book

Technical Math For Dummies®

by Bradley Simkins, Barry Schoenborn

July 2010

Beginner

384 pages

7h 10m

English

For Dummies

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About This BookConventions Used in This BookWhat You're Not to ReadFoolish AssumptionsHow This Book Is OrganizedPart I: Basic Math, Basic ToolsPart II: Making Non-Basic Math Simple and EasyPart III: Basic Algebra, Geometry, and TrigonometryPart IV: Math for the Business of Your WorkPart V: The Part of TensIcons Used in This BookWhere to Go from Here
1.1. Discovering the Benefits of a Technical Math Book1.2. The Basics Are Basically Basic1.3. Meeting Measurement and Conversions and Studying Story Problem Strategies1.4. Using Workhorse Math1.5. Building Your Knowledge of the Branches of Math1.6. Life Math Isn't Classroom Math
2.1. Busting Myths about Math2.1.1. "I don't need to use it."2.1.2. "It's too hard."2.1.3. "I have a phobia."2.2. Remember: Somebody Else Already Did the Hard Work2.3. The Trades, They Are A-Changing2.4. Math Devices That Can Help You Do Your Job2.4.1. Pocket (or phone, or computer) calculators2.4.1.1. Get off your wallet and buy a pocket calculator2.4.1.2. You know your cellphone has one2.4.1.3. Do it with a mouse2.4.1.4. Spreadsheet programs are your friends2.4.2. Specialty calculators2.4.2.1. Machinist calculator2.4.2.2. Conversions and one-time calculations2.4.2.3. Plumbing and pipefitting calculators2.4.2.4. Roof surface area calculator2.4.3. Thermometers and sphygmomanometers2.4.4. Micrometers, calipers, and gauges2.4.5. Automotive tools2.4.6. Carpentry tools2.4.7. Bricklaying tools
3.1. Looking at the Numbers that Count: Natural Numbers3.1.1. Integers: Counting numbers with extras3.1.2. Zero: Making math easier3.2. Going Backward: Negative Numbers3.2.1. Working with negative numbers3.2.2. Traveling down the number line3.3. Getting Between the Integers: Fractions, Decimals, and More3.3.1. Our fractional friends3.3.2. The rational numbers(and their irrational friends)3.4. Taking a Look at the Lesser-Known Numbers3.4.1. Real numbers3.4.2. Imaginary numbers3.4.3. Complex numbers3.4.4. Nominal numbers3.5. Handling Numerical Story Problems3.5.1. Example: Automotive tech — a slippery task3.5.2. Example: Getting the order right
4.1. Making Everything Add Up4.1.1. Adding numbers in a column4.1.2. Adding zero4.1.3. Adding negative numbers4.1.4. Carrying the extra4.1.5. Checking your work4.2. Subtraction: Just Another Kind of Addition4.2.1. Subtracting a positive is the same as adding a negative4.2.2. Subtracting negative numbers4.2.3. Subtracting zero4.2.4. Subtracting multiple items4.2.5. Borrowing when you have to4.2.6. Checking your work4.3. Example: Flour Power4.4. Example: Sheep on Trucking

