Question

Which rational number among the given options lies betwen $\frac{3}{7}$ and $\frac{4}{8}$ ?

• A. $\frac{9}{2}$
• B. $\frac{-11}{8}$
• C. -2
• D. $\frac{13}{28}$

Answer 1

The correct option is D

$\frac{13}{28}$

$\frac{9}{2}$ is greater than both the given rational numbers and hence do not lie between them.
$\frac{-11}{8}$ and -2 are less than both the given rational numbers and hence do not lie between them.
Hence, it can be seen that the only option which lies between the given two rational numbers is 13/28.
Let's now verify whether 13/28 actually lies between the given numbers.

L.C.M of 7 and 8 is 56.
$\frac{3}{7}$ and $\frac{4}{8}$ can be written as $\frac{24}{56}$ and $\frac{28}{56}$.

Now, $\frac{13}{28}$ = $\frac{26}{56}$ lies between $\frac{3}{7}$ and $\frac{4}{8}$.