If you need to do sums online, our calculator will allow you to calculate the sum of up to four numbers automatically. If you do not need to add four numbers, you can leave their values blank and they will not be taken into account to calculate the final result.

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## Parts of sums The summation operation consists of a series of elements that are always present:

• Sign +The sign is obviously the one that marks the type of operation we are performing. In this case, the + indicates that we are dealing with an addition.
• AdditionsThe sum of the numbers involved in the addition is called the summands.
• Sumis the name given to the result of the operation. It can also be seen as 'total'.

## Properties of sums The addition operation has a series of properties you need to know to avoid making mistakes when adding up several numbers:

### Associative property

The associative property states that it does not matter the order in which we group the summands since the result of the sum will not be modified. This can be seen represented below:

(x + y) + z = x + (y + z) = (x + z ) + y

In any of the three possible cases, the result of the operation will always be the same. Let's see it with a practical example to make it much clearer:

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

It does not matter the groupings of addends that we make in the sum because thanks to the associative property, the result will always be similar.

### Commutative property

The commutative property states that in the sum of two numbers, the order of the addends does not matter. since the result will always be the same:

x + y = y + x

If we apply it to a practical example we have that:

4 + 3 = 3 + 4 = 7

### Neutral element

The neutral element in the sum is the number 0.. This means that any number to which we add zero, will result in its initial value:

x + 0 = x

Applying the neutral element to a practical example we have that:

2 + 0 = 2