Properties of opposites in the sum of fractions

Perhaps the most convenient, prior to addressing each of the mathematical properties, which can occur in relation to the opposite of a fraction, is to briefly review some concepts, which will allow us to understand these mathematical laws within their precise context.

Fundamental definitions

It may also be relevant to delimit this theoretical revision to two specific notions, such as the definition of Fractions itself, in order to take into bear in mind the nature of the mathematical expression on the basis of which the notion of Opposite is so applicable of a fraction, which must also be taken into account. Here are each of these concepts:


In this way, we will begin by saying that Mathematics has been given to the task of defining fractions as one of the possible expressions with which fractional numbers count. Thus, fractions will consist of the division of two integers, each of which fulfills the following role:

  • Numerator: First, you will find the numerator, which will correspond to the number that is located in the upper shape, and whose mission is to point out which part is taken altogether.
  • Denominator: on the other hand, the number located at the bottom of the fraction will be identified as the denominator, as well as the person responsible for indicating the whole of which the part that reflects the fraction is taken.

Opposite of a fraction

In another order of ideas, Mathematics will understand as the opposite of a fraction to any fractional expression that possesses equal quantity, but different sign, being inversely proportional in the number line. This inverse situation of a fraction may be expressed mathematically as follows:

Properties of opposites of a fraction

With these definitions in mind, it may certainly be much easier to understand each of the mathematical laws that are enforced around this element, and which has been told in two, and explained in turn as follows:

Law on the opposite of the opposite of a fraction

The first mathematical property that can be found in relation to the opposite of a fraction will be one that indicates how the opposite or inverse of the opposite of a fraction will always be, and without any exception, the fraction itself, law this which can in turn count on the to the following mathematical expression:

By taking this property into account, it can be concluded that it responds to a process of mathematical logic, since if one wants to find the opposite of one element, which at the same time is opposite of another, then there will be no choice but to encounter the very element of which the first opposite has emerged.

Law on the sum of a fraction with its opposite

On the other hand, the second mathematical property that can be seen in relation to the opposite of a fraction, will be directly related to the fractional sum operation. In this sense, Mathematics points out that whenever a fraction sets a sum with its own opposite, the result of this operation will be without exception zero. This property can be expressed mathematically as follows:


Properties of opposites in the sum of fractions
Source: Education  
September 21, 2019

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