Rational Numbers - Revision Notes
CBSE Class 8 Mathematics
Revision Notes
Chapter – 01
Rational Numbers
Revision Notes
Chapter – 01
Rational Numbers
- 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 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 is and vice-versa.
- The reciprocal or multiplicative inverse of the rational number is if x=1
- Distributivity of rational numbers: For all rational numbers a, b and c,
a(b + c) = ab + ac 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. The idea of mean helps us to find rational numbers between two rational numbers.
- Positive Rationals: Numerator and Denominator both are either positive or negative. Example:
- Negative Rationals: Numerator and Denominator both are of opposite signs. Example:
- Additive Inverse: Additive inverse (negative) +=+=0, is the additive inverse of is the additive inverse of .
- Mulitiplicative Inverse (reciprocal): x=1=x where is the reciprocal of . Zero has no reciprocal. The reciprocal of 1 is1 and of -1 is -1.