Rational Numbers

  • 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.


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