## Addition

Any two numbers can be added. When two or more numbers are added, the result is called the **sum**. The order in which we add two or more numbers does not matter. Adding them in any order will give the same answer.

#### Example 1

21 + 34 = 34 + 21 = 55

21 + 34 + 45 = 55 + 45 = 21 + 79 = 100

Remember that **pronumerals **are numbers so:

\(x+2=2+x,\ x+y=y+x\)

\(x+y+z=(x+y)+z=x+(y+z)\)

\(3x+2y+6x=3x+6x+2y=9x+2y\)

All of these examples illustrate the **any-order property** for addition. It states that a list of numbers can be added together in any order to give the sum of the numbers. This property summarises the **commutative** and **associative** laws for addition.

## Subtraction

Subtraction gives the **difference **between two numbers. For example, the difference between 8 and 5 is 3 and this is written 8 − 5 = 3.

The same rule applies when using pronumerals.

#### Example 2

The difference between \(x\) and \(y\) is \(x-y\).

The difference between \(7x\) and \(2x\) is \(7x-2x=5x\).