Question

Write the natural numbers from $102$ to $113$. What fraction of them are prime numbers?

Answer 1

Prime numbers from$102$ to$113$.

The natural numbers are$102,103,104,105,106,107,108109,110,111,112,113$.

The prime numbers are$103,107,109,113$.

There are $4$ prime numbers out of $12$ numbers.

So, the fractions that are prime numbers are as follows:

$\begin{array}{rcl}\frac{\mathrm{number}\mathrm{of}\mathrm{prime}\mathrm{number}}{\mathrm{total}\mathrm{number}\mathrm{from}102\mathrm{to}113}& =& \frac{4}{12}\\ & \Rightarrow & \mathrm{fraction}\mathrm{of}\mathrm{numbers}\mathrm{which}\mathrm{are}\mathrm{prime}=\frac{1}{3}\end{array}$

Hence, the fraction of Prime numbers from $102$ to$113$.is $\frac{1}{3}$.