Division of fractions

fraction is a number that can be obtained when a whole is divided into identical parts . They are represented mathematically by numbers that are written one on top of the other and that are separated from each other by means of a small line, which is known as a fractional line . The basic operations can be applied in sections and among them is division , a process that has many applications in everyday life and in education.

What is a division of fractions?

The division of fractions is a mathematical operation by means of which a multiplication can be done to distribute a number. It is a multiplication between the numerators and the denominators that make up two different fractions.

  • What is the division of fractions?
  • What is it for
  • Methods
  • Division of homogeneous fractions
  • Division of heterogeneous fractions
  • Division of proper fractions
  • Division of improper fractions
  • Importance
  • Examples

What is the division of fractions?

The division of fractions is an arithmetic operation that consists of carrying out a cross multiplication between the numerators and denominators of the fractions to be divided. It is a procedure in which the multiplication of the upper and lower extremes of the fractions is carried out in order to find the numerator and the numbers that are in the lower part of the fraction in order to find the denominator of the result.

What is it for

The divisions of fractions are operations that serve to divide a thing or to distribute a whole in equal or proportionate parts .


There are several methods by which fraction division can be performed. The most commonly used are explained below:

Cross multiplication method

In this method, a multiplication must be carried out between the numerator that belongs to the first fraction by the denominator that the second fraction has , this result must be placed in the numerator of the fraction that we will obtain as the final result. Then we proceed to multiply the denominator of the first fraction by the numerator of the second fraction and this is how the number that must be placed in the denominator of the result of the division is obtained.

Invert and multiply method

In this method you must invert the numbers that the second fraction has , in other words the denominator will be changed by the numerator and vice versa. After this step, we proceed to change the division sign for the multiplication sign and proceed to perform the operation in a straight line , in other words, we will multiply the numerator of the first fraction by the numerator of the second and the same step must be be applied for the denominator.

Method of multiplying internal and external numbers

In this method, one fraction must be placed on top of the other and then, a multiplication will be carried out between the external numbers, the result of this first operation will be the final numerator . Then, you must proceed to multiply the numbers that are located in the internal part and with them it is possible to obtain the final result of the denominator .

Division of homogeneous fractions

Homogeneous fractions are those that have the same denominator , in other words, they have the same number of parts, they are different fractions but with the same denominator. To divide this type of fraction, the following steps must be followed:

  • multiplication is carried out between the numerator of the first fraction that has been given to us by the denominator of the second. This result should be placed in the place of the numerator in the result .
  • Subsequently, the denominator of the first fraction is multiplied by the numerator of the second and thus we obtain the final result that belongs to the denominator.

Division of heterogeneous fractions

A heterogeneous fraction is one that has a different denominator and to divide them the following steps must be followed:

  • The first thing will be to multiply the numerator of the first fraction by the denominator of the second and this result will be set aside.
  • The denominator of the first fraction is multiplied by the numerator of the second and the result will also be set aside.
  • The next step will be to place the result of the first operation x the result of the second in the numerator part of the result.
  • The denominators are placed under the numerator where this multiplication is found and must also be multiplied .
  • We proceed to multiply the numerator, the result of which must also be placed in this position and then the numbers that had been placed in the denominator must be multiplied .

Division of proper fractions

The steps to divide the proper fractions are as follows:

  • Take the numerator of the first fraction and multiply it crosswise by the denominator of the second fraction
  • The denominator of the first fraction will be multiplied by the numerator of the second.
  • If the result is half, the fraction must be simplified .

Division of improper fractions

An improper fraction is one in which the numerator is a number greater than or equal to the number in the denominator. To perform a division between improper fractions, the following steps must be followed:

  • center line is written first .
  • At the top of the line the first fraction of the division will be placed .
  • The second fraction of the division should be placed at the bottom of the lines .
  • Will multiply the ends first and this will be the final numerator.
  • They will multiply the media and this is the result of the denominator.
  • If the fraction can be simplified or reduced, the process must be executed.


Its importance lies in the fact that by dividing fractions a whole can be divided into equal or equitable parts .

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