copy Editor: James R. Hein
Editorial Assistant: Alex C. Tulik Cover Design: Robert M. McCarthy Illustration/Layout: Bethany J. Fisher Nicole S. Polak Nick W. Basham Robert M. McCarthy Digital Resources: Robert E. Stickley Cory S. Butler
The publisher acknowledges Sprecher + Schuh as well as the Air Conditioning Contractors of America for providing technical images and information.
NEC® is a registered trademark of the National Fire Protection Association, Inc. PowerPoint® is a registered trademark of Microsoft Corporation in the United States and/or other countries. QuickLink, Quick Quiz, Quick Quizzes, and Master Math are either registered trademarks or a trademark of American Technical Publishers, Inc.
© 2015 by American Technical Publishers, Inc. All rights reserved 4 5 6 7 8 9 – 15 – 9 8 7 6 5 4 3 2 1 Printed in the United States of America ISBN 978-0-8269-2250-2
This book is printed on recycled paper.
Chapter 1 Working with Whole Numbers
1
Section 1-1
UNDERSTANDING WHOLE NUMBERS __________________________2
Section 1-2
ADDING WHOLE NUMBERS ____________________________________4
Section 1-3
SUBTRACTING WHOLE NUMBERS ______________________________8
Section 1-4
MULTIPLYING WHOLE NUMBERS _____________________________ 11
Section 1-5
DIVIDING WHOLE NUMBERS _________________________________ 16
Chapter 1
REVIEW ______________________________________________________ 21
Chapter 1
TEST _________________________________________________________ 23
Math Exercises: Expressing Whole Numbers
4
Math Exercises: Adding Whole Numbers Practical Applications: Adding Whole Numbers
7 7
Math Exercises: Subtracting Whole Numbers Practical Applications: Subtracting Whole Numbers
10 10
Math Exercises: Multiplying Whole Numbers Practical Applications: Multiplying Whole Numbers
15 15
Math Exercises: Dividing Whole Numbers Practical Applications: Dividing Whole Numbers
Chapter 2 Working with Simple Fractions
19 19
27
Section 2-1
UNDERSTANDING FRACTIONS ________________________________ 28
Section 2-2
UNDERSTANDING FACTORS __________________________________ 32
Section 2-3
FINDING EQUIVALENT FRACTIONS ____________________________ 36
Chapter 2
REVIEW ______________________________________________________ 47
Chapter 2
TEST _________________________________________________________ 49
Math Exercises: Proper Fractions, Improper Fractions, and Mixed Numbers Math Exercises: Finding Prime Factors Math Exercises: Finding Common Factors
Math Exercises: Reducing Fractions to Lowest Terms Practical Applications: Reducing Fractions to Lowest Terms Math Exercises: Reducing Fractions to Lowest Terms with a Given Denominator Practical Applications: Reducing Fractions to Lowest Terms with a Given Denominator Math Exercises: Changing Fractions to Higher Terms with a Given Denominator Practical Applications: Changing Fractions to Higher Terms with a Given Denominator Math Exercises: Finding the Lowest Common Denominator Practical Applications: Finding the Lowest Common Denominator Math Exercises: Changing Fractions to Their Lowest Common Denominator Practical Applications: Changing Fractions to Their Lowest Common Denominator
32 34 36 37 38 39 40 41 41 43 44 45 45
Chapter 3 Working with Complex Fractions
53
Section 3-1
ADDING FRACTIONS___________________________________________ 54
Section 3-2
SUBTRACTING FRACTIONS____________________________________ 60
Section 3-3
MULTIPLYING FRACTIONS_____________________________________ 65
Section 3-4
DIVIDING FRACTIONS_________________________________________ 74
Chapter 3
REVIEW_______________________________________________________ 89
Chapter 3
TEST__________________________________________________________ 91
Math Exercises: Adding Fractions with Common Denominators Practical Applications: Adding Fractions with Common Denominators Math Exercises: Adding Fractions with Uncommon Denominators Practical Applications: Adding Fractions with Uncommon Denominators Math Exercises: Adding Mixed Numbers Practical Applications: Adding Mixed Numbers
