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.
Pages in category "Rational Multiplication"
The following 19 pages are in this category, out of 19 total.
I
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