Technical Math For Dummies E-Book

Barry Schoenborn

• Herausgeber: John Wiley & Sons
• Kategorie: Bildung
• Sprache: Englisch

Seitenzahl: 458

Veröffentlichungsjahr: 2010

Beschreibung

Technical Math For Dummies is your one-stop, hands-on guide to acing the math courses you'll encounter as you work toward getting your degree, certification, or license in the skilled trades. You'll get easy-to-follow, plain-English guidance on mathematical formulas and methods that professionals use every day in the automotive, health, construction, licensed trades, maintenance, and other trades. You'll learn how to apply concepts of algebra, geometry, and trigonometry and their formulas related to occupational areas of study. Plus, you'll find out how to perform basic arithmetic operations and solve word problems as they're applied to specific trades. * Maps to a course commonly required by vocational schools, community and technical college, or for certification in the skilled trades * Covers the basic concepts of arithmetic, algebra, geometry, and trigonometry * Helps professionals keep pace with job demands Whether you're a student currently enrolled in a program or a professional who is already in the work force, Technical Math For Dummies gives you everything you need to improve your math skills and get ahead of the pack.

Leseprobe

Technical Math For Dummies®

Table of Contents

Introduction

About This Book

Conventions Used in This Book

What You’re Not to Read

Foolish Assumptions

How This Book Is Organized

Part I: Basic Math, Basic Tools

Part II: Making Non-Basic Math Simple and Easy

Part III: Basic Algebra, Geometry, and Trigonometry

Part IV: Math for the Business of Your Work

Part V: The Part of Tens

Icons Used in This Book

Where to Go from Here

Part I: Basic Math, Basic Tools

Chapter 1: Math that Works as Hard as You Do

Discovering the Benefits of a Technical Math Book

The Basics Are Basically Basic

Meeting Measurement and Conversions and Studying Story Problem Strategies

Using Workhorse Math

Building Your Knowledge of the Branches of Math

Life Math Isn’t Classroom Math

Chapter 2: Discovering Technical Math and the Tools of the Trades

Busting Myths about Math

“I don’t need to use it.”

“It’s too hard.”

“I have a phobia.”

Remember: Somebody Else Already Did the Hard Work

The Trades, They Are A-Changing

Math Devices That Can Help You Do Your Job

Pocket (or phone, or computer) calculators

Specialty calculators

Thermometers and sphygmomanometers

Micrometers, calipers, and gauges

Automotive tools

Carpentry tools

Bricklaying tools

Chapter 3: Zero to One and Beyond

Looking at the Numbers that Count: Natural Numbers

Integers: Counting numbers with extras

Zero: Making math easier

Going Backward: Negative Numbers

Working with negative numbers

Traveling down the number line

Getting Between the Integers: Fractions, Decimals, and More

Our fractional friends

The rational numbers(and their irrational friends)

Taking a Look at the Lesser-Known Numbers

Real numbers

Imaginary numbers

Complex numbers

Nominal numbers

Handling Numerical Story Problems

Example: Automotive tech — a slippery task

Example: Getting the order right

Chapter 4: Easy Come, Easy Go: Addition and Subtraction

Making Everything Add Up

Adding numbers in a column

Adding zero

Adding negative numbers

Carrying the extra

Checking your work

Subtraction: Just Another Kind of Addition

Subtracting a positive is the same as adding a negative

Subtracting negative numbers

Subtracting zero

Subtracting multiple items

Borrowing when you have to

Checking your work

Example: Flour Power

Example: Sheep on Trucking

Chapter 5: Multiplication and Division: Everybody Needs Them

Go Forth and Multiply!

Mastering multiplication terminology

Memorizing multiplication tables: Faster than a calculator

Doing Simple Multiplication Like Your Grandfather Did It

Checking your work

Easy Street: Multiplying by 0, 1, and 10

A zero pulse: Multiplying by 0

One is the loneliest number: Multiplying by 1

Multiplying by 10

Divide and Conquer

Dealing with division definitions

Dividing by using the inverse

Doing short division

Going long (division)

