Let $\mathbb{Q}$ be the D368: Set of rational numbers.
Let $\cdot$ be the D608: Integer multiplication operation.
The rational multiplication operation is the D554: Binary operation \begin{equation} \mathbb{Q} \times \mathbb{Q} \to \mathbb{Q}, \quad [(a, b)] [(c, d)] = [(a \cdot c, b \cdot d)] \end{equation}