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.