Question

What is $64\%$ as a fraction in simplest form?

Answer 1

Hint: First we will convert 64 percent into fraction as we know percentages are nothing but fraction with denominator 100. Now we will factorize the numerator and denominator and cancel the common factor. Hence we will get the fraction in simplest form.

Complete step by step solution:
Now first let us understand the concept of percentage.
Percentage means nothing but per 100. Hence the percentage tells us parts per 100.
Now let us understand the concept by an example. Suppose we have 100 apples in a basket. Now suppose we take 5 apples out of the basket. Then we can say that we have taken 5 out of 100 apples or 5 percent of the apples from the basket.
The percentage is denoted by the symbol $%$ .
Hence we can say that percentage is nothing but a fraction with denominator 100.
Now consider the given number which is $64\%$ . Now converting this percent into fraction we get, $\dfrac{64}{100}$
Now we want to convert the fraction into the simplest form.
To do so we will factorize the numerator and denominator into prime factors. Hence we get,
$= \dfrac{2\times 2\times 2\times 2\times 2\times 2}{2\times 2\times 5\times 5}$ .
Now we will cancel all the common factors from the numerator and denominator. Hence we get,
$= \dfrac{2\times 2\times 2\times 2}{5\times 5}$
Now again simplifying the numerator and denominator we get,
$= \dfrac{16}{25}$
Now since the numerator and denominator have no common fractions we can say that the fraction is in simplest form.

Note: Now note that when we want to convert a fraction into percentage we must multiply the fraction by 100. Suppose we have a fraction $\dfrac{1}{2}$ then to convert it into percentage we will multiply 100 to the fraction. Hence we get, $\dfrac{1}{2}\times 100=50$ . Hence $\dfrac{1}{2}$ can be written as 50 percent.