Associative property in the sum of fractions

Perhaps it is best to approach an explanation of the Associative Property present in the Sum of Fractions, it is to briefly review some definitions, which will be useful when understanding this mathematical law within its context Precise.


Fundamental definitions

In this sense, it may also be prudent to delimit this theoretical revision to two specific definitions: the first, the very concept of fractions, because this will allow the mathematical expression to be taken into mind, on the basis of which the sum that is established is established gives rise to this property, and the definition of which must also be addressed. Here are each of these notions:

The fraction

In this way, it will begin to say then that in general the different sources have pointed out that the fraction is one of the mathematical forms by which fractional numbers are expressed, that is, those that account for non-whole amounts or and next to integers make up the set of Rational Numbers, also known as the Q numeric set.

Thus, mathematical discipline indicates that the fraction will be expressed as a division of integers, which overlap each other. As for the members that make up the fraction, then the Numerator, identified as the number that occupies the top of the fraction, and who fulfills the task of indicating which part of the whole constitutes the fraction. Second, there will be the Denominator, located at the bottom, and with the mission of pointing out the whole of where the fraction is taken.

Sum of fractions

In another order of ideas, it will also be necessary to revise the definition of Sum of Fractions, which is understood as a mathematical operation, by which it seeks to determine the total resulting from the action of adding or combining the values of the fractions. With regard to the correct way of resolving this type of operations, Mathematics states that two specific circumstances must be taken into account:

  • If fractions have the same denominator: the first case involves fractions that match their denominators. Consequently, as dictated by this discipline, the correct way to approach this operation will be to consider a single denominator, and adding up the values of the numerators.
  • If fractions have different denominator: on the contrary, if it were the case that fractions that function as sums have different denominators, then a common denominator should be determined first, and then the numerators should be added that has emerged in that process.

Associative property in the sum of fractions

With these definitions in mind, it is perhaps certainly easier to approach a definition of associative property in the sum of fractions, which can be understood as the mathematical law that states that whenever it is faced with a sum of fractions in which more than two additions participate, they will be able to establish different associations without this impacting an alteration to the result obtained. This property can be expressed as follows:

Example of associative property in the sum of fractions

However, a concrete example may still be required to see in a practical way how this property is true, as can be seen below:

Picture: pixabay.com

Associative property in the sum of fractions
Source: Education  
September 21, 2019


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