Checking your work

Shortcuts: Dividing into 0 and by 0, 1, 10, and the dividend

Example: In the Machine Shop

Chapter 6: Measurement and Conversion

Main (And Not So Main) Systems of Measurement

The metric system

The American system

The imperial system, or the modern English system

Troy weight: Just for bullets and bullion

Apothecaries’ system: Not a grain of value any more

Other legitimate but specialized measurements

Converting Length, Weight, and Volume

The rules of conversion

American units to American units

American to metric and back again

Converting metric to metric

Example: Don’t Get Bored by Board Feet

Example: Getting the Dosage Right

Chapter 7: Slaying the Story Problem Dragon

Removing the Mystery from Story Problems

How to approach a story problem: A real-life example

The secret formula inside every story problem

The Step-by-Step Story Problem Solution

1. Read the problem

2. List the facts

3. Figure out exactly what the problem is asking for

4. Eliminate excess information

5. See what information is missing

6. Find the keywords

7. Pay attention to units

8. Convert information supplied into information needed

9. Draw a diagram

10. Find or develop a formula

11. Consult a reference

12. Do the math and check your answer to see whether it’s reasonable

Example: Furring Strips

Example: And Now, from the Banks of the Nile

Part II: Making Non-Basic Math Simple and Easy

Chapter 8: Fun with Fractions

Meeting the Numerator and Denominator: Best Friends Forever

Taking a look at numerators

Defining denominators

Dealing with special cases

Tackling the Different Types of Fractions

Proper and improper fractions

Mixed numbers

Ratios

Performing Math Operations with Fractions

Multiplying fractions

Dividing fractions

Adding fractions

Subtracting fractions

Example: Dividing and Selling a Cheesecake

Pricing your cake wholesale

Pricing your cake retail

Example: Cutting Fire Stops for Framing Carpentry

Chapter 9: Decimals: They Have Their Place

Diving into Decimal Basics

Pointing out decimal points and places

Precision, pennies, and parsing

The Four Ops: Working with Decimals in Four Math Operations

Adding excitement

Subtraction gives satisfaction

Multiply with abandon

Division is an important decision

Decimal Conversion

Converting fractions to decimals

Converting decimals to fractions

Round, Round, Get Around, I Get Around

Making Change and Charging Sales Tax

Making change

Charging sales tax

Example: A Journey to Office Supply Heaven

Chapter 10: Playing with Percentages

Pinpointing Percentages: Half a Glass Is Still 50 Percent Full

A percentage is a fraction, but the denominator never changes

A percentage is a ratio, too

Percentages Are Good Converts

Converting percentages to decimals

Turning decimals into percentages

Going from percentages to fractions

Transforming fractions to percentages

Calculating Percentage Increases and Decreases

Percentage increases: You get 10 percent more!

Percentage decreases: You save 10 percent!

The 100 percent increase: You must be 100 percent satisfied!

Dividing a Pie Using Percentages

Example: The World of Pralines

Example: Oily to Bed and Oily to Rise

Chapter 11: Tackling Exponents and Square Roots

Exponentiation: The Power of Powers

The basics of the base

Moving beyond 2 or 3

Different faces of special bases

Exponentiation math

Getting Back to Your(Square)Roots

Square roots the hard way

Square roots the easy way

Square roots the effortless way

Example: Finding the Bytes On a Disk

Part III: Basic Algebra, Geometry, and Trigonometry

Chapter 12: Algebra and the Mystery of X

Variables: Letters Represent Numbers, but the Math Is the Same

Understanding variables

Corralling constants

Examining expressions

Getting a handle on equations

Taking time for terms

Variable Relationships: X and Her Friends

Best friends forever: The constant and the variable

Simplifying variables: Variables of a feather flock together

Math Operations with Variables

Adding variables

Subtracting variables

Multiplying variables

Dividing variables

Example: How Many Oranges Are in that Orange Juice?

Example: Medications In the Pillbox

Chapter 13: Formulas (Secret and Otherwise)

Following the Formula for Building a Formula

Property A: Associativity

Property C: Commutativity

Property D: Distributivity

Working from a Formula to a Solution

Applying the same operation on both sides of the equal sign

Converting units with a special multiplication rule

Calculating Speed, Time, and Distance: Three Results from One Formula

Solving for speed

Solving for time

Solving for distance

Example: Cement Masonry — Pouring City Sidewalks

Example: Lunch Time — Buying Burgers and Fries

Chapter 14: Quick-and-Easy Geometry: The Compressed Version

Looking at Geometry’s Basic Parts

No snakes on this plane: Cartesian coordinates

What’s the point?

What’s your line?

What’s your angle?: Acute, obtuse, and right angles

Examining Simple Geometric Shapes

The square and the rectangle

The triangle: Just because it isn’t a right triangle doesn’t mean it’s wrong

The polygon

The circle

Learn It Once and Forget It: The Pythagorean Theorem

Example: Don’t Fence Me In

Example: The Pen Is Mightier Than the Paddock

Chapter 15: Calculating Areas, Perimeters, and Volumes

Area: All That Space in the Middle

Calculating the area of rectangles and squares

Figuring the area of a parallelogram (a bent-over long rectangle)

Determining the area of a trapezoid (a trapewhat?)

Calculating the area of a triangle

Computing the area of a circle

Perimeters: Along the Edges

Understanding perimeters: What goes around comes around

Calculating the perimeters of polygons

A perimeter by any other name: Finding a circle’s circumference

Volume: The Third Dimension

Getting a handle on American volume units

Calculating the volume of cuboids (also known as boxes)

Finding the volumes of spheres and cylinders

Example: Bore and Stroke for the Auto Guy

Example: Yard Area, the Landscaper’s Nightmare

Chapter 16: Trigonometry, the “Mystery Math”

Handling Triangles: More Angles than a Cornfield Maze

By Their Sines Shall Ye Know Them: Using Trigonometric Functions

Sine, cosine, and tangent: Three great relationships

Cosecant, secant, and cotangent: Three so-so relationships

The law of sines

Example: Surveying a River

Example: Locating a Wildfire

Part IV: Math for the Business of Your Work

Chapter 17: Graphs Are Novel and Charts Are Off the Chart

Defining Charts and Graphs and Their Advantages

Paying Tables Their Proper Respect

Introducing the Three Most Important Types of Charts

Walking the line graph

Sidling up to the bar graph

Getting a piece of the pie chart

Reading Charts and Graphs (And Recognizing a Bad One)

For a start, the parts of a chart

The good, the bad, the ugly, and the inaccurate

Making Charts and Graphs

Creating line graphs

Building bar graphs

Putting together pie charts

Example: Tracking Weight and Height in a Pediatric Practice

Example: Cost of Materials in Residential Construction

Chapter 18: Hold on a Second: Time Math

Dividing Time into Hours, Minutes, and Seconds

There’s a Time for Us, Somewhere a Time for Us: Time Notation Systems

12-hour notation

24-hour notation

Greenwich mean time (GMT)

