for carpenters · ppm practical problems in mathematics for carpenters 9th edition mark w. huth...
TRANSCRIPT
PPMPractical Problems in Mathematics
FOR CARPENTERS
9TH EDITION
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PPMPractical Problems in Mathematics
FOR CARPENTERS
9TH EDITION
Mark W. Huth
Harry C. Huth
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
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© 2009, 2012 Delmar, Cengage Learning
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Practical Problems in Mathematics for Carpenters, 9th editionMark W. Huth and Harry C. Huth
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v
CONTENTS
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
SECTION 1 WHOLE NUMBERS
Unit 1 Addition of Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Unit 2 Subtraction of Whole Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Unit 3 Multiplication of Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Unit 4 Division of Whole Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Unit 5 Combined Operations with Whole Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
SECTION 2 COMMON FRACTIONS
Unit 6 Addition of Common Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Unit 7 Subtraction of Common Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Unit 8 Multiplication of Common Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Unit 9 Division of Common Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Unit 10 Combined Operations with Common Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
SECTION 3 DECIMAL FRACTIONS
Unit 11 Addition of Decimal Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Unit 12 Subtraction of Decimal Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Unit 13 Multiplication of Decimal Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Unit 14 Division of Decimal Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Unit 15 Expressing Common Fractions and Mixed Numbers as Decimals . . . . . . . . . . . 64
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vi CONTENTS
SECTION 4 PERCENT AND PERCENTAGE
Unit 16 Simple Percent and Percentage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Unit 17 Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Unit 18 Discounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
SECTION 5 MEASUREMENT: DIRECT AND COMPUTED
Unit 19 Linear Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Unit 20 Working with Feet and Inches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Unit 21 Square Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Unit 22 Surface Measurement—Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Unit 23 Th e Framing Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
Unit 24 Surface Measurement—Irregular Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Unit 25 Surface Measurement—Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Unit 26 Volume Measurement—Cubes and Rectangular Solids . . . . . . . . . . . . . . . . . . . . . . . . . 125
Unit 27 Board Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
Unit 28 Volume Measurement—Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Unit 29 Weight Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
SECTION 6 POWERS AND ROOTS
Unit 30 Applications of Exponents in Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Unit 31 Using Square Root to Find Sides of Right Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
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viiCONTENTS
SECTION 7 COMBINED OPERATIONS APPLIED
TO BUILDING CONSTRUCTION
Unit 32 Girders, Sills, and Floor Joists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Unit 33 Wall Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Unit 34 Studding and Fire- Stops or Draft Stops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Unit 35 Common Rafters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
Unit 36 Hip Rafters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Unit 37 Sheathing and Subfl ooring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Unit 38 Trim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Unit 39 Roofi ng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Unit 40 Doors and Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
Unit 41 Siding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
Unit 42 Stairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
ANSWERS TO ODDNUMBERED PRACTICAL PROBLEMS . . . . . . . . . . . 221
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ix
PREFACE
In order to succeed as a carpenter, one must have the ability to do mathematics. Th e ninth edi-
tion of Practical Problems in Mathematics for Carpenters has been revised to provide beginning
students with these needed skills. Th is clearly organized worktext will help students gain expe-
rience and confi dence in computing problems that are common in a wide variety of carpentry
applications.
Practical Problems in Mathematics for Carpenters, 9th edition, starts with basic arithmetic and
progresses through applications of mathematics that are often required of carpenters. Th e expla-
nations and examples at the beginning of each unit help students build a better understanding
of the concepts being presented. Most of the problems are word problems designed to encour-
age the student to use logical deduction to arrive at an answer. Many of these word problems
are multistepped. Problems related to carpentry are used throughout the text to help students
understand terms and practices used in the fi eld.
In addition, students will develop an awareness of construction drawings and carpentry
symbols, common trade terminology, and calculator use as they work through this text. The
answers to odd-numbered problems are provided in the back of the text along with a com-
plete appendix.
Delmar’s PPM Series
Th is text is one of a series of workbooks designed to off er students practical problem-solving ex-
perience in various occupations. Th e workbooks take a step-by-step approach to mastering basic
math skills. Each workbook includes relevant and easily understood problems in a specifi c vo-
cational fi eld. Th e workbooks are suitable for any student from junior high through high school
and up to the two-year college level. Each text includes a glossary to help students with technical
terms. Practical Problems in Mathematics for Carpenters includes an appendix with information
on basic operations, English and SI measurements, important formulas, and answers to odd-
numbered questions. For more information about this series and a current list of titles, please
visit www.cengagebrain.com.
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x PREFACE
Series Features
Th e workbooks in Delmar’s PPM series take a step-by-step approach to mastering essential math
skills. At the start of each unit, a brief introductory section provides a basic explanation of the
concepts necessary to complete the problems in the unit. Examples are presented to help the
learner review the mathematical principles. Th e problems in each unit progress from basic ex-
amples of the math concepts to more complex examples that require critical thinking. As stu-
dents progress through each unit, they will become more profi cient at solving a wide variety of
math problems.
