Mathematics for Wastewater Management (Brooks)

Addition, Subtraction, Multiplication, and Division of Integers and Decimals using a Scientific Calculator

There are many types of scientific calculators available in the retail market, on our personal computers, and even on our personal devices such as cell phones and tablets. As a result, let’s first distinguish between two types of scientific calculators: A Display calculator and a non-display calculator. Some examples of display calculators are: TI30XIIS, TI-36X Pro, TI-30XS Multiview, and the Casio fx-350ES PLUS. Some examples of non-display calculators are TI-30Xa, most cell phone calculators, and most calculators on personal computers.

For our purposes, we will determine if a calculator is a “Display” calculator or a “non-display” calculator by doing the following:

Type 2 + 3 on your calculator.

• If your screen displays the entire expression 2 + 3, then you have a “Display” calculator.
• If you screen displays only the 3 after typing 2 + 3, then you have a “non-display” calculator.

On Display calculators, we can usually enter the problem as it is written. On a non-display calculator, we usually must enter the problem in reverse order of operations (see Unit 2 for more information).

Let’s revisit some of our earlier examples and calculate them on the scientific calculator. For negative numbers, be sure to use the negative symbol, (-), which is generally at the bottom of the keyboard on a TI calculator and not the subtraction symbol, -, which is usually on the right side of the keyboard. Each calculator is different, so you may have to experiment with your calculator to determine the process.

Fractions

Fractions are real numbers that indicate a portion of a whole. A fraction consists of a numerator and denominator. The denominator represents the number of equal parts of an object and the numerator represents a portion of those equal parts. For example, if pipe is separated into 4 equal parts, ¼ would represent 1 out of 4 of the parts, 2/4 would represent 2 out of the 4 parts, ¾ would represent 3 out of the 4 parts, and 4/4 = 1 would represent all 4 parts or the whole pipe. Likewise, 0/4 would represent 0 of the 4 parts or nothing, hence 0/4 = 0.

The rectangle below is divided into two equal parts. Hence 1 of the pieces out of the 2 pieces would represent 1/2.

Order of Operations

The order of operations represents a mathematical agreement of the order in which calculations should be performed. The order is Grouping Symbols, Exponents, Multiplication and Division as they appear left to right, and Addition and Subtraction as they appear left to right. Traditionally, we use PEMDAS as the acronym to remember the order of operations using Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. To allow us to perform operations on more problems, let’s consider Grouping Symbols as the first order since it would encompass parentheses, brackets, roots, absolute values, and fraction bars. So, let’s learn the acronym GEMDAS, one way to remember the letters is to remember GEMDAS: Greater Education Makes Doctors and Scholars or Good (Environment) Efforts Minimizes Diseased Animals Swimming.