# Properties of Addition for Whole Numbers

Properties of Addition for Whole Numbers are explained.

(1) Closure property

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

Condition for closure property:

x + y = z

Here, x, y and z are whole numbers.

Eg:-

(i) 5+3=8

(ii) 6+3 = 9

Hence, addition is closure for whole numbers.

(2) Commutative property

Whole numbers can be added in any order.

Condition for commutative property:

x + y = y + x

Here, x and y are whole 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 whole numbers.

(3) Associative property

Whole numbers can be grouped differently.

Condition for associative property:

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

Here, x, y and z are whole 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 whole numbers.

(4)Identity Property

Additive identity of a whole number states the

x + identity = x = identity + x

Here, x is a whole number.

Eg:-

(i) 7+0=7

(ii)6+0=6

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

Hence, zero is an additive identity for whole numbers.

(5)Distributive property

Whole 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 by multiply terms with terms of brackets.

Condition for distributive property:

a  (b + c) = ab + ac

a is distribute to b and c by multiplying a inside the terms of brackets.

a + (b + c) will be RHS condition for addition distributive property. We do not have multiplication in this condition. 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.

Helping Topics

Whole Numbers

Properties of Subtraction

Properties of Multiplication

Properties of Division