Question

How do you write 15% as a fraction?

Answer 1

Hint:
To convert any percentage into fraction, one should divide the number from 100. Also, to bring the number into the fractional form both the number and 100 should be divided from the same number (factor for both the numbers). We can also multiply the number to get the desirable number.

Complete step by step solution:
The fractional form of 15% can be written as, $15\mathrm{\%}={\displaystyle \frac{15}{100}}$.
5 is the factor for both, so we can divide the numerator as well as the denominator with 5.
$$\begin{gathered} 15\mathrm{\%}={\displaystyle \frac{15}{100}} \\ \Rightarrow {\displaystyle \frac{15}{100}}={\displaystyle \frac{\left({\displaystyle \frac{15}{5}}\right)}{\left({\displaystyle \frac{100}{5}}\right)}} \\ \Rightarrow {\displaystyle \frac{15}{100}}=\left({\displaystyle \frac{15}{5}}\right)\times \left({\displaystyle \frac{5}{100}}\right) \\ \Rightarrow 15\mathrm{\%}={\displaystyle \frac{3}{20}} \end{gathered}$$
There is a method for writing the above percentage in the fractional form. We can multiply the factor to get the given number. For 15, we can write it as the multiplication of 5 and 3 and 100 can be written as the product of 5 and 20. So, we can write ${\displaystyle \frac{15}{100}}$ as
${\displaystyle \frac{15}{100}}={\displaystyle \frac{5\times 3}{5\times 20}}$
By solving it, we will get,
${\displaystyle \frac{15}{100}}={\displaystyle \frac{3}{20}}$
Now, the fraction is already in its lowest form and hence cannot be divided further.
So, we can write 15% as a fraction as ${\displaystyle \frac{3}{20}}$.

So, the correct answer is ${\displaystyle \frac{3}{20}}$.

Additional information:
When we divide the number, it should be divided to the factors until we get the lowest form of the fraction or the number cannot be further divided. It would be best to divide the number to the greatest factor.

Note:
In case of solving it by multiplication method try to get the greatest factor or try to factorise it till we get the lowest form of the fraction. We can use only one method to get the fraction, we will get the same answer from both methods.