The distributive property can be applied to addition or subtraction.
The concept of distributive property is used in the field of algebra . This is one of the properties of multiplication that applies to addition or subtraction. This property indicates that two or more terms present in a sum or subtraction multiplied by another quantity is equal to the sum or subtraction of the multiplication of each of the terms of the addition or subtraction by the number.
In other words: a figure multiplied by the sum of two addends is identical to the sum of the products of each of the addends by said number .
Distributive property in an algebraic expression
To understand the distributive property, however, it is simpler to look at the factors in an algebraic expression:
A x (B + C) = A x B + A x C
Let's replace the letters with numbers to check 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
Other properties
We cannot ignore that when talking about the 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, multiplying 3×2 gives the same result as 2×3. In both cases the result will be identical: 6.
-Associative property. In this case, it means that in a multiplication the result will not vary if there is a change in the way of grouping the factors involved in it. That is, it gives the same result if you multiply (2 x 4) x 3 as if you multiply it with 2 x (4 x 3).
In school mathematics classes the distributive property is studied.
In Primary School we are already betting 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, at these educational levels, in addition to those already stated, another series of important tips such as these are established:
-The term 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 the number 1, since any number multiplied by it equals itself. That is, 2 x 1 is 2, 3 x 1 is 3…
Distributive property in subtraction
The distributive property can also be applied with respect to 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 addition into a multiplication by extracting the factor in question.