Associative property

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.

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 themath .

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