Math Exercises: Subtracting Fractions with Common Denominators Practical Applications: Subtracting Fractions with Common Denominators Math Exercises: Subtracting Fractions with Uncommon Denominators Practical Applications: Subtracting Fractions with Uncommon Denominators Math Exercises: Subtracting Mixed Numbers Practical Applications: Subtracting Mixed Numbers Math Exercises: Multiplying Two or More Fractions Practical Applications: Multiplying Two or More Fractions Math Exercises: Multiplying Improper Fractions Math Exercises: Multiplying a Fraction by a Whole Number Practical Applications: Multiplying a Fraction by a Whole Number Math Exercises: Multiplying a Mixed Number by a Whole Number Practical Applications: Multiplying a Mixed Number by a Whole Number Math Exercises: Multiplying Mixed Numbers Practical Applications: Multiplying Mixed Numbers Math Exercises: Dividing Two Fractions Practical Applications: Dividing Two Fractions Math Exercises: Dividing a Fraction by a Whole Number Practical Applications: Dividing a Fraction by a Whole Number Math Exercises: Dividing a Mixed Number by a Whole Number Practical Applications: Dividing a Mixed Number by a Whole Number Math Exercises: Dividing a Whole Number by a Fraction Practical Applications: Dividing a Whole Number by a Fraction Math Exercises: Dividing Mixed Numbers Practical Applications: Dividing Mixed Numbers Math Exercises: Dividing Complex Fractions Practical Applications: Dividing Complex Fractions
55 55 57 57 58 59 60 61 62 62 64 64 66 67 68 70 70 71 72 73 74 75 76 77 78 79 80 81 81 83 83 87 87
Chapter 4 Working with Decimals
97
Section 4-1
UNDERSTANDING DECIMALS__________________________________ 98
Section 4-2
ADDING AND SUBTRACTING DECIMALS______________________ 101
Section 4-3
MULTIPLYING DECIMALS_____________________________________ 103
Section 4-4
DIVIDING DECIMALS_________________________________________ 106
Section 4-5
CHANGING FRACTIONS TO DECIMALS________________________ 110
Math Exercises: Rounding Decimals
Math Exercises: Adding and Subtracting Decimals Practical Applications: Adding and Subtracting Decimals Math Exercises: Multiplying Decimals Practical Applications: Multiplying Decimals Math Exercises: Dividing Decimals Practical Applications: Dividing Decimals
Math Exercises: Changing Fractions to Decimals Practical Applications: Changing Fractions to Decimals
100 102 103 105 106 109 110 111 112
Section 4-6 CHANGING DECIMALS TO FRACTIONS________________________ 112 Math Exercises: Changing Decimals to Fractions Practical Applications: Changing Decimals to Fractions Math Exercises: Changing Decimals to Fractions with a Given Denominator Practical Applications: Changing Decimals to Fractions with a Given Denominator
114 114 116 117
CHAPTER 4 REVIEW______________________________________________________ 119 CHAPTER 4 TEST_________________________________________________________ 121
Chapter 5 Working with Percentages
127
Section 5-1
UNDERSTANDING PERCENTAGES____________________________ 128
Section 5-2
SOLVING PERCENTAGE PROBLEMS___________________________ 132
Section 5-3
CALCULATING COSTS________________________________________ 137
Math Exercises: Percentages and Their Fraction and Decimal Equivalents Math Exercises: Calculating Percentage Practical Applications: Calculating Percentage Math Exercises: Calculating Percent Rate Practical Applications: Calculating Percent Rate Math Exercises: Calculating Base Amount Practical Applications: Calculating Base Amount
Math Exercises: Calculating Costs Practical Applications: Calculating Costs Math Exercises: Calculating Tax and Total Cost Practical Applications: Calculating Tax and Total Cost
131 133 133 135 135 136 137 141 142 144 144
CHAPTER 5 REVIEW______________________________________________________ 147 CHAPTER 5 TEST_________________________________________________________ 149
Chapter 6 Working with Measurements
155
Section 6-1
UNDERSTANDING UNITS OF MEASURE_______________________ 156
Section 6-2
CONVERTING UNITS OF MEASURE___________________________ 161
Section 6-3
ADDING AND SUBTRACTING UNITS OF MEASURE____________ 170
Section 6-4
MULTIPLYING AND DIVIDING UNITS OF MEASURE____________ 173
Chapter 6
REVIEW______________________________________________________ 177
Chapter 6
TEST_________________________________________________________ 179
