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 c, b d)] \end{equation}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Ringoid

▾ Semiring

▾ Ring

▾ Multiplicative group

▾ Multiplicative monoid

▾ Multiplicative semigroup

▾ Multiplicative groupoid

▾ Multiplicative binary operation

▾ Natural number multiplication operation

▾ Integer multiplication operation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Ringoid

▾ Semiring

▾ Ring

▾ Multiplicative group

▾ Multiplicative monoid

▾ Multiplicative semigroup

▾ Multiplicative groupoid

▾ Multiplicative binary operation

▾ Natural number multiplication operation

▾ Integer multiplication operation

Formulation 0

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 c, b d)]
\end{equation}

Let $\cdot$ be the D608: Integer multiplication operation.

The

Formulation 1

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}

Let $\cdot$ be the D608: Integer multiplication operation.

The

Child definitions