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Technical Math For Dummies®

Book Description

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, certifacation, 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.

Table of Contents

  1. Copyright
  2. About the Authors
  3. Authors' Acknowledgments
  4. Publisher's Acknowledgments
  5. Introduction
    1. About This Book
    2. Conventions Used in This Book
    3. What You're Not to Read
    4. Foolish Assumptions
    5. How This Book Is Organized
      1. Part I: Basic Math, Basic Tools
      2. Part II: Making Non-Basic Math Simple and Easy
      3. Part III: Basic Algebra, Geometry, and Trigonometry
      4. Part IV: Math for the Business of Your Work
      5. Part V: The Part of Tens
    6. Icons Used in This Book
    7. Where to Go from Here
  6. 1. Basic Math, Basic Tools
    1. 1. Math that Works as Hard as You Do
      1. 1.1. Discovering the Benefits of a Technical Math Book
      2. 1.2. The Basics Are Basically Basic
      3. 1.3. Meeting Measurement and Conversions and Studying Story Problem Strategies
      4. 1.4. Using Workhorse Math
      5. 1.5. Building Your Knowledge of the Branches of Math
      6. 1.6. Life Math Isn't Classroom Math
    2. 2. Discovering Technical Math and the Tools of the Trades
      1. 2.1. Busting Myths about Math
        1. 2.1.1. "I don't need to use it."
        2. 2.1.2. "It's too hard."
        3. 2.1.3. "I have a phobia."
      2. 2.2. Remember: Somebody Else Already Did the Hard Work
      3. 2.3. The Trades, They Are A-Changing
      4. 2.4. Math Devices That Can Help You Do Your Job
        1. 2.4.1. Pocket (or phone, or computer) calculators
          1. 2.4.1.1. Get off your wallet and buy a pocket calculator
          2. 2.4.1.2. You know your cellphone has one
          3. 2.4.1.3. Do it with a mouse
          4. 2.4.1.4. Spreadsheet programs are your friends
        2. 2.4.2. Specialty calculators
          1. 2.4.2.1. Machinist calculator
          2. 2.4.2.2. Conversions and one-time calculations
          3. 2.4.2.3. Plumbing and pipefitting calculators
          4. 2.4.2.4. Roof surface area calculator
        3. 2.4.3. Thermometers and sphygmomanometers
        4. 2.4.4. Micrometers, calipers, and gauges
        5. 2.4.5. Automotive tools
        6. 2.4.6. Carpentry tools
        7. 2.4.7. Bricklaying tools
    3. 3. Zero to One and Beyond
      1. 3.1. Looking at the Numbers that Count: Natural Numbers
        1. 3.1.1. Integers: Counting numbers with extras
        2. 3.1.2. Zero: Making math easier
      2. 3.2. Going Backward: Negative Numbers
        1. 3.2.1. Working with negative numbers
        2. 3.2.2. Traveling down the number line
      3. 3.3. Getting Between the Integers: Fractions, Decimals, and More
        1. 3.3.1. Our fractional friends
        2. 3.3.2. The rational numbers(and their irrational friends)
      4. 3.4. Taking a Look at the Lesser-Known Numbers
        1. 3.4.1. Real numbers
        2. 3.4.2. Imaginary numbers
        3. 3.4.3. Complex numbers
        4. 3.4.4. Nominal numbers
      5. 3.5. Handling Numerical Story Problems
        1. 3.5.1. Example: Automotive tech — a slippery task
        2. 3.5.2. Example: Getting the order right
    4. 4. Easy Come, Easy Go: Addition and Subtraction
      1. 4.1. Making Everything Add Up
        1. 4.1.1. Adding numbers in a column
        2. 4.1.2. Adding zero
        3. 4.1.3. Adding negative numbers
        4. 4.1.4. Carrying the extra
        5. 4.1.5. Checking your work
      2. 4.2. Subtraction: Just Another Kind of Addition
        1. 4.2.1. Subtracting a positive is the same as adding a negative
        2. 4.2.2. Subtracting negative numbers
        3. 4.2.3. Subtracting zero
        4. 4.2.4. Subtracting multiple items
        5. 4.2.5. Borrowing when you have to
        6. 4.2.6. Checking your work
      3. 4.3. Example: Flour Power
      4. 4.4. Example: Sheep on Trucking
    5. 5. Multiplication and Division: Everybody Needs Them
      1. 5.1. Go Forth and Multiply!
