3 + 2 = 5 with apples, a popular choice in textbooks.

Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+)

For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples. Therefore, 3 + 2 = 5. Besides counting fruits, addition can also represent combining other physical and abstract quantities using different kinds of numbers: negative numbers, fractions, irrational numbers, vectors, decimals and more.

## Operation

${\displaystyle A+B=C}$

Where

${\displaystyle A}$
${\displaystyle B}$
${\displaystyle C}$

• Commutative Law: ${\displaystyle a+b=b+a}$ .
• Associative Law: ${\displaystyle (a+b)+c=a+(b+c)}$ .
• Additive Identity: ${\displaystyle a+0=a}$ .
• Additive Inverse: ${\displaystyle a+(-a)=0}$ .

## Example

• ${\displaystyle 2+3=3+2=5}$
• ${\displaystyle 2+3+6=(2+3)+6=2+(3+6)=11}$
• ${\displaystyle 2+0=2}$
• ${\displaystyle 2+(-2)=0}$