5.1. Go Forth and Multiply!5.1.1. Mastering multiplication terminology5.1.2. Memorizing multiplication tables: Faster than a calculator5.2. Doing Simple Multiplication Like Your Grandfather Did It5.2.1. Checking your work5.3. Easy Street: Multiplying by 0, 1, and 105.3.1. A zero pulse: Multiplying by 05.3.2. One is the loneliest number: Multiplying by 15.3.3. Multiplying by 105.4. Divide and Conquer5.4.1. Dealing with division definitions5.4.2. Dividing by using the inverse5.4.3. Doing short division5.4.3.1. A simple case of short division5.4.3.2. Simple short division turns more complex5.4.4. Going long (division)5.4.5. Checking your work5.4.6. Shortcuts: Dividing into 0 and by 0, 1, 10, and the dividend5.4.6.1. Dividing into 05.4.6.2. Dividing by 05.4.6.3. Dividing by 1 or the dividend5.4.6.4. Dividing by 105.5. Example: In the Machine Shop
6.1. Main (And Not So Main) Systems of Measurement6.1.1. The metric system6.1.2. The American system6.1.3. The imperial system, or the modern English system6.1.4. Troy weight: Just for bullets and bullion6.1.5. Apothecaries' system: Not a grain of value any more6.1.6. Other legitimate but specialized measurements6.2. Converting Length, Weight, and Volume6.2.1. The rules of conversion6.2.1.1. Know the formula6.2.1.2. Use identical units: Don't add feet to furlongs!6.2.1.3. Use the right conversion tools6.2.2. American units to American units6.2.2.1. Length and distance6.2.2.2. Weight (mass)6.2.2.3. Volume6.2.3. American to metric and back again6.2.3.1. Length and distance6.2.3.2. Weight (mass)6.2.3.3. Volume6.2.4. Converting metric to metric6.2.4.1. Length and distance6.2.4.2. Weight (mass)6.2.4.3. Volume6.3. Example: Don't Get Bored by Board Feet6.4. Example: Getting the Dosage Right
7.1. Removing the Mystery from Story Problems7.1.1. How to approach a story problem: A real-life example7.1.2. The secret formula inside every story problem7.1.2.1. Recognizing the real-life factors7.1.2.2. Identifying the keywords7.2. The Step-by-Step Story Problem Solution7.2.1. 1. Read the problem7.2.2. 2. List the facts7.2.3. margin-left:82.0pt;text-indent:-22.0pt'7.2.4. 4. Eliminate excess information7.2.5. 5. See what information is missing7.2.6. 6. Find the keywords7.2.7. 7. Pay attention to units7.2.8. 8. Convert information supplied into information needed7.2.9. 9. Draw a diagram7.2.10. 10. Find or develop a formula7.2.11. 11. Consult a reference7.2.12. 12. Do the math and check your answer to see whether it's reasonable7.3. Example: Furring Strips7.4. Example: And Now, from the Banks of the Nile
8.1. Meeting the Numerator and Denominator: Best Friends Forever8.1.1. Taking a look at numerators8.1.2. Defining denominators8.1.3. Dealing with special cases8.2. Tackling the Different Types of Fractions8.2.1. Proper and improper fractions8.2.2. Mixed numbers8.2.2.1. A mixed fraction example8.2.2.2. Another mixed fraction example8.2.2.3. Yet another mixed fraction example8.2.3. Ratios8.3. Performing Math Operations with Fractions8.3.1. Multiplying fractions8.3.1.1. Multiplying a fraction by an equivalent fraction8.3.1.2. Multiplying a fraction by 18.3.1.3. Multiplying a fraction by 08.3.2. Dividing fractions8.3.2.1. Reducing a fraction8.3.2.2. Fractions as a representation of division8.3.3. Adding fractions8.3.3.1. Adding fractions with the same denominator8.3.3.2. Adding fractions with different denominators8.3.4. Subtracting fractions8.3.4.1. Subtracting fractions with the same denominator8.3.4.2. Subtracting fractions with different denominators8.4. Example: Dividing and Selling a Cheesecake8.4.1. Pricing your cake wholesale8.4.2. Pricing your cake retail8.5. Example: Cutting Fire Stops for Framing Carpentry
9.1. Diving into Decimal Basics9.1.1. Pointing out decimal points and places9.1.2. Precision, pennies, and parsing9.1.2.1. Precisely, my dear Watson9.1.2.2. Pennies are the root of all money9.1.2.3. Parse the vegetables, please9.2. The Four Ops: Working with Decimals in Four Math Operations9.2.1. Adding excitement9.2.2. Subtraction gives satisfaction9.2.3. Multiply with abandon9.2.4. Division is an important decision9.3. Decimal Conversion9.3.1. Converting fractions to decimals9.3.2. Converting decimals to fractions9.4. Round, Round, Get Around, I Get Around9.5. Making Change and Charging Sales Tax9.5.1. Making change9.5.2. Charging sales tax9.6. Example: A Journey to Office Supply Heaven
