# Reciprocal

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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 $\frac{1}{x}$ .