Convert a mixed fraction to a decimal number

Perhaps best of all, before addressing an explanation of the correct way in which a mixed fraction should be transformed into a decimal number, is to briefly revise some definitions, which will allow us to understand this operation in its precise mathematical context.

Perhaps best of all, before addressing an explanation of the correct way in which a mixed fraction should be transfo...

Convert a mixed fraction to a decimal number

Fundamental definitions

In this sense, it may be best to delimit this theoretical revision to four specific notions: Fractions, Integers, Mixed Fractions, and Decimal Numbers, as these are mathematical expressions inherent in the operation of expressing the same amount, in both Mixed Fractions and Decimal Numbers. Here are each of these definitions:

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In this way, it will begin by saying that the Mathematics has defined Fractions as one of the two possible expressions with which fractional numbers count, therefore, fractions will be used to represent non-exact or non-whole amounts. Likewise, the mathematical discipline states that fractions will consist of two elements, each of which are defined in turn as follows:

  • Numerator: First, the Numerator will be the element at the top of the expression, and it is on a mission to point out what part of the whole has been taken, or of which the fraction speaks.
  • Denominator: Second, the Denominator will consist of the element to which the lower part is assigned. Your task will be to indicate in how many parts the whole is divided, of which the fraction represents a part, indicated in turn by the denominator.


For its part, the Whole Numbers shall be those numerical elements or signs, by means of which the whole or exact quantities are represented. Thus, mathematics notes that within the Integers all positive integers, their negative inverses and zero will be found, so then these types of numbers will serve respectively to account for whole amounts, absence or missing specific quantities, and even the total absence of quantity. Integers are the Z numeric set.

Mixed fractions

Similarly, mathematical discipline has been given to the task of defining what are mixed fractions, which will then be understood as those expressions made up of both an integer and a fraction of their own, that is, those that have numerators of lower value than the accompanying denominator.

In line with what the different sources point out, the mixed fractions correspond to a much more colloquial than mathematical terrain, being used in situations where a whole is made up of different units, which in turn have been divided into parts equal, and of which some units are taken completely, and only some parts of another.

Decimal numbers

Finally, decimal numbers will be those that are characterized by having an entire part, that is, consisting of an integer, and a second one made up of a quantity less than the unit, which in turn represents quantities that can have a part whole and one fractional.

Both quantities are separated by a comma – even though there are other countries that prefer to use the dot to distinguish between units and fractional numbers. These types of numbers are also used to express the situation where it has been taken from a whole of some units and only some parts of another.

Convert a mixed fraction to a decimal number

Once each of these concepts has been revised, an approximation of the operation can be made by which an amount indicated by a mixed fraction in the form of a decimal number can be expressed, which then requires the following steps:

  • When converting a mixed fraction to a decimal number, it will be necessary to start by considering the whole number of the mixed expression as the first number with which you will count the decimal number.
  • Secondly, we will proceed to divide into the numerator of the fraction between the denominator with which the expression is formed. You will get a decimal number, that is, an expression composed of an integer part and a fractional part, which will be separated by a comma.
  • Next, the whole number that was originally owned from the mixed fraction will be summed with the decimal number that was obtained from dividing the fraction numerator by its denominator. The result will be interpreted as the decimal number in which the mixed fraction has been transformed.

Examples of how to convert a mixed fraction to a decimal number

However, the most efficient way to close an explanation of the correct way to perform such operations may be through the exposure of a particular example, which allows you to see in the practice the application of each of the steps that should be followed in the procedure intended to convert a mixed fraction into a decimal number, in order to be able to give expression to the same amount of any of these two possible ways, as you can see below:

Convert the following mixed expression to a decimal number:

Convert a mixed fraction to a decimal number

To begin with, the same part of the mixed fraction will be taken as the whole part, while the numerator will be divided by the denominator:

1: 2 = 0, 5

The decimal number obtained shall then be added, with the original whole part of the mixed fraction:

3 + 0,5= 3,5

And this will be the result of the operation.


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