\begin{definition}[Definition:Multiplication/Rational Numbers]
The '''multiplication operation''' in the domain of rational numbers $\Q$ is written $\times$.
Let $a = \dfrac p q, b = \dfrac r s$ where $p, q \in \Z, r, s \in \Z \setminus \set 0$.
Then $a \times b$ is defined as $\dfrac p q \times \dfrac r s = \dfrac {p \times r} {q \times s}$.
This definition follows from the definition of and proof of existence of the field of quotients of any integral domain, of which the set of integers is one.
\end{definition}