How to convert mixed fractions into improper fractions

Perhaps best of all, before advancing an explanation of how the procedure should be performed correctly to convert a mixed fraction into an improper fraction, is to carry out a brief theoretical review, which allows to take into account certain definitions, indispensable to understanding this operation within its precise mathematical context.

Fundamental definitions

In this sense, it may also be prudent to delimit this revision to four specific notions, these being the concepts of Fractions, Unsuitable Fractions, Integers and Mixed Fractions, each of which arises as necessary when it comes to understand the nature of the expressions related to this operation. Here’s each one:


In this way, it will begin by saying that the Mathematics has defined fractions as a mathematical expression, by means of which fractional numbers, that is, non-exact or non-integer amounts, can be represented. Likewise, this discipline states that fractions will be composed of two elements, each of which have been defined as follows:

  • Numerator: first, you will find the numerator, which will be the element that is located at the top of the expression, having also the mission to indicate how many parts of the whole have been taken, or are represented in the fraction.
  • Denominator: for its part, the denominator will be located at the bottom of the fraction, serving to indicate how many equal parts the whole or unit, from which parts have been taken, indicated by the numerator.

Improper fractions

Likewise, it will be necessary to take into account the concept of Improper Fractions, which are understood as fractions, that is, expressions of fractional or non-integer numbers, whose main characteristic is to have a numerator with greater value than the denominator, together with which the fraction makes up.


On the other hand, whole numbers have been generally explained by different mathematical sources as a number type or numeric element, used to account for exact or whole amounts. Thus, Mathematics highlights how these types of numbers make up the z numeric set, being in turn consisting of positive integers, their negative integers, and zero.

With regard to the different uses that these types of numbers may have, Mathematics has indicated that whole numbers will be seen as the elements with which whole amounts can be expressed respectively (through positive integers); absence or lack of specific whole amounts (thanks to negative integers) or even the total absence of quantity (thanks to zero).

Mixed fractions

Finally, it will also be important to cast lights on the definition of Mixed Fractions, which will be understood as a mathematical expression, used to account for non-exact or non-exact amounts, and which will be characterized mainly by being consisting of an integer and a fraction of its own, that is, a fraction where the numerator will always be less than the denominator that accompanies it.

Examples of such fractions will be as follows:

How to convert mixed fractions to improper fractions

Bearing in mind each of these definitions, it may be much easier to understand the nature of each of the expressions involved in the operation used to convert a mixed fraction into an improper fraction, a procedure that is done to give account of the same amount, since both expressions are equivalent, and that it is performed because it is the much more common mixed fraction in colloquial language than in the mathematician, a discipline that prefers the expression of a certain amount not accurate through the inappropriate fraction.

In this way, Mathematics has also specified what steps should be taken when converting a mixed fraction to an improper fraction, and which would be composed of the following:

  1. First, the whole number must be multiplied by the denominator that also makes up the mixed fraction.
  2. The product obtained must be added with the number that serves as the numerator of the fraction that is part of the mixed fraction. The result will be taken as the numerator of the improper fraction, to which the mixed fraction has been converted.
  3. Finally, the same denominator that originally had the fraction that was part of the mixed expression will be taken as the denominator of the improper fraction.

This operation may be expressed mathematically as follows:

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

However, the most efficient way to conclude an explanation of the correct way to convert a mixed fraction into an improper fraction may be through a concrete example, which allows us to see in a practical way how each of the steps, inherent conversion operation, as shown below:

Convert the next mixed fraction to an improper fraction:

For this, the indicated procedure will then be used, multiplying the whole number by the denominator, and then adding to the product the numerator, in order to calculate the numerator of the improper fraction, while the same will be assumed for the new expression Called:

Whenever a mixed fraction is converted to a fraction, the fraction will be an improper fraction, that is, it will have a numerator of greater value than the denominator that accompanies it.


How to convert mixed fractions into improper fractions
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Bibliography ► (September 26, 2019). How to convert mixed fractions into improper fractions. Bogotá: E-Cultura Group. Recovered from