# Addition and Subtraction of Integers

## What are Integers?

Integers are numbers that are not fractions such as 1,2,3… 45, 265 etc.

Fractions or numbers that also have parts of numbers are not integers.

**For Example :**

1.5, 2/3, ½, 23.21, 733.21 are not integers.

### What do you do with Integers?

Integers can be added and subtracted to each other. They can also be divided and multiplied. But while doing so they have certain integer properties.

## Properties of Integers

### 1. The Commutative Property of Integer Addition

If you are adding two or more integers to each other, they add up to the same answer, no matter what order you add them up in.

3 + 5 + 2 = 10

2 + 3 + 5 = 10

5 + 3 + 2 = 10

Each time it is the same answer!

### 2. The Commutative Property of Integer Multiplication

If you are multiplying two or more integers to each other, they add up to the same answer, no matter what order you add them up in.

3 x 5 x 2 = 30

2 x 3 x 5 = 30

5 x 3 x 2 = 30

Same answer each time!

## 3. The Associative Property of Integer Addition

Even if you group the integers in different ways and then add them, they will have the same answers.

(3 + 5) + 2 = 8 + 2 = 10

(2 + 3) + 5 = 5 + 5 = 10

5 + (3 + 2) = 5 + 5 = 10

And again, same answer!

### 4. The Associative Property of Integer Multiplication

Even if you group the integers in different ways and then multiply them – they will have the same answers.

(3 x 5) x 2 = 15 x 2= 30

(2 x 3) x 5 = 6 x 5 = 30

5 x (3 x 2) = 5 x 6= 30

Same answer!

### 5. The Distributive Property of Integer Addition and Multiplication

The distributive property of Integer Addition happens when you are multiplying integers with a group of integers you have added together. For example :

4 x (2 + 5) = ?

In this case, you have to follow the distributive law which states that each integer inside the brackets is multiplied to each integer outside the brackets.

So

4 x (2 + 5) = (4 x 2) + (4 x 5)

or

6 x (7 + 9) = (6 x7) + (6 x 9)

## What are Positive Integers and Negative Integers?

Positive integers are all the integers that are greater than 0

+1, +2, +3, +4, …. +254 are all positive integers.

Usually when we write down positive integers we do not use the ‘+’ sign and this includes numbers in infinity.

Negative integers are all the integers that are less than 0

-1,-2,-3…. -254 are all negative integers

## Rules for adding Integers

A positive integer when added to another positive integer is always going to be another positive integer.

(+4) + (+24) = (+28)

A negative integer when added to another negative integer will always result into another negative integer

(-13) + (-4) = -17

## Rules for subtracting Integers

When a negative integer is subtracted from a positive integer, you need to change all the ‘-’ signs to ‘+’.

5 – (-6) =?

Does the sign change here?

– (-6) = + (+6)

Now use the same rules for addition :

So,

5 – ( -6) =

(+5) + (+6) = 11