How to convert improper fractions to mixed fractions

Perhaps best ly advised, before moving forward with an explanation of the mathematical procedure to be followed when converting an improper fraction into a mixed fraction, is to briefly revise some definitions, which allow us to understand this operation mathematics within its precise context.

Fundamental definitions

In this sense, it may also be necessary to focus this review on four specific notions, these being the concepts of Fractions, Improper Fractions, Integers and Mixed Fractions, as these are the mathematical expressions involved directly in the conversion operation that would lead to expressing the same amount in two different ways, either through an improper fraction or a mixed fraction, as desired a more mathematical expression, or on the contrary much more colloquial. Here are each of these definitions:


In this way, it will begin by saying that Mathematics has generally defined fractions as a type of expression by which fractional numbers, i.e. non-exact, or non-whole amounts, are represented. Thus, the mathematical discipline has pointed out that expressions called fractions will always be composed of two elements, each defined as follows:

  • Numerator: In the first instance, the Numerator will be considered as the number that occupies the top of the expression, and whose mission is to indicate how many parts of the whole represents the fraction.
  • Denominator: Second, the Denominator will be characterized by being located without exception at the bottom of the expression. This element will be tasked with indicating in how many parts the whole has been divided, from which one or more parts have been taken, pointed to by the Numerator.

Improper fractions

On the other hand, it will also be necessary to indicate what is the definition given by the Mathematics on Improper Fractions, expressions that have then been explained as those mathematical forms used to account for fractional numbers, that is, of non-integerorors or not exact quantities, and which are particularly characterized by having a numerator whose quantity is of greater value than the denominator next to which the fraction makes up.


As for whole numbers, these have been explained by Mathematics as those elements by which they are given expression to whole or exact amounts. Likewise, the mathematical discipline indicates that the Integers will consist of all positive integers, negative integers and zero, numbers which in turn will constitute the numerical set Z, while being used to express specifically exact amounts, absence or debt of exact amounts, or even the total absence of amount.

Mixed fractions

Finally, it will also be important to cast lights on the definition of Mixed Fractions, which have then been explained as a type of representation of fractional numbers, or non-exact amounts, characterized specifically by counting in their conformation with an integer and a fraction. These types of expressions are used – mostly in the colloquial realm – to express how several units, divided into equal parts, have completely taken some and only parts of others.

How to turn unsuitable fractions into mixed fractions

Bearing in mind each of these concepts, it is perhaps certainly easier to approach the procedure by which an improper fraction can be converted into a mixed fraction, an operation that can be carried out as both expressions is done by looking for a much more colloquial expression, such as the mixed fraction, because the inappropriate fraction is much more inherent in the mathematical realm, and less manageable to people in general.

Consequently, the Mathematics indicates that this conversion operation must be carried out, following certain steps, which have been described as follows:

  1. Having the inappropriate fraction, that is, with a numerator of greater value than the denominator, we will proceed to divide the numerator by the denominator.
  2. Having done this operation, the obtained quotient will be taken, considering it as the whole number of the mixed fraction.
  3. For its part, the rest obtained from this division will be taken as the numerator of the fraction that will be part of the mixed fraction.
  4. Finally, as the denominator of the fraction that makes up the mixed fraction, the denominator that the improper fraction originally had will be preserved.

This operation may also be represented mathematically as follows:

Example of how to convert an improper fraction into a mixed fraction

However, the most efficient way to terminate an explanation of the correct way to perform a conversion that leads to the expression of an improper fraction in the form of a mixed fraction may be through the exposure of a particular example, which allows to see practically how each of the steps to be followed is carried out for this purpose, as can be seen in the exercise below:

Convert the next improper fraction to a mixed fraction:

To perform this operation, you must start by dividing the numerator into the denominator:

The whole number of the quotient will then be taken, which will be assumed as the whole number of the mixed fraction. Likewise, the first number obtained from the rest will be allocated as the numerator of the fraction belonging to the mixed expression to be formed. Finally, the denominator that originally had the inappropriate fraction shall be retained as the denominator:

If you would like to check whether the given expression is in effect correct, then it is sufficient to convert the mixed fraction to an improper fraction, using the operation intended for this:

Having then, the following:

Therefore, the operation is considered correct, and the fractions obtained are equivalent.


How to convert improper fractions to mixed fractions
Source: Education  
September 26, 2019

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