Closure Property

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Closure property for addition :

If a and b are two whole numbers and their sum is c, i.e. a + b = c, then c is will always a whole number.
For any two whole numbers a and b, (a + b) is also a whole number. This is called the Closure-Property of Addition for the set of W.


Whole number + whole number = Whole number

Some solved examples :

1) 3 + 4 = 7

Here 3 and 4 are whole numbers.

The addition of 3 and 4 which is 7 is also a whole number.

So, property of closure is true for addition.

2) 4 - 3 = 1

Here, 4 and 3 are whole numbers and 1 is also a whole number.

So the property is true.

But 3 - 4 = -1

Here 3 and 4 are whole numbers.

The subtraction of 3 and 4 is -1 which is not a whole number.

So the property of closure for subtraction is not always true.

3) 12 + 0 = 12

Here, 12 and 0 both are whole numbers.

The addition of them which is 12 again is also a whole number.

So the property of closure is true.

Closure property for multiplication :

If a and b are whole numbers then their multiplication is also a whole number.

For any two whole numbers a and b, (a x b) is also a whole number.This is called the property of closure for Multiplication for the set of W.

Whole number x whole number = whole number

Some solved examples :

1) 30 x 7 = 210
Here 30 and 7 are whole numbers.

The multiplication of 30 and 7 which is 210 is also a whole number.

So property of closure for multiplication is true.

2) 40 x 0 = 0

Here 40 and 0 both are whole numbers.

Their multiplication 0 which is the smallest whole number.

Note : Property of closure is not always true for division.

Example : 45 ÷ 0 = not defined
As division with zero is not possible.


Whole Number

Closure property
Commutative property
Associative property
Additive Identity
Distributive property

From closure to Whole numbers

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