# Introduction

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

When adding integers, for example, $(+10)+(-5)$, this is similar to $10-5=5$

However, when adding $(-5)+(-5)$, this is essentially $-5-5=-10$

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

Subtracting integers is more complicated. For example, $(-5)-(+2)$, 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 $(-5)-(+2)$, if we rewrite this as $-5-+2$, note we have a (-) and (+) next to each other, which equals a (-). Therefore, we replace the equation with $-5-2=-7$

A more complicated example is $(-5)-(-5)$. Removing the brackets, we have $-5-5$. Since 2 minuses equals a plus, we have $-5+5=0$

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 $(-5)-(+5)$, we can write $-5-5$. Alternatively, if we have $(+5)-(-5)$, we rewrite this as $5-(-5)$ 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 $(+5)*(-5)=-25$ because there is a mixture of (+) and (-). Alternatively, $(-5)*(-5)=25$, because there is a repeating/same (-) sign throughout.