Question

What percent of 84 is 12?

Answer 1

Hint: To obtain what percentage of 84 is 12 we will use percentage definition. Firstly we will divide 12 by 84 as we have to find the percent of 84 is 12. Then we will simplify the fraction obtained by dividing the numerator and denominator by the same number till we get a set of co-prime numbers. Finally we will multiply the obtained fraction with 100 and simplify it and get the desired answer.

Complete step-by-step solution:
To obtain what percent of 84 is 12 we will divide 12 by 84 as follows:
$\dfrac{12}{84}$
Now, as we can see that both numerator and denominator have two common factors i.e. 3 and 4
So, we will simplify the above value by dividing the numerator and denominator by 3 and get,
$\begin{align}
  & \Rightarrow \dfrac{\dfrac{12}{3}}{\dfrac{84}{3}} \\
 & \Rightarrow \dfrac{4}{28} \\
\end{align}$
Again on dividing numerator and denominator by 4 we get,
$\begin{align}
  & \Rightarrow \dfrac{\dfrac{4}{4}}{\dfrac{28}{4}} \\
 & \Rightarrow \dfrac{1}{7} \\
\end{align}$
$\therefore \dfrac{12}{84}=\dfrac{1}{7}$…….$\left( 1 \right)$
Now, we will multiply right side of the equation (1) by 100 and get,
$\begin{align}
  & \Rightarrow \dfrac{1}{7}\times 100 \\
 & \Rightarrow 14.286\% \\
\end{align}$
Hence 12 is $14.286\%$ of 84.

Note: Percentage is used to find the ratio which is expressed as a fraction of 100. It is usually denoted by the sign $''\%''$ and it has no unit of measurement. That is the reason it is a dimensionless number. It means a part per 100. Percentage can never be negative just we can say that there is an increase or decrease in percentage depending on the statement given. We can also use a direct method to find the solution. The formula is:
$P\%$ of Number $=X$…..$\left( 2 \right)$
The Number $=84$
$X=12$
Substituting above value in equation (2) we get,
$\begin{align}
  & P\%\times 84=12 \\
 & \dfrac{P}{100}=\dfrac{12}{84} \\
 & P=\dfrac{12}{84}\times 100 \\
 & P=14.286\% \\
\end{align}$