Rational numbers are terminating or recurring decimal numbers written in the form of fraction $\frac{p}{q}$ in which 'p' and 'q' are integers and the denominator 'q' not equal to zero.

Let a,b,c be three rational numbers and the properties of rational numbers are given below:

Rational numbers are commutative and associative under addition and multiplication.**Commutative law:**

- a + b = b + a
- a x b = b x a

**Associative law:**

- a + (b + c) = (a + b) + c
- a x (b x c) = (a x b) x c

Rational numbers holds true for closure law under addition, subtraction and multiplication.

- a + b = a rational number
- a - b = a rational number
- a x b = a rational number
- $\frac{a}{b}$ = not a rational number

Rational numbers have an additive identity of 0 and multiplicative identity of 1.

- a + 0 = a
- a x 1 = a

Rational numbers holds true for distributive property also.

- a + (b x c) = (a + b) x (a + c)
- (a + b) x c = (a x c) + (b x c)

If the product of two rational number is 1, then the rational number is multiplicative inverse of the other.