Question

If $45$ is what percent of $54$ ?

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: $Percentage = \dfrac{{X}}{{Y}} \times 100\% $
Where X = whole , Y = part of whole. Percentage of a number corresponds to the share or share in the whole thing.

Complete step-by-step answer:
In this specific question, we are required to find the percentage that represents the number $45$ out of $54$.
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 aa Percentage = $\dfrac{{X}}{{Y}} \times 100\% $.
Where X = whole , Y = part of whole.
So, the whole corresponds to the number $54$ and the part corresponds to the number $45$ 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{{45}}{{54}} \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{5}{6} \times 100\% $
$ \Rightarrow x\% = \dfrac{{250}}{3}\% $
Now, representing the value in decimal, we get,
$ \Rightarrow x\% = 83.33\% $
So, the value of x is $83.33$. Hence, $45$ is $83.33$ percent of $54$.
This is our required final answer for the given problem.
So, the correct answer is “$83.33$%”.

Note: In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", A percentage is a dimensionless number; it has no unit of measurement. It is dimensionless as it is the ratio of quantities expressed in the same units.