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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".

## 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. ${\displaystyle \sum _{x\in S}x}$

## Rational numbers (fractions)

Two fractions can be added up using this formula: ${\displaystyle {\frac {a}{b}}+{\frac {c}{d}}={\frac {ad+bc}{bd}}}$. However it is easier to use least common denominator.