The **fraction parts** They are divided into three: their numerator, a horizontal or diagonal bar, and their denominator. Therefore, if you want to denote the fraction «a quarter», the notation is 1/4, where the number above the bar is the numerator and the number below is the denominator.

When you talk about fractions, you are really talking about the parts into which the whole of something must be divided. The numbers that make up a fraction are integers, that is, the numerator and denominator are whole numbers with the proviso that the denominator must always be different from zero.

Therefore, the parts of the fraction are:

The numerator (top). The denominator (bottom).

**Definition**

The formal mathematical definition of fractions is: the set formed by all elements of the form p/q, where «p» and «q» are integers with «q» other than zero.

This set is called the set of rational numbers. Rational numbers are also called broken numbers.

Given any rational number in its decimal expression, you can always find the fraction that generates it.

**Examples of the use of fractions**

The basic way in which a child is taught the concept of a fraction is by dividing up pieces of an object, or a set of objects. For example:

**Birthday cake**

If you want to divide a circular birthday cake among 8 children such that all children are given the same amount of cake.

It begins by dividing said cake into 8 equal parts as in the figure below. Then each child is given a piece of cake.

The way to represent the fraction (portion) of cake that each child got is 1/8, where the numerator is 1, since each child received only one piece of cake, and the denominator is 8, since the cake was cut into 8 equal parts.

**Candies**

Maria bought 5 candies for her two children. He gave Juan 2 candies and Rosa gave him 3 candies.

The total number of candies is 5 and all 5 must be distributed. According to the distribution that María made, Juan received 2 candies out of 5 in total, so the fraction of candies that he received is 2/5.

Since Rosa was given 3 candies out of a total of 5 candies, the fraction of candies that Rosa received was 3/5.

**rectangle fence**

Roberto and José must paint a rectangular fence which is divided into 17 vertical boards of equal dimensions as shown in the figure below. If Roberto painted 8 boards, what fraction of the fence did José paint?

The total number of vertical boards of the same size in the fence is 17. The fraction of the fence that Roberto painted is obtained using the number of boards painted by Roberto as the numerator of the fraction and the denominator is the total number of boards, that is, 17 .

Then, the fraction of the fence painted by Roberto was 8/17. To complete painting the entire fence, it is necessary to paint 9 more boards.

These 9 tables were painted by José. This indicates that the fraction of the fence that José painted was 9/17.

**References**

Almaguer, G. (2002). *Mathematics 1.* Editorial Limusa.

Bussel, L. (2008). *Pizza by pieces: fractions!* Gareth Stevens.

Cofré, A., & Tapia, L. (1995). *How to Develop Mathematical Logical Reasoning.* University Press.

From sea. (1962). *Mathematics for the workshop.* reverse.

Lira, M. L. (1994). *Simon and mathematics: mathematics text for the second grade: student’s book.* Andres Bello.

Palmer, CI, & Bibb, SF (1979). *Practical Math: Arithmetic, Algebra, Geometry, Trigonometry, and Slide Rule* (reprint ed.). reverse.