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The closure property of whole numbers states that while operating addition and multiplication with two or more whole numbers, the result of the operation is also a whole number.
While doing the operation of whole numbers if the result of the operation is a whole number, then we can say that it satisfies the closure property.
The result of the addition and multiplication of any two whole numbers is always a whole number.
Consider \(a\) and \(b\) are two whole numbers then:
- The addition \(a + b\) is a whole number.
- The multiplication \(a × b\) is also a whole number.
Example:
3 and 9 are two whole numbers then, is also a whole number.
1 and 8 are two whole numbers then, is also a whole number.
Important!
The result of the subtraction and division is not always a whole number. If \(a\) and \(b\) are two whole numbers, then and is not always a whole number.
Example:
i) is a whole number.
ii) is a negative number, not a whole number.
iii) is a whole number.
iv) is a decimal number, not a whole number.
Therefore the closure property of whole numbers states that while operating addition and multiplication with two or more whole numbers, the result of the operation is also a whole number.
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