Technical Math For Dummies ( PDFDrive )

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Introduction

At the risk of sounding like a late-night infomercial, we'd like to point out some of this book's unique features. For example, the text might 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.

Basic Math, Basic Tools

We assume that you went to elementary and high school where you were exposed to the basics of mathematics. Because a lot of people get bored, numb, or disillusioned with math in high school.

Making Non-Basic Math Simple and EasyMath Simple and Easy

Basic Algebra, Geometry, and Trigonometryand Trigonometry

Math for the Business of Your WorkBusiness of Your Work

The Part of Tens

If you are comfortable with some mathematical concepts, take a look at the early chapters of this book. If you are uncomfortable with some math concepts (and some of them have really weird and intimidating names), take a look at those chapters.

Basic Math, Basic Tools

It also gives you a survey of tools (especially new digital tools) that make your job (especially measurement) in trading easier and more fun. Sorry to say it, but the world speaks measurements in different units and the modern technician needs to know unit conversions.

Math that Works as Hard as You Do

The word arithmetic comes from the Latin word arithmetica, which is derived from the Greek words for "counting", "number" and "art". Yes, it is the art of counting numbers. Why do I need all these things?” Answer: Sometimes these mathematical tools can be very valuable in your personal life.

Discovering Technical Math and the Tools of the Trades

Another big math myth is, “It's too hard.” This myth was probably started by someone who said that about everything. In other words, if you read about something in a math book, it is proven to be true.

Discovering Technical Math and the Tools of the Trades Spreadsheet programs are your friends

Then you take into account the overhang of the roof, the thickness of the walls and the pitch of the roof. Try saying "sfig-mo" and combine that with "man-ometer." This is a device with an inflatable cuff and gauges.

Zero to One and Beyond

The placement of 1 means that 1 is the number of hundreds because it is in the third column from the right. The placement of 2 means that 2 is the number of tens because it is in the second column from the right.

Where did zero really come from?

For example, the countdown—the process of counting down hours, minutes, and seconds until something happens—is a "positive" application of negative numbers. You were first exposed to π in elementary school, and you can use it in work when you calculate circular areas or the volumes of cylinders.

Indefinite and fictitious numbers

Take a look at the entire quantity to be counted
Count the containers
Count the soft drinks
Count the burritos
Count the tacos

But you have a pretty basic entry-level job at the dealer, and your boss asks you to determine the amount of BMW engine oil on hand. Then you would use multiplication to multiply the number of rows by 28 to get the total number of cans.

Easy Come, Easy Go

Addition and Subtraction

Easy Come, Easy Go: Addition and Subtraction

Form a column with the flour amounts
Add the amounts
Subtract the number of sheep left from the number of sheep you had at the start of the day
Figure out how many trucks hauled the sheep away

Your Aunt Ida might have said, "Jane, if you had three apples and I took two, how many would you have left?" The mathematically and politically correct answer is: "An apple, Aunt Ida." The other answer—the one that will get you into trouble—is, "I'd still have three, you greedy old woman, because I wouldn't let you take any. The number of miles you've traveled is the difference between the first and second distances." 2. You can borrow freely from the column to the left of the column you are working on.

To make the 3 in the ones column in 13, simply borrow a single 10 from the tens column.

Baa, baa, black sheep

Multiplication and Division

Everybody Needs Them

Multiplication and Division: Everybody Needs Them

Write out the multiplication problem
Multiply the each column in the multiplier by the multiplicand
Follow Steps 1 and 2 of the basic multiplication process earlier in this section
Repeat Step 1 with the digit in the tens column of the multiplier, insert- ing a placeholder of 0 (zero) in the ones column of this multiplying step
Repeat Step 2 for the remaining digits in the multiplier, adding place- holder zeroes as appropriate

The result is higher than 10, so just write the 2's in the one column and carry the 1's. Repeat step 1 with the digit in the tens column of the multiplier and insert a placeholder 0 (zero) in the ones column of this multiplication step. So adding this placeholder reminds you to account for the zero in the lone place of 40.

Repeat Step 2 for the remaining digits in the multiplier, adding placeholder zeros as appropriate.

