Introduction

Integers are whole numbers, whether they are negative or positive. The set includes -10, -9, -8, etc… 8, 9, 10, etc…

Adding and subtracting integers

When adding integers, for example, , this is similar to

However, when adding , this is essentially

It is necessary to know the number scale well in order to do these calculations.

Subtracting integers is more complicated. For example, , remember the rule that:

• When there is a (+) and (+) next to each other, it equals a (+)
• When there is a (+) and (-), or a (-) and (+) next to each other, it equals a (-)
• When there is a (-) and (-) next to each other, it equals a (+)

For , if we rewrite this as , note we have a (-) and (+) next to each other, which equals a (-). Therefore, we replace the equation with

A more complicated example is . Removing the brackets, we have . Since 2 minuses equals a plus, we have

In maths, usually, we don’t bracket each number however. We only insert brackets to prevent 2 signs next to each other, as it can be often difficult to read otherwise. For example, instead of writing , we can write . Alternatively, if we have , we rewrite this as before simplifying.

Multiplying and dividing integers

When multiplying/dividing integers, there are 2 parts. The first part is to multiply/divide the number as necessary. The next is to determine the sign. The rules are that:

• When multiplying a (+) and (+), you get a (+)
• When multiplying a (+) and (-), or a (-) and (+), you get a (-)
• When multiplying a (-) and (-), you get a (+)

For example because there is a mixture of (+) and (-). Alternatively, , because there is a repeating/same (-) sign throughout.