# Properties of Rational Numbers

There are some properties for rational numbers, like closure property, commutative property and associative property. Let us recall the properties one by one.

Closure Property

**(i)** **Whole numbers**

*a*and

*b*are two whole numbers, then

*a + b = c*should also be a whole number.

The property is that the sum, difference, product or the quotient of whole number should always be a whole number.

Whole numbers are closed under addition and multiplication.

**Example : **2 + 3 = 5, a whole number

5 â€“ 2 = 3, a whole number. But, 2 â€“ 5 = -3, which is not a whole number.

2 Ã— 7 = 14, a whole number

6 Ã· 3 = 2, a whole number, but 5 Ã· 2 = , which is not a whole number.**>**

**(ii) ****Integers :**

*a*and

*b*are integers then their sum, difference, product and quotient should also be an integer.

Addition: â€“1 +3 = 2, an integer

Subtraction: â€“5 â€“ 6 = â€“11, an integer.

Multiplication: (-2) Ã— (7) = -14, -14 is also an integer.

Division: â€“9Ã· 2= this is not an integer.

So, integers are not closed for division.

Integers are closed for addition, subtraction and multiplication.

**(iii) ****Rational numbers** **:**

If is a rational number, then their sum, difference, product and quotient should also be a rational number.

â‡’ , a rational number.

â‡’ , a rational number.

â‡’ , a rational number.

â‡’ Ã· =1, a rational number

But, Ã· 0 is undefined.

So, division does not satisfy the closure property.

**Rational numbers** are closed under addition, subtraction and multiplication.