10.1. Pinpointing Percentages: Half a Glass Is Still 50 Percent Full10.1.1. A percentage is a fraction, but the denominator never changes10.1.2. A percentage is a ratio, too10.2. Percentages Are Good Converts10.2.1. Converting percentages to decimals10.2.2. Turning decimals into percentages10.2.3. Going from percentages to fractions10.2.4. Transforming fractions to percentages10.3. Calculating Percentage Increases and Decreases10.3.1. Percentage increases: You get 10 percent more!10.3.2. Percentage decreases: You save 10 percent!10.3.3. The 100 percent increase: You must be 100 percent satisfied!10.4. Dividing a Pie Using Percentages10.5. Example: The World of Pralines10.6. Example: Oily to Bed and Oily to Rise
11.1. Exponentiation: The Power of Powers11.1.1. The basics of the base11.1.2. Moving beyond 2 or 311.1.3. Different faces of special bases11.1.3.1. Powers with base 1011.1.3.2. Powers with base 211.1.3.3. Powers with base 111.1.3.4. Powers with base 011.1.3.5. Powers with base (−1)11.1.3.6. Powers of 1 and 011.1.4. Exponentiation math11.2. Getting Back to Your (Square) Roots11.2.1. Square roots the hard way11.2.2. Square roots the easy way11.2.3. Square roots the effortless way11.3. Example: Finding the Bytes On a Disk
12.1. Variables: Letters Represent Numbers, but the Math Is the Same12.1.1. Understanding variables12.1.2. Corralling constants12.1.3. Examining expressions12.1.4. Getting a handle on equations12.1.5. Taking time for terms12.2. Variable Relationships: X and Her Friends12.2.1. Best friends forever: The constant and the variable12.2.2. Simplifying variables: Variables of a feather flock together12.3. Math Operations with Variables12.3.1. Adding variables12.3.2. Subtracting variables12.3.3. Multiplying variables12.3.3.1. Multiplying simple variable terms12.3.3.2. Dealing with more complex multiplication12.3.4. Dividing variables12.3.4.1. Tackling simple variable division12.3.4.2. Diving into more complicated variable division12.4. Example: How Many Oranges Are in that Orange Juice?12.4.1.12.4.1.1. Converting oranges into pounds of oranges12.5. Example: Medications In the Pillbox
13.1. Following the Formula for Building a Formula13.1.1. Property A: Associativity13.1.2. Property C: Commutativity13.1.3. Property D: Distributivity13.2. Working from a Formula to a Solution13.2.1. Applying the same operation on both sides of the equal sign13.2.1.1. Adding it up13.2.1.2. What about subtraction?13.2.1.3. Mixing in multiplication13.2.1.4. Conquering the great divide13.2.2. Converting units with a special multiplication rule13.3. Calculating Speed, Time, and Distance: Three Results from One Formula13.3.1. Solving for speed13.3.2. Solving for time13.3.3. Solving for distance13.4. Example: Cement Masonry — Pouring City Sidewalks13.5. Example: Lunch Time — Buying Burgers and Fries
14.1. Looking at Geometry's Basic Parts14.1.1. No snakes on this plane: Cartesian coordinates14.1.2. What's the point?14.1.3. What's your line?14.1.4. What's your angle?: Acute, obtuse, and right angles14.2. Examining Simple Geometric Shapes14.2.1. The square and the rectangle14.2.2. The triangle: Just because it isn't a right triangle doesn't mean it's wrong14.2.3. The polygon14.2.4. The circle14.3. Learn It Once and Forget It: The Pythagorean Theorem14.4. Example: Don't Fence Me In14.5. Example: The Pen Is Mightier Than the Paddock
15.1. Area: All That Space in the Middle15.1.1. Calculating the area of rectangles and squares15.1.2. Figuring the area of a parallelogram (a bent-over long rectangle)15.1.3. Determining the area of a trapezoid (a trapewhat?)15.1.4. Calculating the area of a triangle15.1.5. Computing the area of a circle15.2. Perimeters: Along the Edges15.2.1. Understanding perimeters: What goes around comes around15.2.2. Calculating the perimeters of polygons15.2.3. A perimeter by any other name: Finding a circle's circumference15.3. Volume: The Third Dimension15.3.1. Getting a handle on American volume units15.3.2. Calculating the volume of cuboids (also known as boxes)15.3.3. Finding the volumes of spheres and cylinders15.4. Example: Bore and Stroke for the Auto Guy15.5. Example: Yard Area, the Landscaper's Nightmare
16.1. Handling Triangles: More Angles than a Cornfield Maze16.2. By Their Sines Shall Ye Know Them: Using Trigonometric Functions16.2.1. Sine, cosine, and tangent: Three great relationships16.2.2. Cosecant, secant, and cotangent: Three so-so relationships16.2.3. The law of sines16.3. Example: Surveying a River16.4. Example: Locating a Wildfire
