# 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