        1. 5.1.1. Mastering multiplication terminology
        2. 5.1.2. Memorizing multiplication tables: Faster than a calculator
      2. 5.2. Doing Simple Multiplication Like Your Grandfather Did It
        1. 5.2.1. Checking your work
      3. 5.3. Easy Street: Multiplying by 0, 1, and 10
        1. 5.3.1. A zero pulse: Multiplying by 0
        2. 5.3.2. One is the loneliest number: Multiplying by 1
        3. 5.3.3. Multiplying by 10
      4. 5.4. Divide and Conquer
        1. 5.4.1. Dealing with division definitions
        2. 5.4.2. Dividing by using the inverse
        3. 5.4.3. Doing short division
          1. 5.4.3.1. A simple case of short division
          2. 5.4.3.2. Simple short division turns more complex
        4. 5.4.4. Going long (division)
        5. 5.4.5. Checking your work
        6. 5.4.6. Shortcuts: Dividing into 0 and by 0, 1, 10, and the dividend
          1. 5.4.6.1. Dividing into 0
          2. 5.4.6.2. Dividing by 0
          3. 5.4.6.3. Dividing by 1 or the dividend
          4. 5.4.6.4. Dividing by 10
      5. 5.5. Example: In the Machine Shop
    6. 6. Measurement and Conversion
      1. 6.1. Main (And Not So Main) Systems of Measurement
        1. 6.1.1. The metric system
        2. 6.1.2. The American system
        3. 6.1.3. The imperial system, or the modern English system
        4. 6.1.4. Troy weight: Just for bullets and bullion
        5. 6.1.5. Apothecaries' system: Not a grain of value any more
        6. 6.1.6. Other legitimate but specialized measurements
      2. 6.2. Converting Length, Weight, and Volume
        1. 6.2.1. The rules of conversion
          1. 6.2.1.1. Know the formula
          2. 6.2.1.2. Use identical units: Don't add feet to furlongs!
          3. 6.2.1.3. Use the right conversion tools
        2. 6.2.2. American units to American units
          1. 6.2.2.1. Length and distance
          2. 6.2.2.2. Weight (mass)
          3. 6.2.2.3. Volume
        3. 6.2.3. American to metric and back again
          1. 6.2.3.1. Length and distance
          2. 6.2.3.2. Weight (mass)
          3. 6.2.3.3. Volume
        4. 6.2.4. Converting metric to metric
          1. 6.2.4.1. Length and distance
          2. 6.2.4.2. Weight (mass)
          3. 6.2.4.3. Volume
      3. 6.3. Example: Don't Get Bored by Board Feet
      4. 6.4. Example: Getting the Dosage Right
    7. 7. Slaying the Story Problem Dragon
      1. 7.1. Removing the Mystery from Story Problems
        1. 7.1.1. How to approach a story problem: A real-life example
        2. 7.1.2. The secret formula inside every story problem
          1. 7.1.2.1. Recognizing the real-life factors
          2. 7.1.2.2. Identifying the keywords
      2. 7.2. The Step-by-Step Story Problem Solution
        1. 7.2.1. 1. Read the problem
        2. 7.2.2. 2. List the facts
        3. 7.2.3. margin-left:82.0pt;text-indent:-22.0pt'
        4. 7.2.4. 4. Eliminate excess information
        5. 7.2.5. 5. See what information is missing
        6. 7.2.6. 6. Find the keywords
        7. 7.2.7. 7. Pay attention to units
        8. 7.2.8. 8. Convert information supplied into information needed
        9. 7.2.9. 9. Draw a diagram
        10. 7.2.10. 10. Find or develop a formula
        11. 7.2.11. 11. Consult a reference
        12. 7.2.12. 12. Do the math and check your answer to see whether it's reasonable
      3. 7.3. Example: Furring Strips
      4. 7.4. Example: And Now, from the Banks of the Nile
  7. 2. Making Non-Basic Math Simple and Easy
    1. 8. Fun with Fractions
      1. 8.1. Meeting the Numerator and Denominator: Best Friends Forever
        1. 8.1.1. Taking a look at numerators
        2. 8.1.2. Defining denominators
        3. 8.1.3. Dealing with special cases
      2. 8.2. Tackling the Different Types of Fractions
        1. 8.2.1. Proper and improper fractions
        2. 8.2.2. Mixed numbers
          1. 8.2.2.1. A mixed fraction example
          2. 8.2.2.2. Another mixed fraction example
          3. 8.2.2.3. Yet another mixed fraction example
        3. 8.2.3. Ratios
      3. 8.3. Performing Math Operations with Fractions
        1. 8.3.1. Multiplying fractions
          1. 8.3.1.1. Multiplying a fraction by an equivalent fraction
          2. 8.3.1.2. Multiplying a fraction by 1
          3. 8.3.1.3. Multiplying a fraction by 0
        2. 8.3.2. Dividing fractions
          1. 8.3.2.1. Reducing a fraction
