multiplicative inverse

in mathematics, the multiplicative inverse is an operation of arity 1

also known as reciprocal, for a number $x$ is the number that when multiplied by $x$ gives the number $1$

not to be confused with inverse function

notation

the reciprocal of $x$ is depicted as $\frac{1}{x}$
$x^{-1}$

the reciprocal of $\frac{a}{b}$ is depicted as $\frac{b}{a}\vee (\frac{a}{b}{)}^{-1}$