Math Exercises: Converting to Lower Units of Measure Practical Applications: Converting to Lower Units of Measure Math Exercises: Converting to Higher Units of Measure Practical Applications: Converting to Higher Units of Measure Math Exercises: Converting Between Measurement Systems Practical Applications: Converting Between Measurement Systems Math Exercises: Converting Temperature Practical Applications: Converting Temperature Math Exercises: Adding and Subtracting Units of Measure Practical Applications: Adding and Subtracting Units of Measure
Math Exercises: Multiplying and Dividing Units of Measure Practical Applications: Multiplying and Dividing Units of Measure
Chapter 7 Working with Exponents
163 163 165 165 168 168 170 170 172 172 174 175
183
Section 7-1
UNDERSTANDING EXPONENTS_______________________________ 184
Section 7-2
UNDERSTANDING SQUARE ROOTS___________________________ 193
Chapter 7
REVIEW______________________________________________________ 197
Chapter 7
TEST_________________________________________________________ 199
Math Exercises: Exponents Practical Applications: Exponents
Math Exercises: Square Roots Practical Applications: Square Roots
192 193 195 196
Chapter 8 Working with Ratios and Proportions
203
Section 8-1
USING RATIOS_______________________________________________ 204
Section 8-2
USING PROPORTIONS________________________________________ 208
Chapter 8
REVIEW______________________________________________________ 217
Chapter 8
TEST_________________________________________________________ 219
Math Exercises: Ratios Practical Applications: Ratios
Math Exercises: Proportions Practical Applications: Proportions
Chapter 9 Working with Plane and Solid Figures
207 208 210 214
223
Section 9-1
UNDERSTANDING PLANE FIGURES___________________________ 224
Section 9-2
UNDERSTANDING SOLID FIGURES____________________________ 234
Chapter 9
REVIEW______________________________________________________ 247
Chapter 9
TEST_________________________________________________________ 249
Math Exercises: Squares and Rectangles Practical Applications: Squares and Rectangles Math Exercises: Triangles Practical Applications: Triangles Math Exercises: Circles Practical Applications: Circles Math Exercises: Rectangular Solids Practical Applications: Rectangular Solids Math Exercises: Cylinders Practical Applications: Cylinders Math Exercises: Square Pyramids Practical Applications: Square Pyramids Math Exercises: Cones Practical Applications: Cones Math Exercises: Spheres Practical Applications: Spheres
227 228 230 231 233 234 236 237 238 239 241 242 244 244 246 246
Chapter 10 Working with Graphs
253
Section 10-1 USING LINE GRAPHS ________________________________________ 254 Math Exercises: Line Graphs Practical Applications: Line Graphs
258 260
Section 10-2 USING BAR GRAPHS ________________________________________ 261 Math Exercises: Bar Graphs Practical Applications: Bar Graphs
265 267
Section 10-3 USING PIE GRAPHS _________________________________________ 267 Math Exercises: Pie Graphs Practical Applications: Pie Graphs
269 270
Chapter 10 REVIEW _____________________________________________________ 271 Chapter 10 TEST ________________________________________________________ 273
Answers to Selected Math Exercises and Practical Applications ____________________________ 279 Appendix __________________________________________________________________________________ 285 Glossary __________________________________________________________________________________ 317 Index _____________________________________________________________________________________ 321
Digital Resources • Quick Quizzes® • Illustrated Glossary • Flash Cards • Master Math® Tutorials • Reference Tables • Media Library • ATPeResources.com
