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# MATHS FOR DUMMIES PDF

Saturday, May 11, 2019

Trademarks: Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, A Reference for . Part I: Arming Yourself with the Basics of Basic Math 9. DUMmIES ‰ Technical Math FOR DUMmIES ‰ by Barry Schoenborn and Bradley Simkins Technical Math For Dummies® Published by Wiley Publishing, Inc. Trademarks: Wiley, the Wiley Publishing logo, For Dummies, the Dummies Man logo, Mark Zegarelli is the author of Basic Math & Pre-Algebra For Dummies.

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For Pubic Release: Distribution Unlimited. The Air Force Research Laboratory. The Handbook of. Essential Mathematics. Formulas, Processes, and Tables. Trademarks: Wiley, the Wiley logo, For Dummies, the Dummies Man logo, A Reference for the Barry's the coauthor of Technical Math For Dummies, Medical. The Differences between Pre-Calculus and Calculus. Every good thing must come to an end, and for pre-calculus, the end is actually the beginn In Pre-.

Contents Rates of Change: Change in discrete steps, Two sides of the same coin, Some guesses Continuous change: A derivative, Properties of the derivative, Higher-order polynomials, The second derivative, Maxima and minima Infinity and beyond! Integration: Definite and indefinite integrals, The fundamental theorem of calculus, Properties of the integral, Applications, Averages, Work, Probability.

Improper integrals: Integrating a function that blows up, Limits of integration at infinity. Mahobe recommends this book to anyone taking a Calculus class unless they happen to be an absolute math genius. Even then we are sure that the geniuses will get a kick out of the humor interlaced through out the book. The topics this time around are many flavors of regression including simple, multiple, nonlinear, and logistic ; ANOVA one-way and two-way ; Chi-square tests for independence and goodness-of-fit ; and nonparametric procedures.

There is also interpretation of computer output for data analysis purposes and how to interpret the results found in the output.

There are full explanations of intermediate statistical ideas. Throughout the book are many examples that use statistical software to analyze the data. In each case, the computer output is given as well as an explanation of how the output was achieved and what it means.

There are an extensive number of examples to cover the many different types of problems you will face. Lots of tips, strategies, and warnings. If you put numbers on a line, you get are you ready? 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. Chapter 1: A number line.

Another basic component of math is arithmetic. Even if you knew them and then forgot them, you can get a refresher in Chapters 4 and 5. 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. Basic Math, Basic Tools comes in. 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. 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. The laboratory and the machine shop are two places where you find a lot of decimal numbers. Chapter 9 gives you the details. Percentages are fractions based on Head to Chapter 10 for more. 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. No knowledge is a dangerous thing. 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 A little learning is a dangerous thing; drink deep, or taste not the Pierian spring: You may even use the Pythagorean theorem to find the lengths of sides of a triangle.

Figure shows a classic geometrical view of the theorem. Graphic of the Pythagorean theorem. Basic Math, Basic Tools In Figure , a2 represents the square of length a, and b2 is the square of length b. Also, c2 is the square of side c. And check out Chapter 15 for help with areas, perimeters, and volumes. 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. The principles are solid, and the math is conceptual as well as real. However, the math of life is what you face every day. They help you use graphics particularly charts and graphs , do excellent time accounting for payroll and client billing , and make smart downloads of computers and high-tech instruments computer math.

Why do I need all this stuff? Sometimes these math tools can be very valuable in your personal life. Math that Works as Hard as You Do be rising. Is that true? Figure shows a comparison of annual wages and annual healthcare costs over several years.

Healthcare costs are in fact overtaking your salary at a rapid rate. 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. Finding answers to the questions and concerns that come up on the job is really satisfying.

I get it! 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. 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. Yes, you do have to use math. First, you need math to get through most programs of education trade-related or otherwise. You may think no math is involved in the culinary arts the world of cooking, pastry, baking, and candy making , but think again. The 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 and down turning a recipe that serves into one that serves 6. 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.

Chapter 2: Walking is hard. 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: 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.

Know the fundamentals and practice. But knowing the fundamentals and practicing eventually make the difference. 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. So really, having a math phobia is even more reason to do math. Basic Math, Basic Tools Remember: 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.

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. 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.

