### Theory:

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:

1 and 9 are two whole numbers then, $1+9=10$ is also a whole number.

5 and 9 are two whole numbers then, $5\times 9=45$ 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 $a-b$ and $a\xf7b$ is not always a whole number.

Example:

**i)**$9-1=8$ is a whole number.

**ii)**$1-9=-8$ is a negative number, not a whole number.

**iii)**$\frac{10}{5}=2$ is a whole number.

**iv)**$\frac{1}{9}=0.111$ 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**