Sum of fractions with equal denominator

Perhaps the best thing, prior to addressing an explanation concerning the sum of fractions of equal denominator, is to briefly revise some definitions, which will allow us to understand this operation in its indicated context.

Fundamental definitions

In this sense, it may also be necessary to delimit this theoretical revision to two basic notions. First, it will be prudent to approach the very concept of Fraction, in order to be clear about the nature of the mathematical expression on the basis of which this operation takes place. It will also be necessary to revise the general concept of Sum of Fractions. Here’s each one:


In this way, we will begin by saying that Mathematics generally understands fractions as one of the expressions with which fractional numbers count. It should also be noted that this discipline states that fractions are constituted by a division held between two integers, each of which has this definition and function:

Numerator: The numerator shall consist of the number at the top of the fraction. The mission of this element will be to show what part of the whole the fraction refers to.

Denominator: On the other hand, the denominator will be the element that will occupy the bottom of the fraction. For its part, it will fulfill the task of expressing the whole of which the fraction stands as a portion of it.

Sum of fractions

In another order of ideas, it will also be necessary to review the definition of sum of fractions, an operation that can be understood as the procedure by which the values of fractions, which they exercise as sums, are combined result in a total. However, the homogeneity or heterogeneity between fractions participating in the operation will determine the correct way in which this mathematical operation should be resolved.

Sum of fractions with equal denominator

One of these cases, where the characteristics and level of homogeneity between fractions determine the method to be followed to solve the sum between fractions is this, where all the expressions involved have the same denominator, and that implies then the following steps, when adding their values:

  • First, the values of the different denominators should be reviewed in order to establish that all fractions participating in the sum actually have the same denominator.
  • Once it is established that this is the case, then we proceed to take a single denominator – since it is common to all fractions involved, and express the sum as a single expression, noting how the numerators are in turn added together.
  • Subsequently, the values of the numerators of each of the fractions that have participated in the operation are summed up.
  • The result will be a fraction consisting of the total calculated based on the sum of the numerator values, and the denominator common to all expressions that have participated.

Example of sum of fractions with equal denominator

However, an example may still be needed to understand how to do the least of fractions with the same denominator, such as the following:

Sum the following fractions:


Sum of fractions with equal denominator
Source: Education  
September 21, 2019

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