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Distributive property


The concept of distributive property it is used in the field of algebra . It is one of the properties of the multiplication which applies to a sum or a subtraction. This property indicates that two or more terms present in a sum or in a subtraction multiplied by another quantity, is equal to the sum or subtraction of the multiplication of each of the terms of the sum or subtraction by the number.

In other words: a figure multiplied by the sum of two addends results identical to the sum of the products of each of the addends by said number .

To understand the distributive property, however, it is simpler to observe the factors in an algebraic expression:

A x (B + C) = A x B + A x C

Let us replace the letters with numbers to check the equality and, therefore, the operation of the distributive property. If A = 4, B = 2 and C = 8:

4 x (2 + 8) = 4 x 2 + 4 x 8
4 x 10 = 8 + 32
40 = 40

We cannot ignore that when talking about distributive property, it is practically inevitable to mention other properties also used within the field of mathematics. Specifically, we are referring to the following:
-Commutative property, which makes it clear that the order of the factors does not alter the product. That is, it gives the same result multiply 3 × 2 than 2 × 3. In both cases the result will be identical: 6.
-Associative property. In this case, it comes to say that in a multiplication the result will not vary if there is a change in what is the way to group the factors involved in it. That is, it gives the same result if it is multiplied (2 x 4) x 3 than if it is done with 2 x (4 x 3).

In Primary, you already bet that children begin to know these mathematical properties and, of course, to practice them, since they are very useful when carrying out numerous operations. Thus, in those educational levels, in addition to those already exposed, another series of important tips such as these are being set:
-The term of internal operation is used to make it clear that the result of multiplying two natural numbers is another natural number.
-There is what is known as a neutral element within the multiplications of natural numbers. This is number 1, since any number multiplied by it results in itself. That is, 2 x 1 is 2, 3 x 1 is 3 ...

Distributive property can also be applied with respect to a subtraction . Let's see how it works with the same values ​​that we used in the previous example:

4 x (2 - 8) = 4 x 2 - 4 x 8
4 x -6 = 8 - 32
-24 = -24

The distributive property is considered to have an inverse process: the so-called common factor . When different addends have a common factor, it is possible to transform the sum into a multiplication from the extraction of the factor in question.