Figure 5-2 shows a classic multiplication table. It’s a 9 x 9 but includes 0 as well (so technically, it’s 10 x 10)

Using a calculator for multiplication and division

Write the dividend and divisor in the tableau
Divide the divisor into the first digit or digits larger than the divisor and write the quotient above the digit
Repeat Step 2 for the remaining digits
Divide the divisor into the first digit where it fits
Divide into the second digit, using any remainder from the previous step as a tens digit
Divide the divisor into the first digits where it fits
Multiply the quotient from Step 2 by the divisor, write the product below the first two digits of the dividend, and then subtract
Bring down the next digit from the dividend and place it next to the remainder from Step 3; divide the divisor into this new number, writ-
Repeat Steps 3 and 4 until you can’t divide into the dividend any more
Put the numbers from the problem into the tableau
Divide the divisor (34) into the first digits where it fits
Multiply the quotient (1) by 34 and write it below the first two digits (45); then subtract
Bring down the next digit (2); divide 34 into 112 and write the answer above the tableau
Multiply the quotient (3) by 34 and write it below the 112; subtract (leaving a remainder of 10) and bring down the next digit (2)
Divide 34 into 102 and write the result (3) in the quotient area; subtract

Write a 2 above the 9 in the quotient area, and put a small 1 to the right of the nine. Take the next digit from the dividend and place it next to the remainder from step 3; divide the divisor of this new number, write the remainder from step 3; divide the divisor by this new number and write the answer in the quotient area. The next number in the dividend is 4, so subtract it next to the remaining 8 from step 3 to get 84.

You now have 13 in the quotient range. remainder 10) and drop the next number (2).

Measurement and Conversion

In 1791, the French Academy of Sciences defined the meter (or metre, as much of the world spells it) as one ten-millionth of the distance from the equator to the North Pole through Paris. In 1983, the General Conference on Weights and Measures redefined the meter as the length of the path traveled by light in vacuum during a time interval of. But this system did not take into account absolute zero - the lowest temperature theoretically possible - so now 0 kelvin (0 K) is defined as -273.15 degrees Celsius, or absolute 0.

The big advantage of using metric units (aside from most of the world using them) is that most of the conversions are multiples of 10.

Table 6-1 Comparing Main American and Main Metric Units

What is a grain, anyway?

Convert the 8-foot dimension to inches, so all units for the 4 x 4 are in inches
Multiply thickness, width, and length to get the volume of a single 4 x 4
Divide by the conversion factor (1 board foot = 144 cubic inches) to get the result in board feet
Convert the 5 grains into grams
Convert the grams into milligrams

You can almost always find a formula online or in a book to convert from one unit to another. But if you measure a baby's weight as 142 ounces, you need to convert. The answer is in the definition: The prefix kilo is from the Greek and means 1000.

The answer is 324 milligrams, which is almost exactly the same as the 325 milligram tablets in the bottle.

Slaying the Story Problem Dragon

Read the problem
List the facts
Figure out exactly what the problem is asking foris asking for
Eliminate excess information
See what information is missing
Find the keywords
Pay attention to units
Convert information supplied into information neededinto information needed
Draw a diagram
Find or develop a formula
Consult a reference
Do the math and check your answer to see whether it’s reasonableto see whether it’s reasonable
Read and reread the problem
Identify things that you know
Determine what the problem is asking you to find
Eliminate any irrelevant information
Make a formula to solve the problem
Check your work
Count the houses
Determine the number of cats
Compute the number of mice, grains, and hekats
Add up the houses, cats, mice, grains, and hekats

Then read the problem again so you understand what answer you need and what information you have (steps we cover in later sections). Unfortunately, problems sometimes use units that are not the same as those required for the answer. The problem clearly states that you want to know how many pieces of each kind of lumber are in the load.

The problem says, "How many pieces of each kind of wood do you have?" Because you know the total number of pieces (942), you can get the number of the other kind of wood by subtracting when you know the number of pieces of one kind of wood.

Table 7-1 shows some typical keywords and their probable meanings.

Making Non-Basic Math Simple

Arithmetic with integers is fine, but the world is not based on integers.

Fun with Fractions

How fractions appear in this chapter

You can have one fifth of something or one third of something, but you cannot have one zero of anything. The denominator of a proper fraction is greater than the numerator, and the denominator of an improper fraction is less than the numerator. Since you need one half cup to make a dozen muffins, you can bake 31 dozen muffins.

You can express the percentage of people who are dating again as 94/100 and the percentage of people who are not dating again as 6/100.

There’s nothing vulgar about decimals

Multiply the numerators and the denominators

Reduce the result, if you can

Fun with Fractions Multiplying a fraction by 0

Invert the divisor
Multiply the numerators and the denominators
Reduce the fraction, if you want, by dividing both the top and bottom by a common factor
Multiply the top and bottom of the first fraction by the equivalent frac- tion that results in the common denominator
Repeat Step 1 for the second fraction, using a different equivalent fraction that results in the same common denominator
Using the new fractions formed in Steps 1 and 2, add the numerators
If you choose, convert to a mixed number when appropriate
Multiply the top and bottom of the first fraction by the equivalent fraction that results in the common denominator
Do the same thing to the second fraction, using a different equivalent fraction that results in the same common denominator
Using the new fractions formed in Steps 1 and 2, subtract the numerators
Multiply the length of one fire stop (14 1 ⁄ 2 inches) by five
Make another guess a bit higher than five
Try a number between your high and low guesses

You can divide the top and bottom numbers of a fraction by the same number (an equivalent fraction). The key to adding fractions is that their denominators (the bottom numbers) must be the same. Repeat Step 1 for the second fraction and use another equivalent fraction that results in the same common denominator.

