Property of the neutral element in the sum of fractions

Perhaps best, prior to addressing an explanation concerning the Neutral Element for the sum of fractions, is to revise some definitions, which will allow us to understand this Mathematical Law in its precise context.

Fundamental definitions

In this sense, it may be prudent to focus this theoretical review on two basic notions: the first, the very concept of Fractions, in order to take into account the nature of the mathematical expression or number type on the basis of which both the operation – the definition of which will be the second to be addressed – as the Law of the Neutral Element itself. Here are each of these concepts:


It will therefore begin to say that fractions are one of the two forms of representation with which rational numbers count, and that it consists of the division held between two integers. Thus, Mathematics considers it important to repair in the elements that make up the fraction, and which have been defined in turn as follows:

  • Numerator: This is the element at the top. It is intended to point out how many parts the fraction represents.
  • Denominator: for its part, the denominator will be the element at the bottom of the fraction, and whose mission will be to indicate what is the whole on which the fraction is set.

Sum of fractions

In another order of ideas, it will also be necessary to review the definition of Sum of Fractions, which has been understood as the mathematical operation by which it seeks to obtain the total of the combination of the values of two or more fractions that serve like summing.

With regard to the correct way to solve such operations, Mathematics distinguishes at least three different cases:

  • If fractions have equal denominator: in this type of fraction sum, it is sufficient to simply add the value of the numerators, leaving the same denominator.
  • If fractions have different denominator: on the contrary, if the fractions participating in the sum aren´t homogeneous, that is, they do not have equal denominators, it will be necessary to start the operation by calculating the common denominator, in order to make it fractions agree on their denominators, and then they can continue with the sum of their numerators.

Property of the Neutral Element for the sum of fractions

With these definitions in mind, it is likely to be much easier to approach a definition of the mathematical property of the Neutral Element for the sum of fractions, which can basically be described as the Law indicating that in this mathematical operation, however and without any exception, that a fraction is added with zero, the result will be the fraction itself.

In this way, it is also inferred that the Neutral Element in the sum of fractions will always be zero. This property can be expressed mathematically as follows:

Examples of the Neutral Element in the sum of fractions

However, it may still be necessary to set out a specific example, which allows you to see in a practical way how this mathematical property is fulfilled, that is, how each time a fraction adds or combines its value with zero, the result is the same sum, without occurring any kind of alteration in it, as can be seen below:


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

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