          2. 8.3.2.2. Fractions as a representation of division
        3. 8.3.3. Adding fractions
          1. 8.3.3.1. Adding fractions with the same denominator
          2. 8.3.3.2. Adding fractions with different denominators
        4. 8.3.4. Subtracting fractions
          1. 8.3.4.1. Subtracting fractions with the same denominator
          2. 8.3.4.2. Subtracting fractions with different denominators
      4. 8.4. Example: Dividing and Selling a Cheesecake
        1. 8.4.1. Pricing your cake wholesale
        2. 8.4.2. Pricing your cake retail
      5. 8.5. Example: Cutting Fire Stops for Framing Carpentry
    2. 9. Decimals: They Have Their Place
      1. 9.1. Diving into Decimal Basics
        1. 9.1.1. Pointing out decimal points and places
        2. 9.1.2. Precision, pennies, and parsing
          1. 9.1.2.1. Precisely, my dear Watson
          2. 9.1.2.2. Pennies are the root of all money
          3. 9.1.2.3. Parse the vegetables, please
      2. 9.2. The Four Ops: Working with Decimals in Four Math Operations
        1. 9.2.1. Adding excitement
        2. 9.2.2. Subtraction gives satisfaction
        3. 9.2.3. Multiply with abandon
        4. 9.2.4. Division is an important decision
      3. 9.3. Decimal Conversion
        1. 9.3.1. Converting fractions to decimals
        2. 9.3.2. Converting decimals to fractions
      4. 9.4. Round, Round, Get Around, I Get Around
      5. 9.5. Making Change and Charging Sales Tax
        1. 9.5.1. Making change
        2. 9.5.2. Charging sales tax
      6. 9.6. Example: A Journey to Office Supply Heaven
    3. 10. Playing with Percentages
      1. 10.1. Pinpointing Percentages: Half a Glass Is Still 50 Percent Full
        1. 10.1.1. A percentage is a fraction, but the denominator never changes
        2. 10.1.2. A percentage is a ratio, too
      2. 10.2. Percentages Are Good Converts
        1. 10.2.1. Converting percentages to decimals
        2. 10.2.2. Turning decimals into percentages
        3. 10.2.3. Going from percentages to fractions
        4. 10.2.4. Transforming fractions to percentages
      3. 10.3. Calculating Percentage Increases and Decreases
        1. 10.3.1. Percentage increases: You get 10 percent more!
        2. 10.3.2. Percentage decreases: You save 10 percent!
        3. 10.3.3. The 100 percent increase: You must be 100 percent satisfied!
      4. 10.4. Dividing a Pie Using Percentages
      5. 10.5. Example: The World of Pralines
      6. 10.6. Example: Oily to Bed and Oily to Rise
    4. 11. Tackling Exponents and Square Roots
      1. 11.1. Exponentiation: The Power of Powers
        1. 11.1.1. The basics of the base
        2. 11.1.2. Moving beyond 2 or 3
        3. 11.1.3. Different faces of special bases
          1. 11.1.3.1. Powers with base 10
          2. 11.1.3.2. Powers with base 2
          3. 11.1.3.3. Powers with base 1
          4. 11.1.3.4. Powers with base 0
          5. 11.1.3.5. Powers with base (−1)
          6. 11.1.3.6. Powers of 1 and 0
        4. 11.1.4. Exponentiation math
      2. 11.2. Getting Back to Your (Square) Roots
        1. 11.2.1. Square roots the hard way
        2. 11.2.2. Square roots the easy way
        3. 11.2.3. Square roots the effortless way
      3. 11.3. Example: Finding the Bytes On a Disk
  8. 3. Basic Algebra, Geometry, and Trigonometry
    1. 12. Algebra and the Mystery of X
      1. 12.1. Variables: Letters Represent Numbers, but the Math Is the Same
        1. 12.1.1. Understanding variables
        2. 12.1.2. Corralling constants
        3. 12.1.3. Examining expressions
        4. 12.1.4. Getting a handle on equations
        5. 12.1.5. Taking time for terms
      2. 12.2. Variable Relationships: X and Her Friends
        1. 12.2.1. Best friends forever: The constant and the variable
        2. 12.2.2. Simplifying variables: Variables of a feather flock together
      3. 12.3. Math Operations with Variables
        1. 12.3.1. Adding variables
        2. 12.3.2. Subtracting variables
        3. 12.3.3. Multiplying variables
          1. 12.3.3.1. Multiplying simple variable terms
          2. 12.3.3.2. Dealing with more complex multiplication
        4. 12.3.4. Dividing variables
          1. 12.3.4.1. Tackling simple variable division
          2. 12.3.4.2. Diving into more complicated variable division
      4. 12.4. Example: How Many Oranges Are in that Orange Juice?