UTC and Zulu time

Swahili time

Bible time

Converting Time

Going from minutes to seconds and back again

Changing hours to minutes and back again

Working with time as a fraction

Time Math: Calculating Time

Addition

Subtraction

Multiplication

Division

Example: The Timesheet for All Trades

Example: Microwave Magic

Chapter 19: Math for Computer Techs and Users

Try a Bit of This Byte: Understanding Basic Computer Terms

The Sum of the (Computer) Parts, and the Numbers Involved

Disk capacity

Flash memory

Rama lama ding dong: RAM memory

Speed out of the gate: Processor rate

The Internet is running on “slow” today: Network speed

Burn, baby, burn: DVD write speed

Example: Total Capacity of a Mass Storage System

Part V: The Part of Tens

Chapter 20: Ten Tips for Solving Any Math Problem

Figure Out Exactly What the Problem Asks For

List the Facts

Convert Supplied Information into Needed Information

Determine What Information You’re Missing

Eliminate Excess Information

Draw a Diagram

Find or Develop a Formula

Consult a Reference

Pay Attention to Units

Check Your Answer to See whether It’s Reasonable

Chapter 21: Ten Formulas You’ll Use Most Often

Area of a Square, Rectangle, or Triangle

Area of a Circle

Feet to Meters and Inches to Centimeters

Miles to Kilometers and Kilometers to Miles

Pounds to Kilograms and Ounces to Grams

Gallons to Liters and Liters to Gallons

Temperature Conversions

Hours to Minutes and Minutes to Hours

Distance, Time, and Speed

Volts, Amps, and Watts

Chapter 22: Ten Ways to Avoid Everyday Math Stress

Get Help with Your Checkbook

Use Grocery Shopping to Build Confidence

Practice Reading Analog Clocks

Play Games

Memorize Math Signs, Symbols, and Formulas

Make the Multiplication Table a Mantra

Use Paper Maps and Practice Navigating

Try to Estimate Distances

Take Up Music

Integrate Math with Nonmath Skills

Technical Math For Dummies®

by Barry Schoenborn and Bradley Simkins

Technical Math For Dummies®

Published byWiley Publishing, Inc.111 River St.Hoboken, NJ 07030-5774

www.wiley.com

Copyright © 2010 by Wiley Publishing, Inc., Indianapolis, Indiana

Published by Wiley Publishing, Inc., Indianapolis, Indiana

Published simultaneously in Canada

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ISBN: 978-0-470-59874-0

Manufactured in the United States of America

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About the Authors

Barry Schoenborn lives in Nevada City, California. He’s a longtime technical writer with over 30 years’ experience. He’s written hundreds of user manuals and (in the early days) worked dozens of part-time jobs that required practical math. He has been a carpenter for the movies, a stage electrician, a movie theater manager, a shipping clerk, an insurance clerk, and a library clerk. He has a bachelor’s degree in theatre from California State University, Fullerton.

Recently, his company worked with the California Integrated Waste Management Board to teach scientists and administrators how to write clearly. Barry is the coauthor of Storage Area Networks: Designing and Implementing a Mass Storage System (Pearson Education). He was a movie reviewer for the L.A. Herald-Dispatch and wrote a monthly political newspaper column for The Union of Grass Valley, California, for seven years. Barry’s publishing company, Willow Valley Press, published Dandelion Through the Crack, which won the William Saroyan International Prize for Writing.

Bradley Simkins was born and raised in Sacramento, California, and became a sixth-generation journeyman plasterer. But it didn’t take long (after many hours on construction sites) before he figured out that it was easier to use his brain than his muscles. He has a master’s degree in mathematics from California State University, Sacramento. He has taught, assisted, and tutored at the Multimedia Math Learning Center at American River College in Sacramento. He and his family live in Sacramento, where he owns Book Lovers Bookstore, an independent bookstore.

Dedications

Barry: To my teachers at San Juan High School in Citrus Heights, California: Mr. N. E. (Norm) Andersen (math); Mrs. Eada Silverthorne (English); Ms. Susan A. Schwarz (English); Mr. Norman E. Allen (physics); Mr. A. J. Crossfield (chemistry); and Mr. James C. Harvey (biology). They would be surprised and (maybe) pleased.

Bradley: I dedicate my work to my in-laws, Greg and Diane Manolis, who have always extended their hand to help with no complaints, and to my oldest daughter, Ashleigh, who taught me that failing does not make you a failure.

Authors’ Acknowledgments

Barry: This book wouldn’t have been possible without the efforts of coauthor Bradley Simkins. We were supported by a great team at Wiley Publishing (Natalie Harris, Erin Mooney, and Megan Knoll) who worked hard to make this book a reality. They are the nicest people you’ll ever meet! A big thanks, too, to Matt Wagner of Fresh Books Literary Agency, who presented us to Wiley.

Our patient readers were Priscilla Borquez (who is fast, accurate, and sensible, and who also has a great sense of humor); Jim Collins (an excellent and thorough technical communicator); Bill Love (who knows a zillion things about cars, machining, and welding); and Frances Kakugawa (author, poetess, and lecturer to and supporter of Alzheimer’s caregivers, who was our poster child for someone who doesn’t understand story problems).

Many thanks to Patricia Hartman, who was always encouraging, and to Johna Orzalli, my haircutter, who taught me how to mix hair color. Thanks as well to Jeff Perilman at Dave’s Auto Repair for tips about smogging a car and specialized tools. And, finally, thanks and apologies to all the medical and dental staffs I flooded with questions.

Bradley: First, I thank Barry Schoenborn for all his hard work and dedication to make this work possible and for always going the extra mile to understand when my life became too hectic. I thank my beautiful wife, Audrey, and my beautiful children, Ashleigh, Brayden, Alexander, and Natalie, who make my life worth living. Thanks to Jill Marcai and Jens Lorenz for correcting all of our math mistakes. Last, but certainly not least, many thanks to the team at Wiley Publishing for taking on such goofballs.

