- A number that can be expressed in the form p q , where p and q are integers and q ¹ 0, is called a rational number.
- Lowest form of a rational number – A rational number p q is said to be in the lowest form or simplest form if p and q have no common factor other than 1 and q ¹ 0.
- Addition, subtraction, multiplication and division of rational numbers are done in the same way as we do for fractions.
- Rational numbers are closed under the operations of addition, subtraction and multiplication.
- The operations of addition and multiplication for rational numbers are (i) commutative, (ii) associative
- The rational number 0 is the additive identity for rational numbers.
- The rational number 1 is the multiplicative identity for rational numbers.
- The additive inverse of the rational number a b is –a b and vice-versa.
- The reciprocal or multiplicative inverse of the rational number a b is c d if × =1. a c b d
- Distributivity of rational numbers – For all rational numbers a, b and c a (b + c) = ab + ac a (b – c) = ab – ac
- Rational numbers can be represented on a number line.
- Between any two given rational numbers there are infinitely many rational numbers.
- The idea of mean helps us to find rational numbers between two given rational numbers
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