Just like adding fractions, when you subtract fractions, you must make the denominators the same.

Decimals: They Have Their Place

You've also been dead for several thousand years, so you're looking pretty good. If you are of the Nunggubuyu people (in Numbulwar, Northern Territory, Australia), you use a base-5 system. However, when you work with decimal numbers smaller than 1, you are in the world of decimal fractions and life becomes interesting and more meaningful.

The distinguishing marks for decimal fractions are the decimal point and decimal places, which we discuss in the next section.

Decimal numbers for modern times

Decimals: They Have Their Place

The decimal point is a symbol that shows the boundary between the integer part (whole number) and the fractional part (decimal fraction) of a number. You can also call the decimal point the decimal separator, but no one outside the Mathematics Department ever does. In the United States and many countries, the decimal separator is a period (.), but in many other countries it is a comma.

The first number to the right of the decimal point is the first decimal place.

Decimals: They Have Their Place Pennies are the root of all money

Stack the multipliers without worry about decimal alignment
Multiply just as if the multipliers were integers
Place the decimal point
Figure out how many places you want to round to
Look at the numbers to the right of your chosen rounding place
Round up or down depending on the number to the immediate right of your chosen rounding place
Convert the sales tax rate from a percent to a decimal
Multiply the amount of the purchase by the sales tax rate
Add the result from Step 3 to the purchase amount to get the final amount of the purchase

This is the problem child of the Four Ops because the results have variations, but you will love it. Machinists and cabinetmakers who use computer-aided design are not the only people affected by fractional intolerance. The problem asks, "What is the largest amount of money that cannot be counted out using only coins of specified denominations?" The answer depends on the coins in your particular problem.

What's the largest number of McNuggets you can't make up by buying whole boxes? Before McDonald's introduced the four-nugget Happy Meal, the answer was 43 nuggets, but now it's down to 11.

Decimals: They Have Their Place Table 9-1 Figures for Restaurant Shopping Trip

Add the items to be purchased
Calculate the 10-percent discount
Round the discount to two decimal places
Calculate the sales tax on the discounted amount
Round the discount to two decimal places
Add the tax to the purchase to get the total

Playing with Percentages

Drop the percent sign and use the numerical portion of the term
Set the percentage number as a numerator over a denominator
Simplify your fraction
Turn the number into a fraction
Reduce the first fraction by dividing both parts by a common factor (if possible)
Turn the numbers into fractions
Repeat Step 2 to reduce the second fraction
Figure how many giant slices you can get from the pie and how much (if any) of the pie is left over
Determine how many of the skinny minislices you can get from the rest of the pie
Divide the pie by cutting it into the number of slices you determine

When you move the tenth to the left, the result is 0.200 liters, or 0.2 liters - the same answer you got with the actual division. But what about "or more?" If the discounts go over 20 percent, why didn't the dealer say so? 200 percent is double something, not triple it!” That's correct, but in this case, you're getting a 200 percent increase—you have to factor in the original amount as well.

Determine how many of the skinny little slices you can get from the rest of the pie.

Beware: Percentages can lie!

Determine the percentage decrease from the recipe quantity (90 dozen) to the desired quantity (3 dozen)
Multiply the decimal by 100 to convert the decimal to a percentage
Multiply each ingredient by 333 percent (or 0.0333) to develop the decreased amounts
Convert the decreased amounts from decimals into units more suited for home cooking
Playing with Percentages Table 10-2 Converting Decreased Amounts

You've lived in New Orleans all your life and you have your grandmother's famous recipe for pralines. You want to make 3 dozen pralines, but you have long forgotten the amount of the original recipe ingredient; however, you know your commercial amounts. Although some of the units here may seem a little unconventional, they make the math easier for the purposes of this example.

In some cases you just convert decimals to fractions, but some ingredients actually change units, so be careful.

Table 10-1 Decreasing Ingredient Amounts

Organize your info

Calculate the percentage of your supply each grade comprises

When you complete the three conversions, put them in a table to check your work

Tackling Exponents and Square Roots

Examine the situation
Split the difference between your too-high and too-low numbers
If your result isn’t quite right, try again, splitting the difference between your most recent guess and a lower number (if your guess
Repeat Step 3 until you get the most accurate answer you can

The previous section "Base Basics" shows you that a square is another way to describe a number raised to the power of 2. But what if you have a square and need to figure out what the square is. A square root is just finding the value of the base when you only know the result of squaring the value.

Excel's square root function is =SQRT(nnn), where nnn is the number whose square root you want to find.