Publisher’s Acknowledgments

We’re proud of this book; please send us your comments at http://dummies.custhelp.com. For other comments, please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993, or fax [phone].

Some of the people who helped bring this book to market include the following:

Acquisitions, Editorial, and Media Development

Project Editor: Natalie Harris

Acquisitions Editor: Mike Baker

Copy Editors: Megan Knoll, Caitie Copple

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Editorial Program Coordinator: Joe Niesen

Technical Editors: Jens Lorenz, Jill Macari

Editorial Manager: Christine Meloy Beck

Senior Editorial Assistant: David Lutton

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Publishing for Technology Dummies

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Composition Services

Debbie Stailey, Director of Composition Services

Introduction

Technical careers require technical mathematics (technical math). That’s why we wrote Technical Math For Dummies. Whether you’re currently working in a technical trade or studying in school, you have probably made the discovery that most jobs require some math.

Most parts of technical math are simple. You may think some parts are hard, but look closer. After you read them, you’ll hit your forehead with the heel of your palm and say, “Yes! Of course! I sorta knew that all along, but now I really get it!” We think we’ve filled a gap in the world of math guides, and we hope you enjoy the book.

About This Book

This book is a reference. It’s also a repair manual that can help you fill voids you may have in your math background. It’s different from other math books in three major ways:

It’s all about practical math. You won’t find anything about symplectic geometry or sigma-algebra here. Our focus is on math for technical careers — it looks at problems you may deal with every day and the math skills you need to handle them. But we also include general principles when necessary.

It’s comprehensive. It covers all major math concepts; other math books are about individual concepts (for example, algebra, geometry or trigonometry).

It’s not dull (we hope) as other math books often are. One of us (Barry) is a long-time technical writer, and he’s written far too many deadly dull user manuals. That nonsense stops here. Because it’s a For Dummies book, you can be sure it’s easy to read and has touches of humor.

Technical Math For Dummies applies basic math to basic tasks in many careers. You get practical examples, and most of them are based on real-life experiences. And in what other book can you work with math and also find out how to make 90 dozen pralines or figure the distance from a fire watch tower to a wildfire? You can also apply a lot of this math to your personal life as well as your work life.

At the risk of sounding like a late-night infomercial, we want to point out a couple of this book’s unique features. We gar-on-tee you won’t find them anywhere else.

Conventions Used in This Book

We designed this book to be user-friendly, maybe even user-affectionate. If it were any friendlier, it would drive itself to your house and bring coffee and doughnuts. To help you get the most out of your new friend, we use the following conventions:

Italic type highlights new terms. We follow each term with a short and often informal definition. Occasionally, we give you clues about how to pronounce difficult words.

Web addresses are in monofont. They’re usually very short and shouldn’t break across two lines of text. But if they do, we haven’t added any extra characters (such as a hyphen) to indicate the break. Just type in what you see.

Although our English teachers would cringe at our breaking the rules, we usually write numbers as numerals, not words. For example, the text may say “add 9 to 3 to get 12,” not “add nine to three to get twelve.” We think this setup makes the ideas clearer in a math book.

What You’re Not to Read

We’d love for you to read every word in this book in the order it appears, but life is short. You don’t have to read chapters that don’t interest you. This reference book is designed to let you read only the parts you need.

You don’t have to read anything with a Technical Stuff or Did You Know? icon. That text is there to give you overly technical or trivial info. Sidebars (that’s what they’re called in publishing) are the shaded blocks of text you find every so often throughout the book. They’re interesting (we think) but not critical to your understanding of the main text, so you can skip ’em if you want.

Foolish Assumptions

Although we know what happens when you assume, we went ahead and made a couple of presumptions about you anyway:

We assume that you went to elementary and middle school, where you were exposed to math fundamentals. Why don’t we include high school? Because high school is where many people get bored, dazed, or frustrated with mathematics. You may have been in class, but maybe your mind was somewhere else.

We assume you have access to a computer and the Internet. It’s not essential, but it’s very handy. Use a good search engine to find out more about any topic in this book.

How This Book Is Organized

Technical Math For Dummies has five parts, moving from simpler topics (such as counting) to more complex topics (such as trigonometry). Here’s how it’s set up.

Part I: Basic Math, Basic Tools

In this part, you get math basics (and we do mean basics). Chapter 1 gives you an overview of broad technical math concepts. Chapter 2 dispels myths about math and provides some history about technical careers. Technical professions are very old and go back (at least) to making arrowheads and spear points. And with all due respect to art history and library science majors, stonemasons built the pyramids. You also learn about the tools of the trades in this chapter.

The remaining chapters in this part are a complete review of basics — numbers, addition, subtraction, multiplication, division, measurement, and conversion. You see how to do these operations faster and better. We also tackle something that everybody says fills them with fear and loathing — the notorious word or story problem. Story problems can be filled with tricks and traps, but in this chapter you see how easily you can deal with them all.

Part II: Making Non-Basic Math Simple and Easy

In Part II, you review the workhorses of technical math, the processes that are a simple step above arithmetic. Most careers can’t function without them.

Part III: Basic Algebra, Geometry, and Trigonometry

You may think some topics (algebra, geometry, and trigonometry) are tough, but in this part you find out that they aren’t. The basic techniques are easy to understand, and those are the techniques you need. Now that’s a happy coincidence!

This part removes the mystery from formulas and shows you how to make your own custom formulas. It’s also filled with practical applications for areas, perimeters, and volume, as well as a little theory.

