Rational Multiplicative Inverses
Why
What is the multiplicative inverse of $\eqc{(a, b)}$ in the rationals?
Result
The multiplicative inverse of $\eqc{(a, b)} \in
\Q $ if $b \neq 0_{\Z }$ is $\eqc{(b,a)}$.
Notation
We denote the multiplicative inverse of $q \in \Q $ by $\inv{q}$. We denote $q \cdot (\inv{r})$ by $q/r$.
Division
We call the operation $(a, b) \mapsto a/b$ rational division.