Question

Find the value of $50\% $ of $164$.

Answer 1

Hint: In the given question, we are required to calculate the percentage of a given number. We must remember the formula for finding a specific percentage of a number as: $Percentage = \dfrac{{Part}}{{Whole}} \times 100\% $. Percentage of a number corresponds to the share or share in the whole thing.

Complete step-by-step solution:
In this specific question, we are required to find $50\% $ of the number given to us, $164$.
So, we find the number that corresponds to $50\% $ of $164$ by using the formula for percentage as $Percentage = \dfrac{{Part}}{{Whole}} \times 100\% $.
Let us assume $50\% $ of $164$ to be equal to x.
So, the whole corresponds to the number $164$ and the part corresponds to the number x in this case. Also, the percentage is given to us as $50\% $. So, we substitute these known values in the above mentioned formula. So, we get,
$ \Rightarrow 50\% = \dfrac{x}{{164}} \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. So, we multiply both sides of the equation by $164$.
$ \Rightarrow 164 \times 50 = 100x$
Simplifying the calculations, we get,
$ \Rightarrow 100x = 8200$
Now, dividing both sides of equation by $100$, we get,
$ \Rightarrow x = \dfrac{{8200}}{{100}}$
Simplifying the calculations by cancelling common factors in numerator and denominator, we get,
$ \Rightarrow x = 82$
So, $50\% $ of $164$ is $82$.
This is our required final answer for the given problem.

Note: There are various methods to find an answer to the given question, but the method described above is the simplest one. We must remember the formula for calculating the percentage of numbers to solve such questions. Care must be taken while doing calculations and cancelling factors in numerator and denominator.