Practical Math covers essential math concepts and how they are applied on the job in agriculture, alternative energy, culinary arts, boiler operation, construction, electrical, HVAC, manufacturing, maintenance, mechanics, pipefitting, plumbing, and welding. Each chapter presents math concepts with visual steps and includes both math exercises and practical applications that reinforce learning. Selected answers to math exercises and practical applications are listed at the back of the book. Features of this edition include the following: • Each chapter is divided into several sections to maximize both learning and instructional flexibility. • Over 300 practical applications provide opportunities for learners to apply essential math concepts in 13 different occupational fields. • Online learner resources reinforce math concepts and encourage practice in a variety of formats. • Each chapter ends with a formative review and a summative test to assess math comprehension achieved. • The expanded appendix includes occupational reference tables as well as essential math tables. Objectives identify key concepts addressed in a chapter and help guide learning.
Practical Applications provide opportunities to apply essential math concepts typically required on the job.
Key Terms identify vocabulary that is key to understanding the concepts in a chapter.
Digital Resources offer engaging online tools that reinforce learning.
Math Exercises allow learners to demonstrate their knowledge of math concepts.
Examples show step-by-step calculations and a Quick Reference or Calculator in selected problems to enhance efficient learning.
This edition of Practical Math includes access to digital resources that enhance and reinforce learning. These online Learner Resources can be accessed using either of the following methods. • Key ATPeResources.com/QuickLinks into a web browser and enter QuickLink™ code 764460. • Use a Quick Response (QR) reader app on a mobile device to scan the QR code located on the opening page
of each chapter.
Digital Resources ATPeResources.com/QuickLinks Access Code:
Learner Resources The online Learner Resources provide the following interactive tools to maximize both comprehension and retention. • Quick Quizzes® provide 10 interactive questions for each chapter and include reference links to the textbook
and Illustrated Glossary. • The Illustrated Glossary serves as a helpful reference to math terms and definitions, with selected terms
linked to illustrations. • Flash Cards serve as a review tool for key terms and definitions and for practicing a variety of math exercises • • • •
that reinforce learning. Master Math® Tutorials demonstrate how common math calculations are performed step-by-step. Reference Tables are printable tables of both math and occupational reference information. The Media Library provides videos that demonstrate the application of key math concepts. ATPeResources.com provides access to online reference materials that support continued learning.
This edition of Practical Math also offers a set of digital resources that empower instructors to tailor their presentations, demonstrations, and assessments within a specific course or program.
Instructor Resources The online Practical Math Instructor Resources provide the following set of dynamic teaching and learning tools to maximize instructional effectiveness. • The Instructional Guide provides an overview of how to structure a course and includes a step-by-step
• • •
• •
instructional plan for each chapter. The Instructional Plans are divided by section and correlated to learning objectives. Premium PowerPoint® Presentations include objectives and key content in each chapter of the book. Section breaks are denoted, and presentation notes are provided. The Image Library provides all numbered figures in a format that can be resized by the instructor for maximum instructional flexibility. Assessments include a pretest, a posttest, and test banks based on the objectives for each chapter that can be used to document knowledge and skills attained. Each test bank is provided in several formats to facilitate use in testing software or a learning management system (LMS). Answer Keys list answers to the pretest, the posttest, and all of the math exercises and practical applications in the textbook. Learner Resources (Quick Quizzes, Illustrated Glossary, Flash Cards, Master Math® Tutorials, Reference Tables, Media Library, and a link to ATPeResources.com) are included.
To obtain information on other related training materials, visit www.atplearning.com. The Publisher
