# Properties of Addition of Numbers

Properties of Addition of Numbers are explained.

Addition of any two numbers gives numbers. It is known as numbers are closed under addition.

Condition for closure property:

x + y = z

Here, x, y and z are numbers.

Eg:-

(i) 5+3=8

(ii) 6+3 = 9

Hence, addition is closure for numbers.

(2) Commutative property

Numbers can be added in any order.

Condition for commutative property:

x + y = y + x

Here, x and y are numbers.

Eg:-

(i) 5+7=7+5

11=11

(ii) 6 + 9 = 9 + 6

15 = 15

In both examples, we are getting same result after addition in both sides.

Hence, addition is commutative for numbers.

(3) Associative property

Numbers can be grouped differently.

Condition for associative property:

x + (y + z) = (y + x) + z

Here, x, y and z are numbers.

Eg:-

(i) 5+ (6+8) can be grouped as (5+6) +8

Now, check the total

5+ (6+8) =19and

(5+6)+8=19

Results are same.

(ii) 3+ (2+5) = (3+2)+5

3+2+5=3+2+5

10=10

Results are same.

Hence, addition is associative for numbers.

(4)Identity property

Additive identity of a number states that

x + identity = x = identity + x

Here, x is a number.

Eg:-

(i) 7+0=7

(ii)6+0=6

In both examples when we add 0 we get same number.

Hence, zero is an additive identity for numbers.

(5)Distributive property

Numbers under addition do not have distributive property.

Because, distributive property can only exists when multiplication and addition both involve in an expression. This property is also known as ‘distributive property of multiplication over addition`. It tells us that we distribute the multiplication over all the terms inside the parenthesis or brackets.

Condition for distributive property for multiplication over addition: RHS of condition for distributive property for addition will be like a + (b + c)

a + (b + c) can not be distribute a inside parenthesis because of (+) sign outside the parenthesis or brackets. It is clear that we do not have sign of multiplication in property of addition . Therefore, it is not possible to distribute addition over all the terms inside the parenthesis or brackets.

Hence, distributive property cannot be executed in addition.

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