        1. 12.4.1.
          1. 12.4.1.1. Converting oranges into pounds of oranges
      5. 12.5. Example: Medications In the Pillbox
    2. 13. Formulas (Secret and Otherwise)
      1. 13.1. Following the Formula for Building a Formula
        1. 13.1.1. Property A: Associativity
        2. 13.1.2. Property C: Commutativity
        3. 13.1.3. Property D: Distributivity
      2. 13.2. Working from a Formula to a Solution
        1. 13.2.1. Applying the same operation on both sides of the equal sign
          1. 13.2.1.1. Adding it up
          2. 13.2.1.2. What about subtraction?
          3. 13.2.1.3. Mixing in multiplication
          4. 13.2.1.4. Conquering the great divide
        2. 13.2.2. Converting units with a special multiplication rule
      3. 13.3. Calculating Speed, Time, and Distance: Three Results from One Formula
        1. 13.3.1. Solving for speed
        2. 13.3.2. Solving for time
        3. 13.3.3. Solving for distance
      4. 13.4. Example: Cement Masonry — Pouring City Sidewalks
      5. 13.5. Example: Lunch Time — Buying Burgers and Fries
    3. 14. Quick-and-Easy Geometry: The Compressed Version
      1. 14.1. Looking at Geometry's Basic Parts
        1. 14.1.1. No snakes on this plane: Cartesian coordinates
        2. 14.1.2. What's the point?
        3. 14.1.3. What's your line?
        4. 14.1.4. What's your angle?: Acute, obtuse, and right angles
      2. 14.2. Examining Simple Geometric Shapes
        1. 14.2.1. The square and the rectangle
        2. 14.2.2. The triangle: Just because it isn't a right triangle doesn't mean it's wrong
        3. 14.2.3. The polygon
        4. 14.2.4. The circle
      3. 14.3. Learn It Once and Forget It: The Pythagorean Theorem
      4. 14.4. Example: Don't Fence Me In
      5. 14.5. Example: The Pen Is Mightier Than the Paddock
    4. 15. Calculating Areas, Perimeters, and Volumes
      1. 15.1. Area: All That Space in the Middle
        1. 15.1.1. Calculating the area of rectangles and squares
        2. 15.1.2. Figuring the area of a parallelogram (a bent-over long rectangle)
        3. 15.1.3. Determining the area of a trapezoid (a trapewhat?)
        4. 15.1.4. Calculating the area of a triangle
        5. 15.1.5. Computing the area of a circle
      2. 15.2. Perimeters: Along the Edges
        1. 15.2.1. Understanding perimeters: What goes around comes around
        2. 15.2.2. Calculating the perimeters of polygons
        3. 15.2.3. A perimeter by any other name: Finding a circle's circumference
      3. 15.3. Volume: The Third Dimension
        1. 15.3.1. Getting a handle on American volume units
        2. 15.3.2. Calculating the volume of cuboids (also known as boxes)
        3. 15.3.3. Finding the volumes of spheres and cylinders
      4. 15.4. Example: Bore and Stroke for the Auto Guy
      5. 15.5. Example: Yard Area, the Landscaper's Nightmare
    5. 16. Trigonometry, the "Mystery Math"
      1. 16.1. Handling Triangles: More Angles than a Cornfield Maze
      2. 16.2. By Their Sines Shall Ye Know Them: Using Trigonometric Functions
        1. 16.2.1. Sine, cosine, and tangent: Three great relationships
        2. 16.2.2. Cosecant, secant, and cotangent: Three so-so relationships
        3. 16.2.3. The law of sines
      3. 16.3. Example: Surveying a River
      4. 16.4. Example: Locating a Wildfire
  9. 4. Math for the Business of Your Work
    1. 17. Graphs Are Novel and Charts Are Off the Chart
      1. 17.1. Defining Charts and Graphs and Their Advantages
      2. 17.2. Paying Tables Their Proper Respect
      3. 17.3. Introducing the Three Most Important Types of Charts
