# Addition

From Citizendium, the Citizens' Compendium

**Addition** is the binary mathematical operation of putting numbers or quantities together (adding). The plus sign "+" means that objects are added up. The numbers that being added are called "addends" and the result is called "sum".

## Contents

## Properties

### Commutativity

Addition is commutative, meaning *a + b = b + a*.

### Associativity

Addition is associative, meaning *a + (b + c) = (a + b) + c*

### Zero and one

Adding 0 to a number is not changing the number: *a + 0 = 0 + a = a*. For any integer *a*, *(a + 1)* means least integer greater than *a*, also known as successor of *a*.

## Sum

If *S* is a finite set of numbers, then all its elements can be added together using sigma notation.

## Addition of natural and real numbers

## Natural numbers

## Integers

## Rational numbers (fractions)

Two fractions can be added up using this formula: . However it is easier to use least common denominator.