Question

Express the following percent as fractions in the simplest forms: $45\%$

Answer 1

Hint: To express the given percent as fraction we need to know how a fraction is converted to percentage. So, a fraction can be converted into a percent by multiplying the value of fraction with $100$. Now for converting the percent value to a fractional value we need to divide the given percent with $100$. That means we need to reverse the first case.

Complete step-by-step solution:
Now let us consider the fraction we need to obtain as the variable $x$ .
The given percent is expressed as $45\%$ .
As a fraction value can be expressed in the form of percentage when it is multiplied with $100$
The equation obtained will be
$x\times 100=45\%$ where the value of $x$ is fraction.
Now to get the value of $x$ divide the number $100$ on both sides of the equation.
$\dfrac{x\times 100}{100}=\dfrac{45}{100}$
Solve the equation
$ \dfrac{x\times 100}{100}=\dfrac{45}{100} $
$ \Rightarrow x=\dfrac{9}{20} $
This fraction value can not be reduced further. Hence the fractional value which represents the percent $45\%$ is given by $x=\dfrac{9}{20}$

Additional information:
We can consider percent as a special way to represent the fractional values. Fractional values are represented by the way of hundredths. However, it is easy to mention a term as a percentage rather than that of a fraction.

Note: Any fractional value can be represented as a percent when the fraction is multiplied with hundred. That means the value of the numerator of the fraction is multiplied with hundred. Contrarily, to find a fractional value for a given percentage we need to divide the percent with hundred.