Question

How do you write the fraction $\dfrac{{28}}{{100}}$ in the simplest form ?

Answer 1

Hint: In order to determine the simplest form of the fraction as given in the above question, we first write the numerator and denominator in the form of their prime factors and try to cancel out factors from numerator and denominator to get the given fraction in the simplest form. This can also be done by dividing the numerator and denominator by their common factor so that the value of fraction remains intact.

Complete step-by-step solution:
We are given a fraction $\dfrac{{28}}{{100}}$ in the problem which we need to convert into the simplest form. To convert it into its simplest form, factorise the numerator as well as denominator into their respective prime factors.
So, we can write the numerator as $28 = 2 \times 2 \times 7$ and the denominator as $100 = 2 \times 2 \times 5 \times 5$.
Rewriting the fraction into their factors form as:
$ \Rightarrow \left( {\dfrac{{2 \times 2 \times 7}}{{2 \times 2 \times 5 \times 5}}} \right)$
Cancelling out $2 \times 2$ as it is present in numerator and denominator.
$ \Rightarrow \left( {\dfrac{7}{{5 \times 5}}} \right)$
Simplifying further,
$ \Rightarrow \left( {\dfrac{7}{{25}}} \right)$
Therefore, $\dfrac{{28}}{{100}}$in simplest form is $\left( {\dfrac{7}{{25}}} \right)$.

Note: A Rational number is a number which can be expressed in the form of $\dfrac{p}{q}$ ,where p and q are any integer value and q is not equal to 0. Such a number is known as a rational number. The simplest form of a fraction can also be converted back to the original fraction by multiplying the numerator and denominator by the same number. Don’t forget to cross check your result.