Part IV: Math for the Business of Your Work

In Part IV, we point out the obvious: “Life math” is different from “classroom math.” Although the previous parts have direct application to your technical work, this part brings some math concepts to the business side of your job.

In this part, you see how to use graphs and charts to your advantage for both problem solving and presenting information to management and clients. We also present a chapter on time math, which we hope clears up a few mysteries about the basic questions “What time is it?” and “How long will it take?”

The last chapter deals with computer math, and it’s a simple mini-education in what’s going on with your computer and your Internet connection. This chapter may help make you a smarter shopper when you’re buying computers, smartphones, MP3 players, and digital instruments for your business or your home.

Part V: The Part of Tens

For Dummies books always have a Part of Tens, and this book is no exception. The world loves lists of ten things, and in these chapters you find a large amount of information in a small space.

Chapter 20 has ten principles for solving any common math problem. Its partner is Chapter 21, which contains the ten most commonly used formulas. It also has some formula variations and some estimating shortcuts. Finally, Chapter 22 shows you ten easy ways to get good at math while doing everyday tasks. Finally, we also include a glossary of terms that you may or may not see in the text but that may pop up in your work.

Icons Used in This Book

We use several icons (the little drawings in the margins of the book) to call out special kinds of information and enhance your reading experience — that’s just the kind of people we are. Here’s a breakdown:

A Tip is a suggestion or a recommendation that usually points out a quick and easy way to get things done.

This icon represents a key idea that’s worth remembering — the information may come in handy later.

Technical Stuff contains information that’s interesting but overly technical and not vital to your understanding the topic.

Text with this icon contains odd facts (such as a legislature trying to regulate the value of pi), pieces of pop culture, strange bits of history, or bizarre terms.

The text with this icon describes a situation where a math principle is used in real-world work.

This icon alerts you to conditions that can spoil your work or result in wrong answers. For example, dividing by zero is never allowed in math. Don’t try it or your hair may catch fire!

Where to Go from Here

You can go to any chapter of the book from here. First, check the table of contents, where you see the names of the parts and the chapters. Then, pick a chapter you’re interested in.

The book isn’t linear, so you can start anywhere. If you’re comfortable with some math concepts, take a glance at the early chapters of this book. This strategy will confirm how much you already know (and you may pick up a couple of interesting new words, too). Then go on.

If you’re uncomfortable with some math concepts (and some of them have truly bizarre and intimidating names), take a look at those chapters. Inside every “complicated” math concept is a simple concept trying to get out.

If you get stuck, you’ll probably find another chapter that can help you out. If you haven’t made a choice, we recommend beginning with Chapter 1, which introduces the broad concepts. If you have a particular problem, find a chapter in the table of contents that deals with it and go straight to it, or simply look up that topic in the index.

Part I

Basic Math, Basic Tools

In this part . . .

Part I starts with the basics. In Chapter 1, you find the broad scope of what technical math involves. Chapter 2 identifies the myths of math and the trades that make the world as you know it possible from earliest to latest. It also gives you a survey of tools (especially new digital tools) that make your work (particularly measuring) in the trades easier and more fun.

The other chapters in this part offer a complete review of numbers and arithmetic. But they’re more than just a good review — they also give you new insights and may even speed up your work. Chapter 6 is about measurement and conversion. Sorry to say it, but the world speaks measurement in different units, and the modern technician needs to know unit conversions. Chapter 7 is about word problems. After you read this chapter, you’ll never run from a story problem again.

Chapter 1

Math that Works as Hard as You Do

In This Chapter

Reviewing the very basics of math

Identifying the tools of the trade

Looking at math’s basic disciplines and branches

Applying math to the business of work

Previewing ten of this and ten of that

Technical mathematics(technical math) is an essential part of the work and the education of everyone in a technical career. If you’re studying a trade in a two-year college or an occupational program, you can’t dodge it, whether you’re taking formal math courses or dealing with math calculations in specialized courses.

For example, Heald College is a famous college in San Francisco and much of California in general, as well as Portland and Honolulu. To get a degree as a medical assistant (Associate in Applied Science), you have to take Math 10, Essential Math; Math 103, Elementary Algebra; and Math 205, Modern Business Mathematics. And that’s for an education in healthcare.

Even if you’re already working in the field you want, you encounter plenty of technical math to do. All the construction trades deal with math to build buildings, pour sidewalks, install flooring, lay carpet, calculate fencing runs, and figure out how much paint goes on the walls. And because these trades are businesses, you have to figure amounts of materials, costs of materials and labor, and client billing. You may try to avoid math, but if you do, you may be avoiding a chance to advance your career.

Bottom line: Math isn’t just something theoretical that professors in universities work with. It’s a practical skill used in most careers. Technical occupations built the world and also made it fit to live in. That takes technical math.

If math gives you the willies, heebie-jeebies, butterflies in the stomach, or palpitations of the heart, suffer no more. Every principle in this book is easy, if you look at it the right way. Technical math is easier (not harder) than you think.

Discovering the Benefits of a Technical Math Book

Regular math books are fine, but we believe that you can get more benefit more quickly from a technical math book. A technical math book is all about practical math, focusing on math for technical careers — the math principles you’re likely to need in everyday work. Abstract math need not apply.

Unlike regular math books, which tend be about a single discipline (for example, algebra, geometry, or trigonometry), a technical math book is comprehensive so that you don’t have to go to several texts to get what you need. This book covers a little bit about a lot of subjects, and no subject goes deeper than you need it to go.

A good technical math book also includes practical examples based on real-life experiences. As a result, you may even discover something about careers other than your own. And you may be able to apply a lot of workplace math to your personal life as well as your work life.

