Subtraction of fractions with the same denominator

Perhaps the best thing to do before explaining an explanation on the correct way in which a Subtraction of fractions operation of the same denominator should be resolved, is to briefly review some definitions, which will allow us to understand this procedure within its precise context.

Fundamental definitions

In this sense, it is also prudent to delimit this theoretical revision to two specific notions: the first one, the concept of Fractions itself, as this will help to keep in mind the nature of the mathematical expressions that participate in the Subtraction of fractions, a definition that should also be addressed, since it is there where the case arises where the fractions involved have equal denominators. Next, each one of them:


In this way, one can begin to say that Fractions are generally understood by Mathematics as one of the two types of expression that fractional numbers count on. Consequently, these will be used to represent non-exact quantities. Likewise, these will be constituted as a division between whole numbers, each of which then assumes a name and a function, which are explained in turn as follows:

  • Numerator: First, the numerator will be found, which will consist of the number that occupies the top of the fraction. Its mission will be to indicate which part of the whole represents the fraction of which it is a part.
  • Denominator: in reference to the denominator, it will occupy the lower part of the fraction, with the task of indicating in how many parts the whole is divided, from which a part represented by the numerator will be taken.

Subtraction of fractions

For its part, the Subtraction of fractions will be understood as the mathematical operation, whose main purpose is to determine what is the difference between two fractions, that is, what is the result of a fraction suppressing a certain amount, indicated by the Another participating fraction. In this type of operation, the first fraction will fulfill the role of minuend, the second subtracting, and the result will be assumed as a difference.

As for the correct way to solve this type of operation, Mathematics has indicated that one cannot speak of only one, since the indicated method will depend on the levels of homogeneity or heterogeneity that exist between the fractions that participate in the Subtraction.

Subtraction of fractions with the same denominator

One of these cases, may be the one that raises a Subtraction of fractions, between homogeneous expressions, that is, these have the same denominator. Being one of the simplest procedures in relation to subtraction of fractions, Mathematics indicates that this operation will be solved as follows:

  • First, the elements of both fractions will be reviewed, in order to determine that these are really homogeneous fractions, which have the same denominator.
  • Having certainty of the nature of the fractions involved in the subtraction, we will then proceed to assume a single denominator, expressing the operation as a single fraction.
  • The value of the numerators will then be subtracted, taking into account their signs.
  • Once the result is obtained, it will be checked if it can be simplified, which will be done if possible.

Example Subtraction of fractions of the same denominator

However, it may be that the most efficient way to complete an explanation about the subtraction of fractions is through the presentation of an example, which allows to understand in a practical way how each of the steps are applied when solving a Subtraction operation of fractions, which have the same denominator, that is, these are homogeneous, such as the one seen below:

Subtract the following fraction:

Once the fractions have been reviewed, and it has been concluded that these are expressions of the same denominator, then the values ​​of the numerators will be subtracted:

In this case, due to the small value of the elements of the fraction, it isn´t necessary to apply simplification, in addition to the fact that the expression does not have a common divisor.


Subtraction of fractions with the same denominator
Source: Education  
September 22, 2019

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