1. Rational numbers are closed under the operations of addition, subtraction and multiplication.
2. The operations addition and multiplication are
(i) Commutative for rational numbers
(ii) Associative for rational numbers.
3. The rational number 0 is the additive identity for rational numbers.
4. The rational number 1 is the multiplicative identity for rational numbers.
5. The additive inverse of the rational number and vice – versa.
6. The reciprocal or multiplicative inverse of the rational number
7. Distributivity of rational numbers: For all rational numbers a, b and c,
a ( b + c ) = a b + ac and a ( b – c ) = a b – ac
8. Rational numbers can be represented on a number line.
9. Between any two given rational numbers there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.