Operations with mixed fractions

It is likely that the best way to address an explanation of each of the basic operations that can be performed with mixed fractions is likely to briefly review some concepts, which will make it possible to understand each of these procedures in their context Indicated.

Fundamental definitions

In this way, it may be relevant to focus this theoretical review on three specific notions: fractions, integers, and mixed fractions, as these are the elements that are involved in each of the operations on which they will be passed Magazine. Here are each of these concepts:


In this sense, it can be started by saying that mathematics has defined fractions as one of the two types of expression with which fractional numbers count, so it can be said that fractions will serve to represent amounts that are not accurate or not Whole. Likewise, this discipline has indicated that fractions are composed of two elements:

  • Numerator: First, the Numerator will occupy the top of the expression, having the task of pointing out how many parts of the whole have been taken.
  • Denominator: For its part, the Denominator will always be located at the bottom of the fraction. Its mission will be to indicate in how many parts the whole is divided, of which some parts have been taken, pointed out by the Numerator.


It will also be relevant to throw lights on the definition of Whole Numbers, which have been explained by Mathematics as a type of numerical element, used to represent whole or exact quantities. These numbers are made up of positive integers, their negative inverses and zero, so respectively they are responsible for expressing exact amounts, debts of specific exact amounts and even the total lack of quantity. Integers make up the z numeric set.

Mixed fractions

Finally, it will also be important to pause for a moment in the concept of Mixed Fractions, which will be seen as expressions, representatives of fractional numbers, which are characterized by being composed of an integer and a fraction of its own, is a fraction whose numerator is less than the denominator.

Thus, mathematics points out that this type of expression corresponds more to the colloquial scope than the mathematician, where the use of improper fractions is preferred. Mixed fractions are used especially when a whole, composed of several units, which have in turn been divided into equal parts, one or more units have been taken completely and some parts of another.

Operations with mixed fractions

Bearing these definitions in mind, perhaps then it is much easier to address the definition of each of the basic operations that can be found in reference to the mixed fractions, which will then be explained as follows:

Sum of mixed fractions

In the first instance, you will find the sum of mixed fractions, which will be understood as an operation by which it is sought to calculate what is the total resulting from combining the values of each of the elements of the fractions that function as summands. As dictated by the Mathematics, this operation should be solved by following the steps referred to below:

  • The values of the integers will be added on the one hand.
  • On the other hand, the own fractions that accompany these whole numbers in the mixed fractions will be added. For this, the method recommended by Mathematics will be used to add fractions:

  • The results are recorded in the place that corresponds to each one, in the mixed fraction. In the event that the sum of fractions has yielded an improper fraction, that is, with a numerator of much greater value than the denominator, it must be converted into a mixed fraction, adding to the whole of the fraction, the total obtained from the sum of original integers.

Subtraction of mixed fractions

As for the subtraction of fractions, the mathematical discipline indicates that it is the operation that is performed in order to obtain the difference between two mixed fractions. The correct way to resolve this operation will be as follows:

It begins by making an improper fraction each of the mixed fractions that are involved in the operation. For this, the procedure will be followed, shown below:

2.- Done this, we will then proceed to perform the subtraction of fractions, for which the following operation will be fulfilled:

3.- The result obtained, which must always be an improper fraction, must be converted again into a mixed fraction, so this operation will be followed:

Multiplication of mixed fractions

For its part, fraction multiplication can be seen as the action of adding a mixed fraction on its own, as many times as a second mixed expression points out, hence the multiplication of mixed fractions is also understood as an abbreviated sum. With regard to the correct way to fix it, the following steps will be taken:

  • Mixed fractions will be converted into improper fractions.
  • The fractions obtained will then be multiplied, for which the following operation will be followed:

  • Obtained the result, the obtained improper fraction will be converted into a mixed fraction.

Mixed fraction division

Finally, the Mixed Fractions Division will be understood as the operation that is performed in order to calculate the quotient between two fractions of this type. This procedure should be guided by the following steps:

  • The mixed fractions between which the operation arises will become unsuitable fractions.
  • The fractional split is carried out, for which the following operation is fulfilled:

  • Finally, the inappropriate fraction obtained is converted back into a mixed fraction.

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Operations with mixed fractions
Source: Education  
September 26, 2019

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