Subtraction of heterogeneous fractions or with different denominator

It is likely that the most appropriate way to approach an explanation of the subtraction of heterogeneous fractions is to start by doing a theoretical review, which allows to review some definitions, necessary to understand this mathematical operation, sustained between fractions with different denominator, in their precise context.

Fundamental definitions

In this sense, it may also be necessary to delimit this revision to two basic notions: the first, the very definition of Fractions, since bringing this concept into a chapter will make it possible to have clear the nature of mathematical expression on the basis of the operation of Subtraction of fractions is carried out, the definition of which must also be taken into account, because it is in which heterogeneous fractions participate. Here are each of these concepts:


In this way, it will be necessary to begin by saying that fractions have been explained by Mathematics as one of the two types of expressions with which fractional numbers count. Therefore, consisting of a division held between two integers, the fraction shall account for a non-whole quantity, hence its name, since it expresses a part or fraction of a quantity.

Likewise, mathematics has indicated that each of the two numbers that make up the fraction, that is, that they participate in this kind of division, constitute the elements of the fraction, being defined by them as follows:

  • Numerator: First, the numerator will be found, which corresponds to the number that occupies the top of the fraction. This element fulfills the task of indicating the amount or part of the whole that represents the fraction of which this number is part.
  • Denominator: on the other hand, the denominator will consist of the number that occupies the bottom of the fraction. Its specific mission is to point out how many parts the whole is divided into.

Rest of fractions

In another order of ideas, it will also be necessary to throw lights on the definition of Fraction sunder, which is understood by Mathematics as the type of operation, where a fraction seeks to suppress in itself the specific amount pointed to by a second Fraction. In this procedure, the first fraction will act as minuenting, the second as subtracting, while the final result will be interpreted as the difference.

Similarly, different sources have indicated that there is no single method for resolving a fraction subtraction operation, since the proper way of doing so will depend mainly on the homogeneous or heterogeneous nature of fractions.

Subtraction of heterogeneous fractions

One of these cases is the Subtraction of fractions where the expressions involved have different denominators, that is, they are heterogeneous. In this regard, the Mathematics indicates that to solve this operation, consisting of this type of fractions, it will be necessary to follow the steps indicated below:

  • In the first instance, the elements of fractions will be reviewed, to verify that they are heterogeneous fractions.
  • Once this has been verified, then a procedure should be performed, in which the numerators are multiplied by the denominator of the other fraction, while the denominators of both fractions do it between them, as seen in the following expression:
  • Calculated the corresponding products, the values of the numerators will then be subtracted.
  • If the possibility is found, the fraction is simplified.

Example of subtraction of heterogeneous fractions

However, perhaps the best way to complete an explanation of how a heterogeneous fraction subtraction operation should be resolved is through the exposure of a particular example, which allows us to see closely how the multiplication aimed at homogenizing fractions, in order to be able to resolve the subtraction proposed, as can be seen below:

Resolve the following operation:

Once it has been determined that these are heterogeneous fractions, the respective operations will be undertaken to ensure that the expression has a common denominator, which allows subtraction:

Obtained each of the products, the subtractions raised between the numerators must then be resolved, since both fractions agree on their denominator.

Obtained the result, it is also verified that there is no number between the numerator and the denominator that can serve as a common divider, so then the operation cannot be simplified. Therefore, it is assumed that this form, originating from the Subtraction of heterogeneous fractions that has developed is the most irreducible expression that can be had.

Likewise, it should not be neglected, the importance of correctly annotating the sign corresponding to the result, because as the multiplication has been raised, the minuendo was less than the subtracting, hence the operation has resulted in a number negative, in which it will then be annotated with its sign.

Any questions that arise from the topic, we will be attentive to try to answer it. If you liked this article, share it on your social networks and tell us your opinion about the subject, in the comments box.


Subtraction of heterogeneous fractions or with different denominator
Source: Education  
September 22, 2019

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