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. The following list gives you an overview of some of these historic contributions. 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. That includes rigorous arguments and proofs. They formalized the concept of zero and made other brilliant discoveries on their own. Isaac Newton gets credit for calculus. Head to Chapter 14 to see more about Cartesian coordinates. They also had the concept of zero. Where the historical record stops, the mystery begins. Perhaps the Hittites originated the credit card, or the Celts first developed the subprime mortgage.

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.

These expansions reflect three broad trends. Basic Math, Basic Tools 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. 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. 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.

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.

Some careers require more measurement than calculation; as a result, you can also find special measurement devices that give you exactly the information you need. The following sections give you a look at some of these calculators and measuring devices. Discovering Technical Math and the Tools of the Trades Pocket or phone, or computer calculators Although your mind is an excellent calculator, life is short and some calculations are long.

For complex math operations or any math operation on items with many digits you probably need a calculator. Get off your wallet and download a pocket calculator A basic calculator sometimes called a four-function calculator is really simple and very inexpensive.

This calculator does four basic math functions: But even the simple ones often include percentage and square root functions. This calculator not only does basic math but also has more buttons so you can do trigonometry functions, exponents and roots beyond square roots, and logarithmic functions that use both base 10 and base e.

Both types are still called pocket calculators. Eventually, they shrunk in size to fit in your pocket, and some are now so small they fit on a keychain. Your new mobile phone has a good calculator. For that matter, so does your older mobile phone. Apple iPhones have a really cool calculator. When you rotate it to the horizontal position landscape mode , it becomes a scientific calculator.

Do it with a mouse Desktop and notebook computers have come with built-in simple calculators for a long time. In the Microsoft Windows operating system, the classic version was a four-function calculator, as shown in Figure Backspace Figure Microsoft Windows fourfunction calculator. The scientific option is shown in Figure Calculator Edit View Help 0.

Hyp Dec Inv Figure Microsoft Windows scientific calculator. The classic Apple Macintosh Mac calculator is a four-function calculator. The dashboard calculator widget an on-screen mini-application that comes with the Mac OS X operating system has three options: It does far more than just calculations, but the calculations alone are impressive — the program contains dozens of built-in functions.

Find it at www. After you know the math behind the formulas, you can use the formulas with confidence. In the following sections, check out some of the many specialty calculators you can find. To get you started, you can find an extensive set of online calculators hundreds of them at www. Machinist calculator Machinist calculators are geared no pun intended for machine shop calculations. Go to www. It was first published in Conversions and one-time calculations The Internet is filled with free, simple conversion programs.

You can find conversions for angles, weight, temperature, fuel consumption, and so on. For example, point your browser to www.

Basic Math, Basic Tools Plumbing and pipefitting calculators Flow calculations are important in many plumbing applications, and a pipe flow calculator is a great example of the computerization of complex formulas. This calculator helps you work out pipe pressure drop and pipe diameters. Visit www. Roof surface area calculator For roof coatings, one estimating calculator uses a table.

You start with the interior square footage of the house to be roofed. Then you make allowances for roof overhang, the thickness of the walls, and the slope of the roof. After that, you consider the type of roof to be coated, as well as wastage. When those figures are all in place, the table gives you the total roof surface area to download coatings for. You can find this tool at www. You can also work out roof surface area from direct measurements or from blueprints, and that may be the smarter way to go because an online roof surface calculator can only provide an approximation.

Thermometers are essential for taking the temperature of the human body. For decades, the temperature was displayed as the height of a thin column of mercury in a glass tube. Now, digital thermometers display temperatures in either degrees Fahrenheit or degrees Celsius. Blood pressure is measured with a blood pressure cuff, or sphygmomanometer. Figure shows you an old-fashioned version, but these days, many blood pressure cuffs are digitized, and the CNA can take the readings directly from the instrument.

The blood pressure cuff measures systolic and diastolic blood pressure. Blood pressure measures two kinds of pressures in the arteries, which is why it includes two numbers.

For more on working with metric units, see Chapter 6. Discovering Technical Math and the Tools of the Trades 90 80 70 60 50 Figure An oldfashioned sphygmomanometer. Pulse is traditionally measured by using a stethoscope and a watch. Micrometers, calipers, and gauges Machinists have incredibly complex jobs, making the parts for just about every item you use.

Even parts made of plastic are machined, or the molds to make them are. At its simplest, a machinist does drilling, milling, turning, and grinding. Nowadays, most machine tools such as mills, turning centers, and drilling machines are computerized. Every step has to be programmed, and the machinist has to calculate feed rates and cutting speeds, based on the material and the cutting tools used. Online and downloadable calculators can help machinists with the needed calculations.

