Arithmetic/Number Operations/Addition

Three plus four equals seven.

Addition is one of the four basic operations of arithmetic. The operation is usually shown by the plus symbol (+). This is the act of combining two numbers into one. This operation may be used on any number, from natural numbers to complex numbers. For example, look at the following equation:

$2+2=4$

This means "Adding two with two gives us four" or put more simply, "Two plus two equals four". In this example, both twos are terms (addends), the numbers being added together, while the 4 is the sum, the result of the addition.

Properties of Addition

Commutativity

When adding two numbers together, it doesn't matter what order the numbers are placed in, since the outcome will be the same. That is to say for any two numbers $x$ and $y$, $x+y=y+x$ For example, the two equations end up with the same result.

$4+5=9$

$5+4=9$

Associativity

When adding multiple numbers together, the order in which you add the numbers doesn't matter, since the outcome will be the same. For any three numbers $x,y$ and $z$, $(x+y)+z=x+(y+z)$ For example, the two equations will end up with the same result.

$(1+2)+3=3+3=6$

$1+(2+3)=1+5=6$

The Additive Identity

The number 0 is known as the additive identity. This means if you add any number with zero, you end up with that original number. For example:

$4+0=4$

$6.24+0=6.24$