Category:Rational Addition
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This category contains results about Rational Addition.
The addition operation in the domain of rational numbers $\Q$ is written $+$.
Let:
- $a = \dfrac p q, b = \dfrac r s$
where:
- $p, q \in \Z$
- $r, s \in \Z_{\ne 0}$
Then $a + b$ is defined as:
- $\dfrac p q + \dfrac r s = \dfrac {p s + r q} {q s}$
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 an example.
Subcategories
This category has only the following subcategory.
A
Pages in category "Rational Addition"
The following 16 pages are in this category, out of 16 total.
P
R
- Rational Addition Identity is Zero
- Rational Addition is Associative
- Rational Addition is Closed
- Rational Addition is Commutative
- Rational Multiplication Distributes over Addition
- Rational Numbers under Addition form Infinite Abelian Group
- Rational Numbers under Addition form Monoid
- Rational Numbers with Denominators Coprime to Prime under Addition form Group