Question

How do you write $76\mathrm{\%}$ as a fraction in simplest form?

Answer 1

Hint: In this type of problem where we need to find the fraction from the percent we must know what percent means. If the person scores $n\mathrm{\%}$ it simply means that he scored $n$ out of $100$ and we can write it in the form of the fraction as ${\displaystyle \frac{n}{100}}$.
Hence we can simply proceed according to the above information.

Complete step by step solution:
Here we are given to find the fraction of the term which is given in the form of the percentage which is $76\mathrm{\%}$ and therefore we must know what the fraction actually means. It can be termed as the term where we have both the numerator and the denominator. It can be made clearer with an example. If the student scored marks $5\text{ out of 10}$ then we can say that $5$ will be our numerator and $10$ will be our denominator. So we can write this as the fraction ${\displaystyle \frac{5}{10}}$. If the person scores $n\mathrm{\%}$ it simply means that he scored $n$ out of $100$ and we can write it in the form of the fraction as ${\displaystyle \frac{n}{100}}$.
Hence we can proceed in the same way as we have understood the meaning of what fraction and percent are and also how percent can be converted into the fraction.
So here we are given the term $76\mathrm{\%}$
So it actually means there are $76$ marks outs of $100$
Hence the fraction of the given term which is $76\mathrm{\%}={\displaystyle \frac{76}{100}}$
Now we can convert it into the simplest form by cancelling the numerator and denominator with their common factors. So we know that $76\text{ and 100}$ are divisible by $4$ as:
$$\begin{gathered} \left(4\right)\left(19\right)=76 \\ \left(4\right)\left(25\right)=100 \end{gathered}$$
Hence we can say that:

${\displaystyle \frac{76}{100}}={\displaystyle \frac{19}{25}}$
Hence it is the simplest form of the fraction.

Note
We must also know that whenever we are given to find the fraction of the decimal term, we need to remove the decimal first by putting in the denominator the value in the power of ten as required to remove the decimal. Then we need to convert that fraction in the simplest form.