The **associative property** can be found within the area of **algebra** and can be applied to two different types of operations: **addition** and **multiplication** . This type of certainly mathematical property tells us that, when there are three or more figures in these operations, the **result** does not depend on the way in which the **terms** are **placed** or grouped. This means that, no matter how the different numbers are put together in a certain operation, addition or multiplication will always give the same **result** regardless of the **order**. The grouping, in this way, has no relation to the result obtained in the mathematical operation.

## What is the associative property?

The associative property is a **property** that is within the area of **algebra** and that can be applied to **addition** and **multiplication** . It indicates that when there are three or more figures in an operation, the **result** will not depend on the way in which the terms are **placed** .

- History of associative ownership
- Associative Property of Sum
- Associative Property of Multiplication
- Examples

## History of associative ownership

In **1830** he published the **Treatise on Algebra** which attempted to explain the term as a logical treatment comparable to the elements of **Euclid** . He was talking about two different types of algebra, **arithmetic ****algebra** and **symbolic algebra** . In the book, he describes symbolic algebra as the science that deals with **combinations** of arbitrary **signs** and symbols by means defined through arbitrary laws. The truth is that it is very difficult to give an exact date when it was created because people already knew that, for example, 2 + 3 = 3 + 2 since ancient times, but finally people realized that this was a **propertygeneral** that could be attributed to operations other than addition and multiplication, and then became something of study. It can be said that it was not a single person who made this discovery.

## Associative Property of Sum

The associative property of **addition** or **addition** states that changing the **order** in which the numbers are **added** does not affect the **result** of the addition. Given that the application of the associative property in addition has no apparent or important effect in itself, some doubts may arise about its usefulness and importance, however, having knowledge about these principles helps us to **master** perfectly these **operations** , especially when **combined** with others, such as subtraction and division; and even more in the case of division to make correct use of the**math** .

## Associative Property of Multiplication

Multiplication is a mathematical operation that has different types of properties. One of them is the property in the case of multiplication, it tells us that the way of grouping the factors will not cause any type of alteration in the final result of the multiplication regardless of the number of factors found in the operation.

## Examples

As a first example we are going to perform the operation: **5 x 4 x 2**

The first thing we must do is **group** the first **two** numbers, in this case they will be 5 and 4. Carrying out this step, then we will obtain the following equation:

(5 x 4) x 2

20 x 2

40

Now, if **we group** the 4 and the 2, we will obtain the following result:

5 x (4 x 2)

5 x 8

40

As can be clearly seen in the above operation, even though the numbers were positioned differently, the **result** remained the **same** . Another example that we can cite is the following:

(2 x 3) x 5 = 2 x (3 x 5)

6 x 5 = 2 x 15

30 = 30