Sum of fractions

Perhaps best, prior to approaching an explanation of the correct way to perform the sum of fractions, is to briefly review some definitions, which will allow us to understand this mathematical operation within its precise context.

Fundamental definitions

Consequently, it may also be helpful to focus this theoretical review on two specific notions: the first, the very concept of fractional numbers, which will allow us to keep in mind the nature of the numbers involved in this Operation. It will also be useful to briefly review the definition of fraction, in order to understand the mathematical expression on the basis of which the sum is made. Here are each of these concepts:

Fractional numbers

In this sense, it will begin to say then that mathematics has explained fractional numbers as those numerical elements used to express non-whole or exact amounts, hence they are called in this way, since they would be giving account for a portion or fraction of a number or a whole.

Thus, this discipline has indicated that fractional numbers may be considered as one of the two elements that make up the eponymous mathematical set, or also known as the Q set. Likewise, this discipline warns that such numbers can be expressed both through a fraction and a decimal expression.


In another order of ideas, it will also be worth focusing on the definition of Fraction, which can basically be defined as one of the forms of expression with which fractional numbers count, consisting of the approach of a division between two natural numbers, each of which fulfills its role, being defined in turn as follows:

  • Numerator: First, you will find the numerator, which will occupy the top of the fraction. Its mission is to point out what part of the whole has been taken, and of which the fraction realizes.
  • Denominator: in the second instance, you will find the denominator, the number that will occupy the bottom of the fraction, demonstrating how many parts the whole to which the fraction refers will be found.

Sum of fractions

With these definitions in mind, it is perhaps certainly much easier to address an explanation about the sum of fractions, an operation that can be defined as the mathematical process, led to finding the total of the addiction of values two or more fractions.

However, this operation will not always be solved in the same way, but will vary according to the conditions of equivalence between the fractions that act as additions, having basically two possible methods:

If fractions have equal denominator

It may be the case, then that the fractions involved in the sum operation all have equal denominator. In this case it will be necessary to simply sum the values of the numerators. The result may need to be simplified. An example of this fraction sum case would be as follows:

If fractions have different denominators

However, if a sum were to be raised between fractions of different denominators, mathematics indicates that the first thing to do is an operation aimed at converting both fractions into equivalents, through the discovery of the common denominator, which is achieves this by applying the following method:

Where both fractions have become equivalent, then they will also proceed to the sum of their denominators. Even though you can also calculate the common multiple of denominators. Similarly, as in the first method, the result can be simplified. An example of such fractionsum cases will be as follows:


Sum of fractions
Source: Education  
September 21, 2019

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