17.1. Defining Charts and Graphs and Their Advantages17.2. Paying Tables Their Proper Respect17.3. Introducing the Three Most Important Types of Charts17.3.1. Walking the line graph17.3.2. Sidling up to the bar graph17.3.3. Getting a piece of the pie chart17.4. Reading Charts and Graphs (And Recognizing a Bad One)17.4.1. For a start, the parts of a chart17.4.2. The good, the bad, the ugly, and the inaccurate17.5. Making Charts and Graphs17.5.1. Creating line graphs17.5.2. Building bar graphs17.5.3. Putting together pie charts17.6. Example: Tracking Weight and Height in a Pediatric Practice17.7. Example: Cost of Materials in Residential Construction
18.1. Dividing Time into Hours, Minutes, and Seconds18.2. There's a Time for Us, Somewhere a Time for Us: Time Notation Systems18.2.1. 12-hour notation18.2.2. 24-hour notation18.2.3. Greenwich mean time (GMT)18.2.4. UTC and Zulu time18.2.5. Swahili time18.2.6. Bible time18.3. Converting Time18.3.1. Going from minutes to seconds and back again18.3.2. Changing hours to minutes and back again18.3.3. Working with time as a fraction18.4. Time Math: Calculating Time18.4.1. Addition18.4.2. Subtraction18.4.3. Multiplication18.4.4. Division18.5. Example: The Timesheet for All Trades18.6. Example: Microwave Magic
19.1. Try a Bit of This Byte: Understanding Basic Computer Terms19.2. The Sum of the (Computer) Parts, and the Numbers Involved19.2.1. Disk capacity19.2.2. Flash memory19.2.3. Rama lama ding dong: RAM memory19.2.4. Speed out of the gate: Processor rate19.2.5. The Internet is running on "slow" today: Network speed19.2.6. Burn, baby, burn: DVD write speed19.3. Example: Total Capacity of a Mass Storage System
20.1. Figure Out Exactly What the Problem Asks For20.2. List the Facts20.3. Convert Supplied Information into Needed Information20.4. Determine What Information You're Missing20.5. Eliminate Excess Information20.6. Draw a Diagram20.7. Find or Develop a Formula20.8. Consult a Reference20.9. Pay Attention to Units20.10. Check Your Answer to See whether It's Reasonable
21.1. Area of a Square, Rectangle, or Triangle21.2. Area of a Circle21.3. Feet to Meters and Inches to Centimeters21.4. Miles to Kilometers and Kilometers to Miles21.5. Pounds to Kilograms and Ounces to Grams21.6. Gallons to Liters and Liters to Gallons21.7. Temperature Conversions21.8. Hours to Minutes and Minutes to Hours21.9. Distance, Time, and Speed21.10. Volts, Amps, and Watts
22.1. Get Help with Your Checkbook22.2. Use Grocery Shopping to Build Confidence22.3. Practice Reading Analog Clocks22.4. Play Games22.5. Memorize Math Signs, Symbols, and Formulas22.6. Make the Multiplication Table a Mantra22.7. Use Paper Maps and Practice Navigating22.8. Try to Estimate Distances22.9. Take Up Music22.10. Integrate Math with Nonmath Skills

Content preview from Technical Math For Dummies®

Chapter 10. Playing with Percentages

In This Chapter

Defining a percentage
Checking out four frequently used conversions
Performing basic percentage math

The words percent and percentage are everywhere. No matter your occupation, you most likely encounter percentages, both as part of your day-to-day tasks and as part of the business side, including buying things, selling things, and paying people. Percentages are also part of common talk and always make appearances in the media, which is just fine when you understand what percentages are and how to use them. But if you don't, you can end up with some big errors and distorted information.

In this chapter, you find out what a percentage is and how to convert numbers to percentages. As a bonus, you convert percentages to numbers. And you even discover some shortcuts, too.

Pinpointing Percentages: Half a Glass Is Still 50 Percent Full

You take half, I'll take half. Isn't that the same as saying we'll split something 50/50 or saying 50 percent for you and 50 percent for me? That's three ways of saying the same thing.

To put it simply, a percentage is a way of saying how large or small a quantity is compared to another quantity. It doesn't get a bit more complicated than that. (You can also call a percentage a percent or a per cent.) For the simplest things in life, simple words like "half" work fine. The old saying asks, "Is the glass half full or half empty?" The optimist looks at how much is in the glass. The pessimist looks at how little ...