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**Hint:**Here in this question, we have to describe the methodology of how the fractions are simplified. Usually, the fractions are of three kinds. By taking all the three kinds of fraction we see the method how it is simplified. We also consider the examples to solve this. hence, we determine the solution.

**Complete step-by-step solution:**

The fraction has two parts one is numerator and another denominator. The value which is present above the line is called a numerator and the value which is present below the line is known as a denominator.

In fraction they are three kinds

Proper fraction: The fraction where the value of numerator less than the value of denominator.

Improper fraction: The fraction where the value of numerator greater than the value of denominator.

Mixed fraction: The combination of fraction and whole number.

The fraction number is represented as \[\dfrac{a}{b}\]

While simplifying the fraction we find the common factor of the number a and the number b. Then by cancelling the common factors we simplify the fraction.

This method is applicable to both proper fraction and Improper fraction.

When we simplify the mixed fraction, we convert the fraction into an improper fraction and then we follow the usual method.

Example: Simplify the fraction \[\dfrac{{25}}{{20}}\]

We take the common factor for the number 25 and 20.

The common factor for 25 and 20 is 5, hence we divide the both numbers by 5.

\[ \Rightarrow \dfrac{{25}}{{20}} = \dfrac{5}{4}\]

**Note:**To solve the fractions we follow the method the same. The greatest common factor is to find the numbers which are present in the fraction. To simplify the fraction, we need to know about the tables of multiplication and the division arithmetic operation. Hence the method is the same for all the fractions.

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