Question

How do you convert $25\% $ into a fraction in simplest form?

Answer 1

Hint:
This is a problem in which the student has to bring the percentage into a fraction in its simplest form. This can be treated as a problem in fraction in which the first step would be to convert a percentage into a fraction by dividing it by $100$. After the first step, the student has to find the greatest common multiple for both the numerator and denominator or the student can also bring both the numbers in their simplest form i.e in terms of prime number multiplication. The third step would be to cancel out the common multiples. This would be the final answer.

Complete Step by Step Solution:
The first step is to convert the given percentage into the form of a fraction
$25\% = \dfrac{{25}}{{100}}.........(1)$
The second step is to bring numerator and denominator in terms of its prime factors.
$\dfrac{{25}}{{100}} = \dfrac{{5 \times 5}}{{5 \times 5 \times 4}}..........(2)$
From the above step, we can see that the fraction has the greatest common multiple$25$. Striking off the common multiple we get the fraction in its simplest form.
$\dfrac{{25}}{{100}} = \dfrac{1}{4}.........(3)$

Thus, the simplest form of the fraction is $\dfrac{1}{4}$

Note:
The only important step in this sum is to first bring the percentage into a fraction and then in terms of its prime factors. Sometimes when the complicated sum like $40\% \times \dfrac{5}{{20}} \times \dfrac{4}{{40}}$ it is advisable that the student first converts all the terms into the form of a fraction and then cancel out common terms after which, he/she should reduce the remaining terms to its the prime factors.