Rational Numbers - Revision Notes

CBSE Class 8 Mathematics
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 ab is ab and vice-versa.
  • The reciprocal or multiplicative inverse of the rational number ab is cd if abxcd=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: 47,34
  • Negative Rationals: Numerator and Denominator both are of opposite signs. Example: 211,49
  • Additive Inverse: Additive inverse (negative) ab+ab=ab+ab=0, ab is the additive inverse of abandab is the additive inverse of ab.
  • Mulitiplicative Inverse (reciprocal): abxcd=1=cdxab where cd is the reciprocal of ab. Zero has no reciprocal. The reciprocal of 1 is1 and of -1 is -1.