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**Hint:**The given fraction in the question is proper fraction, to simplify a fraction divide the top and bottom i.e., numerator and denominator of the given fraction by the highest common factor. This means look for the biggest number then divide into both, if gives the simplest form of the fraction.

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

The given question in the form of \[\dfrac{a}{b}\] where, a is the numerator and b is the denominator this form is known as fraction, there are mainly two types of fraction namely

i) Proper fraction: If the numerator is smaller than the denominator is known as proper fraction.

ii) Improper fraction: If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction. In that case, you could convert it into a whole number or mixed number fraction

iii) Simplification of fraction: To simplify a fraction we divide both the numerator and denominator by the same number. A common factor is a number that divides both the numerator and denominator without leaving any remainders. We divide the fractions till we get 1 as the common factor for both the numerator and denominator.

The given fraction \[\dfrac{{10}}{{25}}\] is the proper fraction, where 10 is numerator and 25 is denominator

First, we find the factors of both numerator and denominator

Factors of 10 is 1, 2, 5 and 10

Factors of 25 is 1 and 5

The highest common factor HCF of 10 and 25 is 5

So, we divide the both numerator and denominator of the fraction by 5

Consider \[ \Rightarrow \,\,\dfrac{{10}}{{25}}\]

Divide the both numerator and denominator by 5,we get

\[ \Rightarrow \,\,\dfrac{2}{5}\]

Hence, the simplest form of given fraction \[\dfrac{{10}}{{25}}\] is \[\,\dfrac{2}{5}\]

**Note:**Candidate must know the table of multiplication to solve or simplify. To simplify the given we divide both numerator and denominator by a number which is a factor of both numerator and denominator. To find the common number we use the concept of HCF and we determine the solution.

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