What is commutative associative and distributive property

Commutative property

In the maths the operations have different properties. The distributive property is applied in multiplication, for example, and indicates that the number multiplied by the sum of two addends is equal to the sum of the products of each of those addends with the number in question. This means: A x (B + C) = A x B + A x C .

The associative property , applicable in multiplication and addition, on the other hand, indicates that the result of the operations is not related to the way in which the numbers are grouped. Put in an algebraic expression: (A + B) + C = A + (B + C)

Now it's time to analyze another one properties : the commutative property what indicates The order of the numbers used in the operation does not change the result . The commutative property is shown in total and the multiplication and defines the possibility of adding or multiplying the numbers Always achieve the same result in any order:

A + B = B + A or A x B = B x A

First, let's see how the property works as a whole. When we have the values A = 5 and B = 7 we get the following equivalence from the commutative property:

5 + 7 = 7 + 5
12 = 12

In the case of multiplication, the reason is the same. So if we work with the same values ​​as in the previous example, we get this equivalence:

5 x 7 = 7 x 5
35 = 35

Knowing the commutative property of additions and multiplications is particularly helpful when solving Equations with unknowns as it takes away the weight of maintaining a particular order for each of its additions and factors. Let's not forget that the examples given above reflect the simplest possibilities, as the following equation could also be given to demonstrate the effectiveness of the commutative property in both operations:

(A × C + Z / A) × B + D + E × Z = D + B × (Z / A + C × A) + Z × E

Note that in this case the commutative property can be applied so that multiple equivalents are obtained, since adding and multiplying increases the number of possible combinations. A much more complex equation could have operations like that submission and empowerment, in addition to constants (fixed values, as opposed to variables) and divisions that cover all or part of a term.

If you are trying to delete an unknown object, you need to know all of the element's properties Operations included in the equation to avoid mistakes. Let us not forget that mathematics is an exact science and that, in general, using it will result in us achieving a single possible value; In other words, one small mistake is enough to invalidate the rest of the work.

On the other hand, it is also very important to know that Commutative ownership is not met in the case of subtraction, division, authorization and deposit . Just invest that to order a simple equation that includes one of these operations to identify this incompatibility. The following examples can be used to test how dangerous it can be to apply the principles of commutative property outside of sums and multiplications: 12 - 8 = 4 while 8 - 12 = -4 ; 4 / 2 = 2 while 2 / 4 = 0,5 ; 3 raised on the eighth potency is equal to 6561 and is far from 8 raised on bucket , which results 512 .