Sum of fractions


With the different fractions that exist in the field of mathematics, a series of different basic mathematical operations can be carried out, such as addition . A procedure that is actually very easy to do, although sometimes, depending on the denominators , a series of steps will have to be followed in order to perform them.


What is a sum of fractions?

The addition of fractions is a mathematical process by means of which two or more fractions can be combined into a number that is equivalent and that is also represented by the mathematical symbol of +.

  • What does it consist of
  • What is it for
  • Sum of homogeneous fractions
  • Sum of heterogeneous fractions
  • Sum of mixed fractions
  • Importance
  • Examples

What does it consist of

Adding fractions is a basic mathematical operation that allows you to combine two or more fractions into an equivalent number . In order to perform the addition of fractions, it must be taken into account that in some cases the fractions may have a different denominator . When these denominators are equal, the mathematical procedure for the addition of fractions will be very easy to perform and in the case of fractions that have different denominators, a certain process must be followed.


What is it for

The addition of fractions is used to obtain results that are easier to handle and to solve a series of problems in scientific, technical, artistic fields and even in situations that are handled in everyday life.

Sum of homogeneous fractions

It is important to remember that homogeneous fractions are those that have the same denominator . To make an addition with this type of fractions, the following steps must be followed:

  • Fractions are placed in position including the + sign.
  • We proceed after they are placed to add the numerators .
  • The denominator to be equal in both fractions proceeds to leave same.

Sum of heterogeneous fractions

The steps that must be followed to be able to add two or more heterogeneous fractions are the following:

  • As the denominators are unequal, the first step is to find the least common multiple of the denominators, which is the positive number of smaller sizes that is at the same time a multiple of the numbers that are being analyzed.
  • Subsequently, we proceed to find the numerator of the first fraction that will be done by multiplying the numerator of the fraction by the least common multiple and the result must be divided by the denominator of that first fraction.
  • Then we proceed to find the numerator of the second fraction, multiplying the numbers of this fraction by the least common multiple and then dividing the result by the denominator.
  • The numerators must be added after these procedures and the denominator of these fractions will also be the least common multiple that had previously been found.

Sum of mixed fractions

Mixed fractions are numbers that are made up of a whole number and a fraction in the numerator. This type of fraction is responsible for representing the number that is obtained when the integer is added with the proper fraction. The steps to follow to perform this type of addition are the following:

  • When the mixed fractions have the same denominator , the easiest way to do the addition is to add the whole parts to obtain the whole number of the final result and then proceed to add the fractions to obtain the final result.
  • When the mixed fractions have a different denominator then the first step will be to obtain the total of the whole numbers .
  • Subsequently, all the fractions that are present in the operation and that are part of the mixed fractions to be added will be added.
  • With the sum of fractions, an improper fraction will be obtained which must be converted to a mixed fraction by means of a division.
  • After obtaining the mixed fraction, the total between the whole numbers is added and then the fraction obtained is placed next to this number.


The addition of fractions is important because through them, daily activities can be carried out more easily, mainly those related to the purchase of products such as flour, rice and sugar. They are necessary for the preparation of recipes and in some cases in the composition of chemical compounds .

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