Applied Math

Basic Calculations I

Whole Numbers - Adding/Subtracting

You have been doing basic math functions like adding, subtracting, multiplying, and dividing since grade school. You are also familiar with the math monster called word problems. Many people have trouble with word problems but, face it, most of the number-related problems you encounter in the real world do not come as nicely set up math equations. In the first two modules of this Applied Math course, we will review many basic calculations and math operations you already know and discuss how you will use these concepts in your job as a chemical operator.

In the real world, we use sentences to describe a problem. Sometimes you can get a clue on how to solve the problem from the words in the sentences. This list shows common words used to describe numerical problems and their related mathematical operations.

Complete this problem equation by entering the correct math operations.


Whole Numbers - Multiplying/Dividing

Good. Use multiplication when you are given the value of each item and need to find the total value of all items. Let’s look at another example.

Another way of stating this problem is “What is the total weight of 12 containers that weigh 800 pounds each?”.

Use division when you are given a total and asked for a value per unit.

The word in is often used when talking about converting one unit to another unit. We say there are 12 inches in a foot. When doing conversions, remember these rules.

To solve these problems, first determine if you are converting from a larger to a smaller unit or smaller to larger.


Fractions - Rules 1 thru 3

In precise manufacturing, most problems do not use only whole number values. Instead, we may need to describe some portion of a whole using fractions or decimals.

This list includes some general rules for working with fractions. Lets start with adding fractions and look at examples for each of these rules.

To add fractions with the same denominator, add the numerators and put the answer over the denominator.

Notice in this problem, the denominators are different. To add 1/2 to 1/4, we need to change how the fraction 1/2 is written. 1/2 is the same as 2/4 so we can write this problem as 2/4 + 1/4 which equals 3/4.


Fractions - Rule 4

When adding or subtracting mixed numbers, add or subtract the whole numbers together, and then the fractions.  Or first convert both numbers to fractions.

Suppose a pipe is needed from joint A to joint B.  Use the tape on the screen to measure this distance.

To fit inside the joints, we need one inch on each end of the pipe.  How long should we cut the pipe?

To convert this mixed number to a fraction, first change 2 to the fraction 6 thirds.  Then add 6 thirds to 2 thirds.

So we can rewrite this problem as 10/10 – 3/10 or 7/10ths.


Fractions - Rules 5 thru 6

1/3 of 5 1/2 can be written as 1/3 X 5 1/2. To multiply 1/3 x 5 1/2 we must first convert 5 1/2 to a single fraction. Next, multiply the numerators and the denominators. Finally, convert 11/6 into a mixed fraction by dividing 6 into 11. 11 divided by 6 is 1 5/6 remaining.


Fractions - Rule 7

15/40 can be reduced to a simpler fraction because both 15 and 40 can be evenly divided by 5.

You try it. What number can be evenly divided into both 6 and 10?

Right. Now write the simple form of this fraction.

When multiplying fractions, values in the denominator can be divided or canceled with ‘like’ values in the numerator. For this example we first convert 3 into the fraction 3 over 1. Next, we cancel like numbers in the denominators and numerators. Canceling is a shortcut way to simplify a fraction.


Fractions - Rule 8

To divide fractions, we invert the divisor and then multiply. In this example, we must first convert 6 to a fraction. Next, invert the divisor, 3/4, and then multiply.

To change this fraction into number of containers, divide 24 by 3.


Decimals - Overview

Electronic gauges, meters and other monitors usually display measurements in decimals. The more decimals that are in the result,the finer the measurement. This diagram shows the fraction represented by each decimal.

2.03 is described as 2 and 3 one hundredths.  This decimal number could be converted to a fraction simply by writing 2 and 3/100.

To change a fraction to a decimal, you must change the denominator to 10, 100, 1000, or other appropriate power of 10 by multiplying the numerator and denominator by a whole number.

Or maybe the quickest way to convert a fraction to a decimal is to divide the numerator by the denominator using long division or a calculator.

Here are some rules for working with decimals.


Decimals - Rules 1 and 2

To calculate with fractions and decimals, first convert to all fractions or all decimals. In this problem, we will convert 2 1/8 to a decimal.

To find the difference, line up the decimals and subtract.

Use zeros after the decimal if the number of decimal places is not the same.


Decimals - Rules 3 and 4

To multiply or divide numbers with decimals, first multiply or divide the digits.

Move over one decimal place for each decimal place in the original values. There are a total of 4 decimal places in the original numbers. Starting from the right, move over 4 places to insert the decimal.

As a side note, notice that if the decimal is less than one, we put a zero in front of the decimal. This is often used to prevent a decimal number from being confused as a whole number.

Decimals are rounded to the specified number of digits or to the number of digits in the original values. The desired number of decimal places is called significant digits. The number of significant digits in an answer will depend on the number of significant digits in the given data.  Non-zero digits are always significant.  Zeros are sometimes significant depending on where they are placed.


Decimals - Rules 5 and 6

Multiplying a number with decimals by 10 moves the decimal to the right 1 place. For whole numbers, the decimal is implie