Recall that we have described arithmetic as a game. In the last section we studied numbers and these numbers are the game pieces

#### What Is an Operator?

Consider this definition of a (telephone or switchboard) **operator** from the Merriam-Webster dictionary: *a person whose job is to help to connect telephone calls*. More generally we think of an operator as a person who foes some kind of work. In mathematics we have many operators but not of the people kind. You will meet four in this section and learn a bit about the work they do.

The operators used in arithmetic are **addition** or “**plus**“, **subtraction** or “**minus**“, **multiplication** and **division**. We’re mathematicians and don’t like writing so we invent symbols to represent our operators. The symbols for addition and subtraction are {+,-}. An example of 3 plus 2 would be 3+2 and an example of 3 minus 2 would be 3-2.

The symbols for multiplication and division, {x,÷}, cause us problems, however. The “x” would be OK for multiplication in arithmetic but won’t work for algebra that you will learn soon enough, because in algebra we use “x” to represent an unknown quantity.

The Kahn Academy uses a special kind of *dot*, “•”, not to be confused with a period “.”. But the “•” symbol does not appear on a computer keyboard. Instead it has to be looked up in a special table, something that is time consuming and may not be possible for you. Computer programmers who type all day use the asterisk, “*”, as a multiplication symbol and that is what we will use. An example of 3 multiplied by 2 would be 3*2.

Division presents even more problems. The standard symbol used as the division operator is “÷”. Like the dot this is not on your keyboard. Text books represent long division by a symbol that looks like this: “)¯¯¯¯”. We can’t even fully express a problem with this symbol. The symbol that is on the keyboard that we will use for division is the forward slash, “/”. An example of 3 divided 2 would be 3/2.

#### Properties of Operators

Operators have a special word that identifies them, the word “operator”. Like the switchborad operator, the arithmetic operators do

#### Arithmetic Expressions

An operator is a person who does some kind of work, often between two people. If your computer breaks and you phone the company for help you may reach a receptionist or operator who will connect you to the right person to speak to.

In arithmetic our 4 operators do work that applies one number to another. The statement for the operation of subtraction that we wrote about above was 3-2. Such statements are called **expressions**. We will use this term a lot.

#### Key Points

In the lists below, ant text in red is for informational purposes only and the student need not remember them in this course.

##### New Words

##### New Symbols:

##### New Rules