Basic Math, Basic Tools When the work is complete, the machinist uses micrometers, calipers, and gauges shown in Figure to make sure the work is accurate.

These are measurement tools, not math tools. Micrometers are also common in engineering applications wherever you must measure small dimensions precisely. You see calipers used in a variety of fields, including automotive technology see the example in Chapter 15 and medicine. Micrometers, calipers, and gauges. Many are specialty tools, such as the gas analyzer in Figure , used only in auto work. Devices like brake thickness gauges, coolant testers, and hand code readers require measurement and recording information, not math.

Because so many cars are managed by one or more computers, it takes a shop diagnostic computer with frequent upgrades to be able to read the codes that cars generate. Many automotive tools, such as the gas analyzer, are unique to mechanics. After a number of visual checks for example, fuel cap, crankcase smoke , the mechanic connects an RPM measurement device and puts a probe in the tailpipe. The computer does the rest, including sending the results over phone lines to the Department of Motor Vehicles.

Tire pressure is a common measurement at the garage, with digital gauges often replacing the older mechanical gauges. If part of his head is covered by the tread, you have more than inch of tread depth remaining. Legal tread depth is defined in 42 states as inch, with some variations in other states. Carpentry tools As a carpenter, your work is measurement- and calculation-intensive. You use it to make measurements and also to apply 29 30 Part I: The math involved is usually arithmetic addition, subtraction, multiplication, and division , which we cover in Chapters 4 and 5.

The steel square may be a contender for second place.

## Technical Math For Dummies

When you lay out a roof pitch, the math is arithmetic, with a bit of ratio work thrown in. See Chapter 8 for more on ratios. The tube contains a bubble; when the level is horizontal, the bubble rests between two marks.

Figure shows you an example. High-class spirit levels may have additional tubes for measuring vertical or degree inclinations. Figure The level has pretty much resisted going high tech.

However, newer laser levels project straight lines with the touch of a button. Yes, a little built-in bubble spirit level. Bricklaying tools Bricklayers need their work to be level and straight.

Chalk lines made with spirit levels such as the one shown in Figure and a tool called a chalk line, shown in Figure are important. Math is secondary in the basic work; the important thing is to use the tools correctly. However, as a bricklayer, you need to use a relatively large amount of math in preparing for work. You use multiplication to determine the area of a wall and division to calculate how many bricks the job requires. This figure in turn leads you to calculate how many bags of cement and sand or pre-mixed mortar you need for the job.

See Chapter 5 for details about multiplication and division. A chalk line. If Og found some mastodons for dinner, he went to his tribe, made the sign for a mastodon, and pointed in the direction where he saw them. Some careers are more number-intensive than others, but every trade uses numbers. This ability is what separates human beings from the lower-order creatures, such as oysters and fire hydrants. The beauty of numbers in counting their simplest application is that answers come with no skills besides counting.

However, even counting requires careful administration. And for speed and efficiency, you can go beyond counting to arithmetic, as we show you in later chapters.

In this chapter, you review the common types of numbers you work with and some uncommon, strange, and unbelievable numbers, too. You also explore the secrets of zero. All this requires no more than a set of fingers and toes to count with. Natural Numbers Natural numbers are basic numbers, which are also called counting numbers.

Most people just call them numbers. Natural numbers have a familiar look: They serve two purposes: Counting is the technique you use for inventory and all stock keeping. Natural numbers are also the fundamental unit of downloading, no matter what your line of business is. Using natural numbers takes on a personal meaning after work. You use natural numbers for ordering, describing things in a certain order. In your personal life, using numbers for ordering becomes painfully clear at the Department of Motor Vehicles.

Zero is part of a larger group of numbers. However, an exception exists in the field of computing: Zero becomes the first counting number and takes the first position in arrays and other data structures. Counting numbers with extras Integers are like counting numbers, but there are more of them. The set not only includes the counting numbers 1, 2, 3, 4, 5, 6, and so forth but includes zero 0 and negative numbers —1, —2, —3, —4, —5, —6, and so forth.

You can Chapter 3: Zero to One and Beyond also call these numbers whole numbers. Say the word integer with a soft g. Integers can be positive or negative, odd or even. Of course, a positive number is greater than zero.

