4 Integers

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, (+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.

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