# Definition:Addition/Rational Numbers

Jump to navigation
Jump to search

## Definition

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.

## Also see

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 2$: Example $2.1$ - 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 4$: Number systems $\text{I}$: The rational numbers

This page may be the result of a refactoring operation.As such, the following source works, along with any process flow, will need to be reviewed. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering.In particular: Work out where this goes in the flowIf you have access to any of these works, then you are invited to review this list, and make any necessary corrections.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{SourceReview}}` from the code. |

- 1951: Nathan Jacobson:
*Lectures in Abstract Algebra: Volume $\text { I }$: Basic Concepts*: Introduction: $\S 4$