Opposite element in the sum of fractions

It is likely that the best thing, before advancing an explanation of the opposite or symmetrical element in the sum of fractions, is to briefly review some concepts, which will allow us to understand this mathematical law within its appropriate context.

Fundamental definitions

In this sense, it may also be prudent to delimit this theoretical review to two specific notions: the concept of fractions and the concept of sum of fractions, since these are the elements and the operation, on the basis of which the property known as Element opposite in the sum of fractions. Here’s each one:


Therefore, it can be said that fractions can be considered as a form of expression of fractional numbers, which is made up of the division between two integers, each of which has the name and function set out below:

  • Numerator: With this name, the first term of the fraction, or in other words, will be known the element that is in the upper position of the fraction. The task of the Numerator will be to indicate what part of the whole represents the fraction.
  • Denominator: secondly, you will find the Denominator, which will occupy the bottom of the fraction, and which performs the task of indicating which is the whole on which the fraction has been established, as a portion of this totality.

Sum of fractions

Thus it will also be relevant to take into account the definition of Sum of Fractions, which will be understood as the mathematical operation whose purpose is to combine the values of the fractions that function as sums. However, the homogeneity of the fractions involved will determine the exact method to be followed to resolve these operations, as seen below:

  • If fractions match their denominators: first, it can happen that fractions that function as additions have the same denominators. In this case, only the values that have the numerators will be added up.
  • If fractions have different denominators: on the contrary, if fractions participating in the sum have denominators of different values, then the relevant operations must be performed in advance to calculate a common denominator , and then proceed with the sum of the numerators.

Opposite element in the sum of fractions

With these definitions in mind, it may actually be much easier to approach a definition on the opposite element that takes place in this operation. In this regard, the different sources agree on the importance of understanding that the opposite, inverse or symmetrical element of an operation will be that fraction that has the same value, but with the opposite sign, which can be mathematically expressed the following way:

Likewise, the Property of the opposite Element in the sum of fractions will dictate that whenever a fraction is added with its inverse or opposite element, then the result will always give, and without any exception, zero. However, it may still be necessary to set out a specific example, which makes it possible to see clearly how whenever a fraction is added with its inverse results in zero, as can be seen below:

Picture: pixabay.com

Opposite element in the sum of fractions
Source: Education  
September 21, 2019

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