An even number can be divided by 2 with no remainder. Zero is an even number. These integers look as orderly and evenly spaced as the chorus line in a Broadway musical. As you can imagine, if you have an infinitely wide stage, the negative integers at the left extend forever.

The positive integers at the right do the same thing. Integers are the numbers you use to perform all simple math. You can do all arithmetic operations addition, subtraction, multiplication, and most division with integers. Integers are also useful for plotting the points on a graph or chart. Where do they get these names?

The word integer comes from Latin and means untouched. Speaking of untouchable, integer is a relative of the word integrity. Making math easier What is zero 0? Zero may look like nothing, but it represents something — it appears in numbers and in calculations where digits ought to be. In a three-digit number, such as , those digits are more than just a 1, a 2, and a 3: But what happens when you have one hundred and three single items?

How do you write that without a placeholder? Ladies and gentlemen, boys and girls, what you need is a placeholder. In the number one hundred and three, let the 1 show one hundred, use a 0 show no tens, and have the 3 show three units, giving you Zero and the decimal system made most other math systems obsolete. Mathematicians point out that the decimal system is a base 10 system. The Maya of Central America used a base 20 system, and they used zero, too.

And for the nerdy band of brothers, the computer age brought forth the base 2 binary and base 16 hexadecimal systems.

Zero can be your biggest friend in mathematics because it makes for quick work: See Chapter 11 for more on powers and exponents. See how nice zero can make your math life? Where did zero really come from? Historians cite many different civilizations that might have developed decimals and zero, but the system may have evolved in the Indus Valley near the western edge of modern-day India , and the Indians may have gotten techniques from China.

Then the word spread to the Middle East. In , Muhammad ibn Musa al-Khwarizmi said if there was no number in a place, you should use a little circle.

The Arabic word for that little circle is safira meaning it was empty or sifr meaning nothing. That led to the modern English word cipher. Sifr also leads us to the Italian word zefiro meaning zephyr or zephyrum and the Venetian contraction zero.

Chapter 3: Zero to One and Beyond Going Backward: You represent negative numbers with a minus sign; for example, —1, —23, and —8, Working with negative numbers In mathematics, negative numbers are a concept.

In your daily activities, you work with negative numbers in the real sense, and they almost always represent a reduction or a deficit. But the reason you get to 0 units is because of inventory draws reductions , and each reduction in inventory is the application of a negative number.

Stock on hand minus the amount of the draw results in a new, lower amount of stock on hand. In virtually all trades, accounting transactions can result in amounts lower than zero.

For example, when a cosmetologist is sick, she has no clients no inflow of cash , but the rent is due on the station at the salon outflow of cash. Not so good. Negative cash flow is a real and painful concept. Traveling down the number line In mathematics, negative numbers are part of series of numbers.

One way to visualize the series is to draw a number line. Put 0 in the center, mark positive numbers to the right of 0, and mark negative numbers to the left of zero. Figure shows a number line. Basic Math, Basic Tools Figure The farther to the left of 0 you go, the more the numbers decrease in value. Looks can be deceiving. For example, the 9 in —9 is has a larger magnitude than the 8 in —8, but the minus sign the negative sign, — makes a difference.

A larger negative number has less value than a smaller negative number. Getting Between the Integers: Fractions, Decimals, and More Life was simpler in the third grade with only integers to deal with. So there comes a time in your career when you must also know about other types of numbers. In between the integers are many other numbers, known as common fractions, decimal fractions, rational numbers, and irrational numbers.

Our fractional friends Fractions are the most common numbers in the technical careers. A fraction is part of a number, more than zero but less than one.

The word comes from the Latin fractus or frangere, which means broken or to break, as opposed to integers, which are unbroken whole numbers. The two kinds of fractions are common fractions, which look like this: Zero to One and Beyond and decimal fractions, which look like 0. If you combine a whole number with a fractional number, the result is called a mixed number. For example, 5. Figure shows how fractions on the number line fall between the integers.

Fractions on the number line. The rational numbers and their irrational friends On the job and in your personal life, you have two kinds of friends: Both kinds are valuable to know except maybe the one who puts bean sprouts and peanut butter on pizza. The same is true with rational and irrational numbers: A rational number can be expressed as a ratio, the quotient of two integers.

