# Properties of Subtraction of Whole Numbers

(1) Closure property

Whole numbers under subtraction do not hold closure property.

Condition for closure property:

x – y = z

Here, x, y and z are whole numbers.

Eg:-

(i) 5-3=2

But, in example given below

(ii) 4 – 6= – 2[integer]

Hence, closure property under subtraction for whole numbers is not true.

(2)Commutative Property

Whole numbers cannot be subtracted in any order.

Condition for commutative property:

x – y = y – x

Here, x and y are whole numbers.

Eg:-

(i) 5-3=2

After changing order-3-5=-8

2and -8 are not equal.

(ii) 4- 2 = 2

After changing order -2 – 4 = – 6

2and -6 are not equal.

In above examples, we are not getting same result after subtracting in both sides.

Hence, subtraction is not commutative for whole numbers.

(3) Associative property

Whole numbers cannot grouped differently in subtraction.

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) = 7and

(5-6)-8= -9

Results are not same.

(ii) 3- (2-5) = (3-2)-5

6 = -4

Results are not same.

Hence, subtraction is not associative for whole numbers.

(4) Identity property

Condition for subtractive identity

Subtractive identity of a whole number states the

x – identity = x = identity – x

Here, x is a whole number.

Eg:-

(i) 7- 0 =7

But,

0 – 7 = -7

Results are not same.

(ii)6 – 0 = 6

But,

0 – 6 = – 6

Results are not same.

Hence, subtraction does not hold identity for whole numbers.

(5)Distributive property

Whole numbers under subtraction 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 subtraction distributive property. We do not have multiplication in this condition. Therefore, it is not possible to distribute subtraction over all the terms inside the parenthesis or brackets.

Hence, distributive property cannot be executed in subtraction.

Helping Topics

Whole numbers 