# Category:Rational Multiplication

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This category contains results about Rational Multiplication.

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.

## Subcategories

This category has only the following subcategory.

### M

## Pages in category "Rational Multiplication"

The following 17 pages are in this category, out of 17 total.

### N

### P

### R

- Rational Multiplication Distributes over Addition
- Rational Multiplication Identity is One
- Rational Multiplication is Associative
- Rational Multiplication is Closed
- Rational Multiplication is Commutative
- Rational Numbers under Multiplication do not form Group
- Rational Numbers under Multiplication form Commutative Monoid
- Rational Numbers under Multiplication form Monoid

### S

- Set of Rational Numbers whose Numerator Divisible by p is Closed under Multiplication
- Strictly Positive Rational Numbers are Closed under Multiplication
- Strictly Positive Rational Numbers under Multiplication form Countably Infinite Abelian Group
- Strictly Positive Rational Numbers under Multiplication form Subgroup of Non-Zero Rational Numbers