        1. 17.3.1. Walking the line graph
        2. 17.3.2. Sidling up to the bar graph
        3. 17.3.3. Getting a piece of the pie chart
      4. 17.4. Reading Charts and Graphs (And Recognizing a Bad One)
        1. 17.4.1. For a start, the parts of a chart
        2. 17.4.2. The good, the bad, the ugly, and the inaccurate
      5. 17.5. Making Charts and Graphs
        1. 17.5.1. Creating line graphs
        2. 17.5.2. Building bar graphs
        3. 17.5.3. Putting together pie charts
      6. 17.6. Example: Tracking Weight and Height in a Pediatric Practice
      7. 17.7. Example: Cost of Materials in Residential Construction
    2. 18. Hold on a Second: Time Math
      1. 18.1. Dividing Time into Hours, Minutes, and Seconds
      2. 18.2. There's a Time for Us, Somewhere a Time for Us: Time Notation Systems
        1. 18.2.1. 12-hour notation
        2. 18.2.2. 24-hour notation
        3. 18.2.3. Greenwich mean time (GMT)
        4. 18.2.4. UTC and Zulu time
        5. 18.2.5. Swahili time
        6. 18.2.6. Bible time
      3. 18.3. Converting Time
        1. 18.3.1. Going from minutes to seconds and back again
        2. 18.3.2. Changing hours to minutes and back again
        3. 18.3.3. Working with time as a fraction
      4. 18.4. Time Math: Calculating Time
        1. 18.4.1. Addition
        2. 18.4.2. Subtraction
        3. 18.4.3. Multiplication
        4. 18.4.4. Division
      5. 18.5. Example: The Timesheet for All Trades
      6. 18.6. Example: Microwave Magic
    3. 19. Math for Computer Techs and Users
      1. 19.1. Try a Bit of This Byte: Understanding Basic Computer Terms
      2. 19.2. The Sum of the (Computer) Parts, and the Numbers Involved
        1. 19.2.1. Disk capacity
        2. 19.2.2. Flash memory
        3. 19.2.3. Rama lama ding dong: RAM memory
        4. 19.2.4. Speed out of the gate: Processor rate
        5. 19.2.5. The Internet is running on "slow" today: Network speed
        6. 19.2.6. Burn, baby, burn: DVD write speed
      3. 19.3. Example: Total Capacity of a Mass Storage System
  10. 5. The Part of Tens
    1. 20. Ten Tips for Solving Any Math Problem
      1. 20.1. Figure Out Exactly What the Problem Asks For
      2. 20.2. List the Facts
      3. 20.3. Convert Supplied Information into Needed Information
      4. 20.4. Determine What Information You're Missing
      5. 20.5. Eliminate Excess Information
      6. 20.6. Draw a Diagram
      7. 20.7. Find or Develop a Formula
      8. 20.8. Consult a Reference
      9. 20.9. Pay Attention to Units
      10. 20.10. Check Your Answer to See whether It's Reasonable
    2. 21. Ten Formulas You'll Use Most Often
      1. 21.1. Area of a Square, Rectangle, or Triangle
      2. 21.2. Area of a Circle
      3. 21.3. Feet to Meters and Inches to Centimeters
      4. 21.4. Miles to Kilometers and Kilometers to Miles
      5. 21.5. Pounds to Kilograms and Ounces to Grams
      6. 21.6. Gallons to Liters and Liters to Gallons
      7. 21.7. Temperature Conversions
      8. 21.8. Hours to Minutes and Minutes to Hours
      9. 21.9. Distance, Time, and Speed
      10. 21.10. Volts, Amps, and Watts
    3. 22. Ten Ways to Avoid Everyday Math Stress
      1. 22.1. Get Help with Your Checkbook
      2. 22.2. Use Grocery Shopping to Build Confidence
      3. 22.3. Practice Reading Analog Clocks
      4. 22.4. Play Games
      5. 22.5. Memorize Math Signs, Symbols, and Formulas
      6. 22.6. Make the Multiplication Table a Mantra
      7. 22.7. Use Paper Maps and Practice Navigating
      8. 22.8. Try to Estimate Distances
      9. 22.9. Take Up Music
      10. 22.10. Integrate Math with Nonmath Skills
  11. Glossary