- Rational numbers are the numbers that can be expressed in p/q form, where p and q are both integers and q ≠0.
- It comes from the word ‘ratio‘. Every rational number can be written as ratio of two integers.
- All fractions are rational numbers, but all rational numbers are not fractions.
- Positive Rationals: Numerator and Denominator both are either positive or negative. Example: 4/7,(-3/4)
- Negative Rationals: Numerator and Denominator both are of opposite signs. Example: (-2/11), (3/-4)
- Rational numbers are closed under the operations of addition, subtraction and multiplication.
- The operations addition and multiplication are
(i) commutative for rational numbers.
(ii) associative for rational numbers.
- The additive identity of rational numbers is 0.
- The multiplicative identity of rational numbers is 1.
- 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 b/a.
- Distributivity of rational numbers: For all rational numbers a, b and c,
a(b + c) = ab + ac and and a(b – c) = ab – ac
- Rational numbers can be represented on a number line.
- Between any two given rational numbers there are countless rational numbers.
- Reciprocal of 1 is 1 and that of -1 is also 1.
- Reciprocal of 0 is Not Defined.