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Addition is a mathematical operation that represents combine collection of objects together into a larger collection.

It is signified by the plus sign (+).

Multiplication and addition are performed by some properties. We shall see the properties of addition below.

We have many addition properties -

• Commutative property
• Associative property
• Identity property
• Inverse property

Commutative property

It says the order in which numbers are added does not effect the sum. For example

A + B = B + A

means 2 + 3 = 3 + 2

So we can say that order of numbers in addition does not effect the final result.

Associative property

It says the way in which addends are grouped does not effect the sum . For example

A+ (B + C) = (A + B) + C

means 2+ (3+ 4) = (2 + 3) + 4

By this property we can understand if we have 3 numbers we can add them according to our wish, final result will be same in all cases.

Identity property

It says the sum of any number and zero is number itself for example A + 0 = A

means 2 + 0 = 2

This is the simplest property of addition, in this 0 is known as additive quantity.

There are many applications of these properties of addition. It may looks very simple but we can use these properties in many things one of that example is computer analogs.

Inverse property

It says that the if the addition of two numbers are zero then one number is inverse of other. For any number its negative is its additive inverse that is A + (-A) = 0. a is inverse of (-A) and vice-versa.

means (-3) + 3 = 0 so (-3) is the additive inverse of 3.

Below you can see examples on properties of addition -

### Solved Examples

Question 1: Add the values (i) 15 and -15 (ii) (4 + 3) + 6 = 4+ (3 + 6)
Solution:

i) 15 + (-15) = 0 (inverse property)

ii) (4 + 3) + 6 = 13

4 + (3 + 6) = 13

13 = 13 (associative property)

Question 2: Find the additive inverse of (-5)
Solution:

Let a be the additive inverse of (-5)

(- 5) + a = 0

a = 0 + 5

a = 5

5 is the additive inverse of (-5)

Question 3: Prove commutative property for 20 and 21
Solution:

Commutative property states that is a and b are two numbers then a + b = b + a

20 + 21 = 41

21 + 20 = 41

20 + 21 = 21 + 20

So it shows commutative property

The inverse property of addition encloses for any real number of variable x, there is a unique real number, denoted by -x.

OR

The inverse property of addition is when you add a real number and its additive inverse and you get the identity element (0).

Example:

a + (-a) = 0.

(- a) + a = 0.

### Solved Example

Question: Find the inverse element of 61 for addition?
Solution:
Given number is 61.

Inverse property result is 0.

61 + x = 0

61 is subtracted on both sides.

61 + x - 61 = 0 - 61

x = -61

 More topics in Addition Properties Associative Property of Addition Closure Property Commutative Property of Addition Distributive Property
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