The Basics Are Basically Basic

The most basic component of math is numbers. The first thing you do with numbers is count, and you started counting when you were very young — as soon as you could talk, your mother probably cajoled you to tell Aunt Lucy how old you were or to count from one to five.

If you put numbers on a line, you get (are you ready?) a number line, shown in Figure 1-1. The number line is an arrangement of whole numbers called integers. (See Chapter 3.) With a number line, you can count as high as you want by going to the right and as low as you want by going to the left.

Figure 1-1: A number line.

Counting is not only the first math thing you probably ever did, but it’s also the first thing that ancient people did. The earliest math discovery is the Ishango bone, a tally stick, and it’s more than 20,000 years old!

Another basic component of math is arithmetic. That’s addition, subtraction, multiplication and division. You learned them in elementary school, but if you didn’t understand them well, you may still have trouble with the processes today. Even if you knew them and then forgot them, you can get a refresher in Chapters 4 and 5.

The word arithmetic comes from the Latin word arithmetica, which comes from the Greek words for “counting,” “number,” and “art.” Yes, it’s the art of counting numbers.

When you know about numbers and know arithmetic, you’re on your way to becoming a technical math terror. They’re basic skills, but those basic skills handle a lot of the math in day-to-day life and prepare you for some more interesting topics.

Meeting Measurement and Conversions and Studying Story Problem Strategies

Measuring quantities and amounts is fundamental to every career; knowing your units is important. It sounds simple, but the world throws you a couple of curve balls with two different common systems of measurement (American and metric), which we cover in Chapter 6.

Chapter 6 also shows you all the basic units of length, area, weight, volume, and liquid volume and how to convert from one unit to another, an essential in technical work. You also see how to convert from one unit system to the other.

When you know your math basics and your conversions, you can slay math monsters faster than Conan the Barbarian slays movie monsters. But Conan had a vital tool you don’t have, the Atlantean Sword. That’s where Chapter 7 comes in. It contains the tricks, traps, and techniques you need for solving story problems; with its help, you’ll laugh, scoff at, deride, and mock the so-called word problems that come up in everyday work life.

Using Workhorse Math

Four math disciplines — fractions, decimals, percentages, and exponents — are the workhorses of your trade. All careers use one or more of them, and some careers use all of them.

You use these four workhorses for many utilitarian purposes, a little like the way draft horses have been used for logging, plowing, pulling beer wagons (yes, the Budweiser Clydesdales are draft horses), hauling freight, and transporting passengers in horsecars. Like the horses, the math disciplines are strong and docile.

The chapters in Part II of this book tell you plenty about fractions, decimals, percentages, and exponents (and the exponent’s trusty sidekick, the square root), but here’s a little taste to whet your appetite:

Fractions: Fractions come in various forms, including stacked, unstacked or inline, decimal, and percentage; check out the following for examples.

You use fractions in just about every trade, and not only in doing your basic job — this math also comes up in working with time, money, and computer capacity. Find out more in Chapter 8.

Decimals: Decimals are a form of fraction, and they’re essential for work in major trades. The laboratory and the machine shop are two places where you find a lot of decimal numbers. Chapter 9 gives you the details.

Percentages: Percentages are fractions based on 100. You need percentages to express portions of a whole quantity, and they’re at the very core of working with money. Head to Chapter 10 for more.

Exponents and square roots: Exponents let you express very big and very small numbers (and do math with them) in a very compact way. Square roots help you solve a couple of pesky problems in your daily work. Chapter 11 has the lowdown on these concepts.

Building Your Knowledge of the Branches of Math

Some people say, “A little knowledge is a dangerous thing,” but that’s not necessarily so. No knowledge is a dangerous thing.

Don’t worry if you have “a little knowledge” about math. The good news is that you only need to know a little and you’ll do fine. But perhaps the best news is that Part III helps you out by expanding what you do know.

Algebra makes any problem solvable after you figure out the formula you need. As Chapter 13 shows, formulas are easy to develop, and they make even complicated story problems (shown in Chapter 7) collapse into solutions.

Geometry, as shown in Chapter 14, lets you draw the various shapes you need to measure landscape jobs, dress patterns, or whatever your job requires. Plus, you develop a great vocabulary about lines, angles, and shapes that can aid you in your daily work.

Alexander Pope, the poet, first wrote this saying in An Essay on Criticism in 1709.

A little learning is a dangerous thing;drink deep, or taste not the Pierian spring:there shallow draughts intoxicate the brain,and drinking largely sobers us again.

You may even use the Pythagorean theorem to find the lengths of sides of a triangle. That’s part of a method for finding the areas of patios, yards, and odd-shaped rooms, and in special cases, you can even use it to find the area of a piece of pie. Figure 1-2 shows a classic geometrical view of the theorem.

Figure 1-2: Graphic of the Pythagorean theorem.

In Figure 1-2, a2 represents the square of length a, and b2 is the square of length b. Also, c2 is the square of side c. Don’t worry about the letters or even the theorem now — we reveal all in Chapter 14. And check out Chapter 15 for help with areas, perimeters, and volumes.

In trigonometry, good math appears to be magic, but it’s really just good math. Trigonometry is essential for surveyors, land engineers, and fire lookouts, to name just a few. When you do a little trig, you can easily figure out how wide a river is without getting your feet wet. The solution to this problem has eluded one of the authors (Barry) since he was Boy Scout, but with the help of Chapter 16, he (and you) can finally cross that bridge.

Life Math Isn’t Classroom Math

The math of the classroom is good. The principles are solid, and the math is conceptual as well as real. Classroom math improves your thinking, and improved thinking can greatly reduce the Homer Simpson “D’oh!” factor in your life.

