Question

What percent is $9$ out of $20$?

Answer 1

Hint: In the given question, we are required to calculate the percentage of a given number that corresponds to another number. We must remember the formula for finding a specific percentage of a number as: $\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $. If the part of the number is bigger than the whole quantity, then the percentage tends to be greater than hundred percent.

Complete step by step answer:
In this specific question, we are required to find the percentage that represents the number $9$ out of $20$. Let us assume the required percentage to be x percent. So, we have to find the value of $x$ to get to the required answer. We will use the formula for finding the percentage of a number in the problem as,
$\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $.
So, the whole corresponds to the number $20$ and the part corresponds to the number $9$ in this case. Also, the percentage is assumed to be x. So, we substitute these known values in the above mentioned formula. So, we get,
$ \Rightarrow x\% = \dfrac{9}{{20}} \times 100\% $

Now, we have to find the value of x in the above equation. We use the method of transposition to shift the terms in the equation and find the value of the variable. Simplifying the calculations and cancelling common factors in numerator and denominator, we get,
$ \Rightarrow x\% = \dfrac{9}{1} \times 5\% $
Carrying out the multiplication, we get,
$ \Rightarrow x\% = 45\% $
So, the value of $x$ is $45$.

Hence, $9$ is $45$ percent of $20$.

Note: The whole quantity in percentage always represents the entire hundred percent. If the partial number is greater than the whole quantity, the corresponding percentage will be greater than $100\% $. The percentage formula $\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $ can be used to find any parameter in the equation given the other parameters using the method of transposition.