Any common fraction fills the bill, as it shows the ratio of the top number to the bottom number. What about 0. This decimal number is really the fraction seventy-five one hundredths, and when shown as a common fraction: Following are examples of rational numbers: Basic Math, Basic Tools Like the integers and like the fractions, mathematicians have proved that an infinite number of rational numbers exist. You can express some numbers as fractions, but they produce infinite decimals in a repeating sequence.

For example: An irrational number is always acting out. Pi the ratio of the diameter of a circle to its circumference. Pi has been calculated to over one trillion! And they never will. At least once, the government has tried to legislate the value of pi.

Oh, how we authors wish we made these things up. In , the Indiana House of Representatives considered a bill that would have set pi to a value of 3. Taking a Look at the Lesser-Known Numbers The numbers you encountered so far in this chapter are the numbers you use in your work and at home. Here is the lightning round of other number types. Real numbers Real numbers is the name for all the numbers covered in this chapter to this point.

That includes natural numbers, integers, fractions, positive numbers, negative numbers, zero, rational numbers, and irrational numbers. Zero to One and Beyond Imaginary numbers An imaginary number is a number that includes the square root of —1. This value is supposedly impossible.

The math expression is: The symbol for the imaginary unit is i. A number that includes i for example, i or 7i or —3i is imaginary.

Early mathematicians thought imaginary numbers were useless. But the world of mathematics evolved, and in time mathematicians found the concept of imaginary numbers to be very useful. You use imaginary numbers in engineering disciplines like signal processing and vibration analysis. A complex number is a combination of a real number and an imaginary number.

Nominal numbers A nominal number sometimes called a categorical number is a number you use for identification only. Here are some examples of nominal numbers: Some locks and safes even use letters instead of numbers. No, not so. Humans are an infinitely clever species. They created the pet rock, the Furby, and the iPod. And indefinite numbers. The following are just a few indefinite numbers.

You know, just a handful. Not to worry. Check Chapter 7 for all the details about story problems. Automotive tech — a slippery task You work at a BMW motorcycle dealership. You hope to study more automotive technology in school and open your own shop some day.

But at the dealership, you have a pretty basic starter job, and your boss asks you to determine the on-hand quantity of BMW motor oil. Determine how many plastic containers of oil you have. Zero to One and Beyond 1. Take a look at the entire quantity to be counted.

The following figure shows the number of containers to be counted: Count the containers. The answer is 48 containers. The boss is pleased. He takes you to another stockroom and gives you a similar problem. The following figure shows a new group of containers to be counted: Simple counting solves the problem.

## Technical Math For Dummies

In the figure above, you have containers. Basic Math, Basic Tools Arithmetic, however is more efficient. With arithmetic, you would have figured out there are 16 rows of containers, with 28 cans in each row. Then you would have used multiplication to multiply the number of rows by 28 to get the total number of cans. The moral of the story and actually there are two: The difference between that and oil?

Getting the order right You and a co-worker are in the drive-through at Taco Palace. Together, your order is three tacos, two burritos, and two soft drinks. Use counting to confirm its correctness. Count the soft drinks.

Either speak the number or use your fingers. Count the burritos. Again, either speak the number or use your fingers. Count the tacos. You ordered three tacos and you only got two. The order is short. Let the person at the pick-up window know. Notice that for this problem only counting was required. The beauty of numbers in counting their simplest application is that answers come with no skills beside how to count.

Although this example is extremely simple, it shows that counting is sometimes the fastest, most accurate way to solve a problem. Chapter 4 Easy Come, Easy Go: In carpentry, you begin by hammering a nail and making a simple cut with a saw. In cooking, you begin with simple recipes. Even in sports, such as boxing, baseball, and the martial arts, you start with a basic stance. Math is the same way. The basics are addition and subtraction. Counting is well and good see Chapter 3 , but eventually you run out of fingers and toes.

That is to say, eventually counting is tedious, and you must go on to addition and subtraction. Basic Math, Basic Tools In this chapter, you review exactly what addition is and the parts of the addition operation. You do the same thing with subtraction.

You also see the easiest ways to check your work. Making Everything Add Up Addition is the process of combining quantities. You probably knew this, because addition is an operation you grow up with.

Each item to be added is an addend. Addition works with all kinds of numbers — integers, zero, rational numbers, fractions, and irrational numbers. That is: Chapter 4: Addition and Subtraction The same is true with decimals. For example, 3. To add in a column, simply arrange the numbers so that they are all aligned on the right side, and begin the addition process. Because these applications are cell-based, vertical columns are the logical approach to addition.