However, the math of life is what you face every day. It’s good, real, and entirely practical. When you do life math, it directly affects your work and the people who depend on you. Your calculations can affect

The appearance and building quality of a client’s new home

Effective wildfire fighting

Precise property line measurements

Accurate reporting of patients’ vital signs

Correct dispensing of drugs to patients

The quantity, taste, and nutrition of what people eat

Luckily, the chapters in Part IV help you deal with this side of math. They help you use graphics (particularly charts and graphs), do excellent time accounting (for payroll and client billing), and make smart purchases of computers and high-tech instruments (computer math).

“But wait,” you say. “I don’t do payroll or buy the computers, and no one has seen a graph at my office since 1972. Why do I need all this stuff?” The answer: Sometimes these math tools can be very valuable in your personal life. Pretend (and it’s not really pretending) that your wages seem flat, yet your family’s health insurance and out-of-pocket healthcare costs seem to be rising. Is that true? Find out by using a line graph (which we cover in Chapter 17). Figure 1-3 shows a comparison of annual wages and annual healthcare costs over several years.

The graph clearly shows something you’d hoped not to see. Healthcare costs are in fact overtaking your salary at a rapid rate.

Figure 1-3: A line graph comparing income to healthcare costs.

Chapter 2

Discovering Technical Math and the Tools of the Trades

In This Chapter

Identifying myths about math

Highlighting important ancient contributions to mathematics

Looking at the evolution of the trades

Examining tools for technical math

Mathematics is useful and fun. Read that sentence again, because it may startle you. Math is useful and fun, and it can get you out of more trouble than Superman and Batman combined. The main reason math is useful is that you can do so much with it; it’s a practical tool for solving problems in many careers. Finding answers to the questions and concerns that come up on the job is really satisfying. You get a great feeling when the light goes on and you say, “Oh! I get it!” And on the job, success is supposed to come to the person who gets the most things right. The trouble is, math gets a bad rap. No one knows who first started to give such a nice skill such a bad reputation — the search still goes on for whoever started spreading lies about math. As a result of this scoundrel, some urban legends about math still persist.

The technical work you do is vital in a world that relies on technology. And highly skilled technical work requires tools to get the work done. Look at the tools you use for technical math. Some are general, while others are very specific. Some simply measure, others calculate, and some do both. So what are the tools of the trades? They vary from career to career, but everyone uses a couple of tools. The two most important tools are your general math skills and the modern calculator. You need to know the math so you can appreciate what the specialty instruments do for you, and so you can do the same operations if you don’t have such instruments handy.

In this chapter, you find out what technical math is all about. Add to that a little history, because if people have been doing this stuff for so long, how hard can it be? And you also get a view of what tools of the trades are available.

Busting Myths about Math

Many myths about math spring from two great myths. If you’re able to recognize those myths, you’re well on your way to busting math myths yourself. The following sections introduce you to “I don’t need to use it” and “It’s too hard,” along with their cousin, “I have a phobia.”

“I don’t need to use it.”

Don’t mean to be rude, but talk to the hand, ’cause the face ain’t listening. Yes, you do have to use math. First, you need math to get through most programs of education (trade-related or otherwise). Then you likely need math on your job; even if the math is limited to counting and measuring, it’s math (and you can be sure we cover counting and measuring in this book).

You may think no math is involved in the culinary arts (the world of cooking, pastry, baking, and candy making), but think again. With all due respect for hamburger flippers, there’s a world of difference between grilling a double bacon cheeseburger and being executive chef at a three-star restaurant. The difference comes from a completing culinary school, which requires (wait for it) math.

The Michelin Guide started awarding stars to the best restaurants in 1926, and stars aren’t easy to get. The 2010 guide lists only 25 three-star restaurants in France and only 85 in the world.

Executive chefs do more than cook. They create, plan, budget, and do cost accounting. The work is a combination of art, cooking, and math. Even the food service operation of a hospital or retirement home requires math, such as scaling recipes up (as in turning a lasagna recipe that serves 6 into one that serves 300) and down (turning a recipe that serves 300 into one that serves 6).

The “I don’t need to use it” myth makes no sense to carpenters, cabinetmakers, concrete masons, lab technicians, cooks, or surveyors, whose careers clearly require math to get the job done. The only exception may be those who don’t want to advance in a career. If you don’t want to go anywhere, don’t study math.

To be much more positive, if you do want to go somewhere, do study math. And take heart! Some fields require only simple arithmetic (addition, subtraction, multiplication, and division), which you need for everyday life anyway.

“It’s too hard.”

Another grand math myth is “It’s too hard.” This myth was probably started by a person who said that about everything. Life isn’t particularly easy, so the mantra probably got a big reception from everybody, not just those who were doing math. Survival isn’t easy. If you go back a zillion years (that’s an approximate date), you see that hunting for food was “too hard,” yet somehow the human race hunted, survived, and got civilized.

You know what’s hard? Walking is hard. A human being isn’t constructed all that well for walking, but the average child learns how to walk by the time she’s about 11 months old. She looks a little clumsy at first but later becomes very proficient at walking as she does more of it.

Driving a car is hard, but most people can do it. They learn how to drive, and then (get ready) they drive. Two things make you a good driver: knowing the fundamentals and practicing.

That concept, of course, is shared by every professional dancer and athlete in the world. And it applies to just about every action or operation a professional does. It’s the same with mathematics. Know the fundamentals and practice. It’s a mantra you can live by. The carpenter’s first try at driving a nail probably bends the nail, and his first saw cut is probably crooked. But knowing the fundamentals and practicing eventually make the difference.

“I have a phobia.”

