The reciprocal or Multiplicative inverse of a real number a is the number a^{-1}=\frac{1}{a} such that if multiplied by a the resulting output is multiplicative identity.

More generally, let (S,+,*) be a ring. Then the reciprocal of x \in S is x^{-1} \in S such that x*x^{-1}=1, where 1 is the multiplicative identity of the ring.

Finding the reciprocal of a real number

The reciprocal of a fraction can be retrieved by swapping its numerator and denominator. Formally speaking, the reciprocal of a real number x is equivalent to \frac{1}{x} .