Figure shows addition in Excel. A Figure Adding numbers in Microsoft Excel. This feature is handy when you want to verify addition of a large number of items in several rows and columns. The technique is called downfooting and crossfooting, and you can find details on the Internet.

Basically, you sum the columns and the rows and compare the results for accuracy. Basic Math, Basic Tools Be careful with certain tools. So does a printing calculator yes, they still make them. And of course, adding 0 to 0 gets you 0.

Adding negative numbers If you had the wisdom, taste, and discernment to read Chapter 3, you know that negative numbers have a minus sign — in front of them and are numbers less than 0. You can add negative numbers.

No problem. The result of adding negative numbers is a larger negative number.

In algebra, you express the idea as: Addition and Subtraction Carrying the extra Adding in any digit position for example, the ones column, the tens column or the hundreds column is easy. But what do you do when the result it more than ten? You carry. The term carry means that when the results of adding a column are higher than 9, you record the right-hand digit the ones number and add the lefthand digit the tens number to the next column.

Just add. But what about adding and ? Not so simple. Well, to be fair to the poor ones column, no column can hold more than a single digit. What to do? Record the 4 and carry the 1 to the next column.

This process is simple, but we describe it fully here anyway for clarity. Look at the addition of 6 and 8 in the ones column. The sum of 6 and 8 is 14, so you write the 4 as part of the sum and carry the 1 to the top of the tens column. So, you write the 11 as 1 in the tens column and carry the one to the top of the hundreds column. Now, one more addition completes the work. Checking your work This tried-and-true tip is old as the hills and twice as dusty.

To check addition, add the column in reverse order. You should get the same sum. The answer should be the same. Addition and Subtraction Subtraction: Just Another Kind of Addition Subtraction is the process of removing a quantity from a quantity. Subtraction is the second math operation you grew up with besides addition. The words essentially mean the same thing and you may see either of them in subtraction problems.

A remainder is the balance of a quantity left after it has been reduced by subtraction. A difference is a numeric comparison between two quantities. The number you have left is the remainder. The number you subtract from which is usually the larger number is called the minuend. The number you are subtracting is the subtrahend. When you subtract, use a minus sign —. A subtraction problem in a column looks like this: Like addition, subtraction works with all kinds of numbers — integers, zero, rational numbers, fractions, and irrational numbers.

Basic Math, Basic Tools Subtracting a positive is the same as adding a negative What does it mean to say that subtraction is the inverse of addition? This may not seem like a big deal now, but it becomes important when you get to algebra see Chapter For more info about positive and negative numbers, flip to Chapter 3.

Subtracting negative numbers You can subtract negative numbers. The peculiar thing is that subtracting a negative is like adding a positive. In algebra, you express the idea as —a — —b The catch is that subtracting a negative number changes the sign.

Subtracting 0 from 0 is equal to 0. Subtracting multiple items You can subtract multiple items all at once, but be careful — doing so may be a little confusing. Addition and Subtraction This column of subtractions really represents multiple individual subtractions. Subtracting multiple items is more obvious in a spreadsheet. Figure shows subtraction in Microsoft Excel. Subtracting numbers in Microsoft Excel. Spreadsheets and printing calculators tell you the whole story, but pocket calculators and smartphones only show the results so far.

You can take shortcuts, such as adding all the negatives first. In the example you can first combine the negatives. Basic Math, Basic Tools The subtractions are lumped-together negatives, and you subtract them from the positive amount: The answer is still 3, just as before. In subtraction, you do it all the time to make subtraction easier.

The term borrowing refers to converting one unit from the next position at the left into the units you are working with. As you know, the positions of the numbers are the ones column, the tens column, the hundreds column and so forth. You can freely borrow from the column at the left of the column you are working in. To illustrate this, say you want to do this subtraction: Look at the ones column.

If you were subtracting 3 from 6, you could easily do it in your head. But how can you take 6 from 3?Even if you knew them and then forgot them, you can get a refresher in Chapters 4 and 5. High-class spirit levels may have additional tubes for measuring vertical or degree inclinations. Write the result next to the 0 placeholder. The inverse of 7 is So for the task of dividing 35 by 7, you can set up this multiplication problem: Instead of recording a tiny 8 in the dividend as you do in short division, just leave the remainder where it is.