Closure Property
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
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