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# Properties of Rational Numbers

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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:

1. a + b = b + a
2. a x b = b x a

Associative law:
1. a + (b + c) = (a + b) + c
2. a x (b x c) = (a x b) x c

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

1. a + b = a rational number
2. a - b = a rational number
3. a x b = a rational number
4. $\frac{a}{b}$ = not a rational number

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

1. a + 0 = a
2. a x 1 = a

Rational numbers holds true for distributive property also.

1. a + (b x c) = (a + b) x (a + c)
2. (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.