Question

What is $45\dfrac{1}{2}\%$ as a fraction?

Answer 1

Hint: To convert a percent into percent, we need to first understand the meaning of the term ‘percent’. Percent means to calculate a quantity per one hundred parts. Now, to convert it into its fractional form, we will first convert the percentage into its decimal form and then convert it into the simplest fractional form.

Complete step by step solution:
Our first step of the solution will be to convert the whole number percentage to improper percentage form. This can be done as follows:
$\begin{align}
  & \Rightarrow 45\dfrac{1}{2}\%=\dfrac{2\times 45+1}{2}\% \\
 & \Rightarrow 45\dfrac{1}{2}\%=\dfrac{91}{2}\% \\
\end{align}$
Now that we have the percentage in the form of an improper fraction, we will convert it into its decimal form by dividing the numerator by the denominator in the above equation. This can be done as follows:
$\Rightarrow \dfrac{91}{2}\%=45.5\%$
Let us say this new simplified percentage is ‘x’, such that:
$\Rightarrow x=45.5\%$
Let us name the above equation as$(1)$, so we have:
$\Rightarrow x=45.5\%$ ......... (1)

Now, we need to find the simplest fractional value of percentage of ‘x’. We know that any percentage can be converted into its fractional quantity by dividing it with one hundred. So, we proceed in our solution in the following manner:
Let the fractional value of ‘x’ be given by ‘y’. Then, we can write that:
$\Rightarrow y=\dfrac{\%x}{100}$
Putting the value of ‘x’ from equation number (1) in the above equation, we get:
$\begin{align}
  & \Rightarrow y=\dfrac{45.5}{100} \\
 & \Rightarrow y=\dfrac{455}{1000} \\
 & \therefore y=\dfrac{91}{200} \\
\end{align}$
Thus, we get the final result in simplest fractional form as $\dfrac{91}{200}$.
Hence, $45\dfrac{1}{2}\%$ as a fraction comes out to be $\dfrac{91}{200}$.

Note: Whenever, we calculate the percentage of any quantity, that is, of a fraction or a decimal, it is always a non-negative term. Another interesting property of percentage is that the terms in it can be reversed, that is, x% of y is equal to y% of x. For example: 5% of 100 is equal to 5 and 100% of 5 is also equal to 5. It can be used to get faster solutions to problems with percentage calculation in it.