Subtraction of mixed fractions

It is likely that it is best to address an explanation of how it should be resolved at the backof mixed fractions is to review some concepts, which will allow us to understand this operation within its precise context.

Fundamental definitions

In this sense, it may also be necessary to focus this theoretical review on four fundamental notions: Fractions, Unsuitable Fractions, Integers, and Mixed Fractions, as these are the related elements in the subtraction operation. Here’s each one:


In this way, one can begin by saying that Mathematics has defined fractions as one of the two forms of expression with which fractional numbers count, that is, those amounts that are not whole or inaccurate. Thus, the mathematical discipline has observed that these expressions will be formed, without exception by two elements, defined in turn as follows:

  • Numerator: on the one hand, the Numerator is conceived as the element of the fraction that occupies the top of it. As for its specific task, this discipline indicates that the Numerator will have the mission of indicating how many parts of the total have been taken or represents the fraction.
  • Denominator: In the second instance, the Denominator of the fraction will be located at the bottom of the expression, having as task to indicate how many parts are divided the whole, from which the parts indicated by the Numerator have been taken.

Improper fractions

For its part, it will also be relevant to throw lights on the definition of Improper Fractions, mathematical expressions that have been explained as a type of element, which serves to account for non-whole or fractional amounts, and which are characterized by counting with a Numerator of higher value than the Denominator, next to which the expression makes up.


Likewise, it will be essential to review the definition of Integers, elements that will be used to express whole amounts, and that are considered composed of positive integers, their negative inverses and zero, elements these that constitute the Z numerical set, while being used respectively to account for whole amounts, the absence or debt of specific amounts and even the total absence of quantity.

Mixed fractions

Finally, it will also be necessary to take into account the concept of mixed fractions, which will then be understood as those mathematical expressions, by means of which fractional numbers or non-exact quantities are represented, and which are characterized specifically because they are made up of an integer and a fraction of its own, that is, whose numerator is of less value than the denominator that accompanies it.

Subtraction of mixed fractions

Having revised each of these definitions, it is perhaps certainly much easier to approach each of the procedures by which the subtraction of mixed fractions is achieved, an operation described in turn as the mathematical operation by means of which a specific mixed fraction is subtracted or deleted by a certain amount, indicated by a second mixed expression. As for the steps required to carry out this operation, you will find the following:

  • First, each of the two mixed fractions involved must be converted to improper fractions, which will be achieved by multiplying the whole number by the denominator, and then adding it with the numerator, in order to obtain the numerator of the fraction improper, which will have the original denominator of the fraction that composed the mixed expression.
  • Once both the Minuendo and the Subtracting are converted to improper fractions, the fractions will then be subtracted, for which the following operation will be applied:

  • Finally, obtained the difference between the two improper fractions, a conversion process will be carried out again, taking the expression to a mixed fraction, a situation for which the following operation will proceed:

Example of subtraction of mixed fractions

However, the most effective way to conclude an explanation of the correct way to perform a subtraction between two mixed fractions may be to set out a specific example, which allows us to see in a practical way how each of the procedures should be performed inherent in the solution of this operation, as can be seen below:

Subtract the following mixed fractions:

It will then begin by converting each mixed expression into its improper fraction equivalent:

Having done this, we will proceed again to raise and resolve the subtraction, this time with the improper fractions:

After the improper fraction, the respective conversion will be performed, in order to express this fraction as a mixed fraction, then composed of an integer and a fraction, and which will eventually be interpreted as the result of the operation:


Subtraction of mixed fractions
Source: Education  
September 30, 2019

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