Th is Book’s Approach
Practical Problems in Mathematics for Carpenters, 9th edition, begins with a review of basic
operations with whole numbers, fractions, and decimals; progresses through percentages, mea-
surements, powers, and roots; and fi nishes with a section on combined operations in building
construction. Topical sections are divided into short units to give teachers maximum fl exibility
in planning and to help students achieve maximum skill mastery. Instructors may choose to use
this book as a stand-alone text or as a supplemental workbook to a theory-based text.
New to Th is Edition
Th e ninth edition of Practical Problems in Mathematics for Carpenters is updated to include:
• New examples showing current industry applications and practices
• New problems highlighting green construction and energy-effi cient technologies
• Improved illustrations to help student visualize problems and solutions
Supplements
Th e supplements package for this edition has been revised and expanded to include a new
Instructor Companion Website and Applied Math CourseMate, a new online tool that can help
students and teachers build lasting math skills.
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xiPREFACE
Instructor Resources
Th e Instructor Companion Website provides the following support for teachers:
• updated answers to all text problems
• computerized test banks in ExamView® software
• Powerpoint® presentations
• an Image Gallery including all text fi gures
Applied Math CourseMate
Every text in Delmar’s PPM series includes Applied Math CourseMate, Cengage Learning’s on-
line solution for building strong math skills. Students and instructors alike will benefi t from the
following CourseMate resources:
• an interactive eBook, with highlighting, note-taking, and search capabilities
• interactive learning tools including:
✓ quizzes
✓ fl ashcards
✓ PowerPoint slides
✓ skill-building games
• and more!
Instructors will be able to use Applied Math CourseMate to access Instructor Resources and
other classroom management tools.
To access these supplemental materials, please visit www.cengagebrain.com. At the
cengagebrain.com homepage, search for the ISBN of your title (from the back cover of your
book) using the search box at the top of the page. Th is will take you to the product page where
these resources can be found.
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xii PREFACE
Acknowledgments
Th is edition is the product of refi nement over the course of eight previous editions plus the ef-
forts of the reviewers who made specifi c suggestions for improving the ninth edition. Th e author
would like to thank all of the reviewers, students, and instructors who have commented on the
previous editions, and especially the following individuals who contributed their time and eff ort
to the ninth edition:
Kenneth N. Bowling, Southeast Kentucky Community and Technical College, Harlan, Kentucky
Jacob Pulsifer, Ridgewater College, Willmar, Minnesota
Earl T. Torgerson, Bismarck State College, Bismarck, North Dakota
Special thanks go to Linda Willey of Clifton Park, New York, whose thorough technical re-
view of all examples, problems, and answers helped create a textbook that is both accurate and
complete.
About the Author
Mark W. Huth brings many years of experience in the industry to this book, having worked as a
carpenter, contractor, and building construction teacher. Mr. Huth is a former editor at Delmar
Cengage Learning, a role that put him inside hundreds of classrooms and let him glean the best
teaching methods for his readers. He has authored several additional Delmar titles, including the
Residential Construction Academy Series’s Basic Principles for Construction and Understanding
Construction Drawings, as well as texts on blueprint reading and construction technology.
Using a Calculator
Th e availability of low-cost calculators has made mathematics calculations much easier. A com-
plicated mathematics problem can be solved more quickly and with less eff ort. For most basic
functions, the ones you will use throughout this book, the calculator can be substituted for pencil
and paper. Th e choice of what tool to use to perform these functions is up to you and your
instructor.
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xiiiPREFACE
Disadvantages
Some pitfalls do exist, and we must be aware of them before using a calculator. Th ese pitfalls can
usually be avoided if an estimate is made in advance of using the calculator. When using the cal-
culator, always compare its answer with your estimate. If they do not agree, repeat the solution
process very carefully. You might have incorrectly placed or omitted a decimal point.
Advantages
1. Calculators are a great help in changing fractions to decimals. However, there is no reverse
gear. You cannot change decimals to fractions.
2. When working with percentages, a calculator can change a percentage to a decimal, for
example, 42.6% to 0.426. Th is time-saver also helps avoid possible errors.
3. When calculating a series of operations on most calculators, you do not have to get an an-
swer at each step. Only after going through all the steps do you press the “equals” button.
4. A hidden advantage of estimating, then using a calculator, is that your skill improves as a
result of continuously estimating.
When purchasing a calculator for use in carpentry, there is no need to get an expensive one with
more functions than you will be using on a regular basis. Addition, subtraction, multiplication,
division, percent, and possibly a square root capability will be all that you need.
An instruction booklet comes with most calculators. Read it completely.
About Units
Th e value of mathematics is its use to solve real-world problems. Th at is what this book is about—
mathematics used to solve carpentry problems. It is rare that the solution to a problem is a bare
value without any reference to some type of unit, such as dollars, hours, board feet, shingles, inches,
and so forth. Some problems are fi rst presented with mixed units, such as feet and inches or hours
and minutes. Converting between these units will be discussed as the problems arise in the units
of Practical Problems in Mathematics for Carpenters. It is important to always keep track of what
units you are working with so the answer to the problem can be expressed in the proper units. Th e
best way to keep track of what units you are working with is to always write the units with the value,
both in the steps to solving a problem and in the answer.
13423_FM.indd xiii13423_FM.indd xiii 6/16/11 3:49 PM6/16/11 3:49 PM
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