Question

Which of the following is a rational number between $\frac{1}{6}$ and $\frac{1}{4}$

• A. $0$
• B. $\frac{5}{24}$
• C. $\frac{24}{5}$
• D. $\frac{25}{5}$

Answer 1

The correct option is B $\frac{5}{24}$

To find the rational number between $\frac{1}{6}$ and $\frac{1}{4}$,
let's find their mean as the mean of two given numbers always lies in between them.

$(\frac{1}{6}+\frac{1}{4})÷2$

$=\left(\frac{2+3}{12}\right)÷2$

$=\frac{5}{12}\times \frac{1}{2}$

$=\frac{5}{24}$
which lies between $\frac{1}{6}$ and $\frac{1}{4}$.

Both the given numbers are positive, so 0 cannot lie between them.

$\frac{24}{5}$ and $\frac{25}{5}$ have values much greater than $\frac{1}{6}$ and $\frac{1}{4}$.
So, these numbers also cannot lie between $\frac{1}{6}$ and $\frac{1}{4}$.

Therefore, out of the given options,
$\frac{5}{24}$ lies between $\frac{1}{6}$ and $\frac{1}{4}$.