Addition, synonym of sum (from latin summa) is to add some things. The term refers to the action and the effect of adding or add. For mathematics, the addition is an operation that allows to find the sum of two or more homogeneous quantities, i.e., of the same nature.

As a mathematical operation, the addition is to add two or more numbers to get the total amount. The process can also bring together two groups of things in order to get a single set. For example: if I have two apples and I use two other, I will have five in all (3 + 2 = 5). The foregoing concerns the homogenous quantities. On the other hand, if I add four pears to these five apples, I will get a result of nine but not nine apples or nine pears. The logical operation is the same (5 + 4 = 9) except that the quantities are not homogeneous, unless one assembles apples and pears in all fruit.

The addition has several properties. It can be commutative (the order of factors does not change the result: 4 + 3 = 7, 3 + 4 = 7), associative and distributive (the addition of two numbers multiplied by a third is equal to the addition of each of these numbers multiplied by the third number). In addition, it has a neutral (4 + 0 = 4, 0 + 8 = 8) and an opposed element (for each number there is an opposite whose addition gives zero as a result).

Addition and subtraction are the most basic mathematical operations, reason why are the first that are taught to children. Indeed, the easiest way to count consists of repetitive action and continues to add the number one (1 + 1 + 1 + 1 = 4).

Finally, we will retain the term addition, in another context, is synonymous with invoice. At the end of the meal in a restaurant, the client requests the addition, either the ticket which details all what has been consumed and the price of each item. The sum of these elements (the addition, so) allows him to know how much it must pay for his meal.