This misconception is a variation of the popular statements of denial in the preceding sections. Unfortunately, the argument doesn’t have legs, because all people approach new experiences with anxiety.

The distinction between anxiety and phobia is important. Anxiety is an everyday emotion. A phobia (a fear) is an anxiety disorder. Phobias are the most common form of anxiety disorders. In a study, the National Institute of Mental Health found that between 8.7 percent and 18.1 percent of Americans suffer from phobias.

You may have a phobia, but actual, legitimate math phobia (fear of not succeeding at math) isn’t common, regardless of what Internet hucksters try to tell (and sell) you. To be fair, math phobia does exist, but it’s not a permanent condition; after sufferers experience even small amounts of math success, they usually overcome it. So really, having a math phobia is even more reason to do math.

Remember: Somebody Else Already Did the Hard Work

Civilization makes math. But here’s a paradox. Math makes civilization. Mathematics started a long time ago in a galaxy far away (well, actually, on this planet). In the beginning, math was just about counting. (See Chapter 3.) And for a time in human existence, that was all people needed.

Well, being a hunter-gatherer is all very fine, but (to tweak an old song), we can show you a better time. That “better time” was nice, stable agriculture, which required some basic math to make it work when it was established about 10,000 years ago. Farming settles people down. It starts cities growing and it also produces specialized trades.

Math lets a culture do more, have more, and be more. As cultures grew more civilized, they needed to measure land and trade with other cultures. That requires math, so technical math grew and got sophisticated.

In the mere thousands of years from the cave dwellers to texting, mathematicians made discovery after discovery. They not only figured concepts out but also did what are called rigorous mathematical proofs. To put it another way, if you read about something in a math book, it’s been proven true.

Ancient cultures from all over each provided something. Several cultures came up with the same concepts independently, and others passed concepts on to other cultures. Historians don’t know for sure exactly who did what when, because trustworthy history is based on written records, which don’t always exist.

The following list gives you an overview of some of these historic contributions. There’s no mystery in this very brief history — just highlights, folks, because the full story is enormous, and some of the details come up in the other chapters of this book. The point of this cultural timeline is to show that the math has been developing for a long time. The concepts in this book have been used by billions of people.

Prehistory marks the birth of counting and tally sticks.

The Babylonians introduced arithmetic, algebra, and geometry around 3,000 BC. Math not only was handy for measuring the farmers’ fields but also helped the king collect taxes and astronomers look at the stars.

The Egyptians gave humanity measurements, the math for agriculture (as early as 5,000 BC), and the math to build 138 pyramids (as early as 2,630 BC).

The Indus Valley civilization produced the concept of the decimal system and the concept of zero (about 100 AD).

The Greeks provided, among other things, the systematic study of mathematics (between 600 BC and 300 BC). That includes rigorous arguments and proofs.

The Romans, among their many contributions, developed the standards still in use today for the weight and purity of gold and for precious metals and gemstones.

The Arabs were the conduit for the discoveries of China and the Indus Valley civilization to Europe. They formalized the concept of zero and made other brilliant discoveries on their own.

The Chinese developed math independently and were making strides as early as 300 BC.

The Europeans produced some wonderful math before and during the Enlightenment. Isaac Newton gets credit for calculus. Copernicus gets credit for modern trigonometry, and René “I think, therefore I am” Descartes had many hits on the top-100 math charts. He’s especially known for Cartesian coordinates. Head to Chapter 14 to see more about Cartesian coordinates.

The Mayans had a super calendar and an excellent number system. They also had the concept of zero.

All the other civilizations surely made unknown contributions. Where the historical record stops, the mystery begins. Perhaps the Hittites originated the credit card, or the Celts first developed the subprime mortgage.

The Trades, They Are A-Changing

Building technologies are probably the oldest trades, and they’re in no danger of disappearing. In fact, they’re more complex than ever. In addition, new trades are popping up regularly. As new careers come into existence and old careers evolve, the education and technologies that go with them must adapt. Trade schools (community colleges, technical colleges, and regional occupational programs) continue to offer vocational programs that expand as society’s needs expand, including creating green programs as environmental consciousness becomes more socially important.

These expansions reflect three broad trends. First, once-new technologies, such as automobiles and air conditioning, are a permanent part of modern life (yes, Virginia, cars and AC weren’t always common), so society must educate people to handle them. The second trend is the need to provide more specialized education for practitioners. The third trend is that education must offer training for the newest careers.

Here’s a tough assignment (NOT): Go see a movie. Make it an animated one if you can. At the end of the film, study the credits as they crawl by — you see the names of dozens of traditional Hollywood specialized crafts, but you also see many new careers. Some skill areas, such as computer generated imagery (CGI), were absolutely unknown not so long ago.

Technical careers continue to evolve. Some jobs haven’t been created yet, so we can’t exactly list them here. Other jobs are turning into professions right now as the required skills become more formalized and people need more advanced education in how to do them. As technology advances, your career will likely evolve into something other than what it is now. If you maintain your current skills — especially your math skills — and keep your eyes open for what a new career requires, you can transition with no problem.

Math Devices That Can Help You Do Your Job

Specialized calculators and measurement tools help you do your work more efficiently, but that doesn’t mean you should ignore general math skills. General math skills are great because they are general.

General skills are in your brain, which is a handy place for them. And you never have to replace batteries. You can use the skills in more than one career, which is excellent because experts say that the average person changes careers several times in a lifetime. Lastly, unlike a lot of tools you use on the job, you take your math skills home or anywhere else.

That said, some specialists make the same kind of calculations all the time, so specialty calculators devoted mainly to calculations needed for a particular trade are great additions to their math skills.