Question

How do you write \[120\% \] as a fraction?

Answer 1

Hint:
Think whenever we convert from any form to percentage we will multiply with $100$ so now it is in reverse form, we need to convert from percentage to fraction so first divide the given number by $100$ which represents the fraction form, now simplify the expression to get the proper fraction.

Complete step by step solution:
Usually whenever we convert one form of a number to percentage form we will multiply the number with $100$ , now we are doing the reverse process that is we need to convert percentage to fraction form, so now divide the given number that is \[120\% \] by $100$ .
Therefore, we get
$120\% = \dfrac{{120}}{{100}}$
On dividing by $100$ we got the fraction form as in the above expression.
When we look at the above expression we have zero common in both the numerator and the denominator which we can cancel each other in order to make simplification easier. Hence, we get
$120\% = \dfrac{{12}}{{10}}$
Now to make it even simpler we need to find the common factor which divides both the numerator value that is $12$ and the denominator value that is $10$.
The number $2$ is the common factor, which divides both the numerator and the denominator, so we get
$120\% = \dfrac{6}{5}$
Therefore the required fraction form of \[120\% \] is $\dfrac{6}{5}$.
As we can see that the numerator value is greater than the denominator value which is an improper fraction. So to make it a proper fraction we need to represent in terms of mixed fraction.
Therefore, $\dfrac{6}{5}$ can be written as
$\dfrac{6}{5} = \left( {\dfrac{{1 \times 5 + 1}}{5}} \right)$
$ \Rightarrow \dfrac{6}{5} = 1 + \dfrac{1}{5} = 1\dfrac{1}{5}$ Which is a mixed fraction of given \[120\% \].

Note:
Here they have just asked us to convert the given percentage form to fraction form, so we can stop when we get $\dfrac{6}{5}$ as the fraction. If they have asked to represent in terms of mixed fraction they can follow the steps to convert. If they didn’t ask for a proper fraction then no need to do that.