Question

What is the value of \[15\% \,\,{\text{of}}\,\,{\text{108}}\]?

Answer 1

Hint: A percentage is a number or ratio which is expressed as a fraction of\[100\] . And it is often denoted the sign as\[\% \]. A percentage also refers to out of \[100\].
A percentage is a dimensionless number; it has no unit of measurement.
Formula: \[x\% = \dfrac{x}{{100}}\]

Complete step-by-step solution:
From the given problem we need to solve \[15\% \,\,{\text{of}}\,\,{\text{108}}\]
So, \[15\% = \dfrac{{15}}{{100}}\]
Now, \[15\% \,\,{\text{of}}\,\,{\text{108 = }}\dfrac{{15}}{{100}} \times 108\]
On simplifying the above equations we get,
\[15\% \,\,{\text{of}}\,\,{\text{108 = }}\dfrac{{1620}}{{100}}\]
Dividing the expressions above we get,
\[15\% \,\,{\text{of}}\,\,{\text{108 = }}16.2\]
Therefore, \[15\% \,\,{\text{of}}\,\,{\text{108 = }}16.2\].
Alternative method:
Let \[x = 15\].
Now to find the \[x\% \,\,{\text{of}}\,\,{\text{108}}\]
We know that \[x\% = \dfrac{x}{{100}}\]
Therefore, \[x\% \,\,{\text{of}}\,\,{\text{108 = }}\dfrac{x}{{100}} \times 108\]
When substituting \[x = 15\] in the above equation we get,
\[15\% \,\,{\text{of}}\,\,{\text{108 = }}\dfrac{{15}}{{100}} \times 108\]
On simplifying the above equations we get,
\[15\% \,\,{\text{of}}\,\,{\text{108 = }}\dfrac{{1620}}{{100}}\]
Dividing the expressions above we get,
\[15\% \,\,{\text{of}}\,\,{\text{108 = }}16.2\]
Therefore, \[15\% \,\,{\text{of}}\,\,{\text{108}}\,{\text{ = }}\,16.2\].
Extra information:
There are more other examples in which we get the clear idea about it.
More examples: (1) \[15\% \,\,{\text{of}}\,\,{\text{150}}\]
Since, \[15\% = \dfrac{{15}}{{100}}\]
Now, \[15\% \,\,{\text{of}}\,\,{\text{150 = }}\dfrac{{15}}{{100}} \times 1{\text{50}}\]
On simplifying the above equations we get,
\[15\% \,\,{\text{of}}\,\,{\text{150 = }}\dfrac{{2250}}{{100}}\]
Dividing the expressions above we get,
\[15\% \,\,{\text{of}}\,\,{\text{150 = }}22.5\]
Therefore, \[15\% \,\,{\text{of}}\,\,{\text{150 = }}22.5\].
(2) \[16\% \,\,{\text{of}}\,\,{\text{180}}\]
Since, \[16\% = \dfrac{{16}}{{100}}\]
Now, \[16\% \,\,{\text{of}}\,\,{\text{180 = }}\dfrac{{16}}{{100}} \times 18{\text{0}}\]
On simplifying the above equations we get,
\[16\% \,\,{\text{of}}\,\,{\text{180 = }}\dfrac{{2880}}{{100}}\]
Dividing the expressions above we get,
\[16\% \,\,{\text{of}}\,\,{\text{180 = }}28.8\]
Therefore, the required answer, \[16\% \,\,{\text{of}}\,\,{\text{180 = }}28.8\].

Note: In the above simplification, the calculation would be done by cancelling each term by numerator and denominator separately term by term. And also by calculating the number by \[100\], we get the decimal expressions by placing or moving the decimal digits from right to left. And also from the two extra above mentioned examples we clearly observed how to find any percentage of a number with any other number given and thus get a clear idea about it.