Find six rational numbers between 3 and 4.

There can be infinitely many rational numbers between 3 and 4, one way to take them is

3=\(\frac{21}{(6+1)} \), 4=\(\frac{28}{(6+1)} \) .

The rational numbers between 3 and 4 therefore, will become
\(\frac{22}{7} ,\frac{23}{7} ,\frac{24}{7} ,\frac{25}{7} ,\frac{26}{7} ,\frac{27}{7}. \)


Another way to find middle rational number between two number
\(\Rightarrow \) \(\frac{\frac{21}{7} + \frac{28}{7} }{2} \)
= \(\frac{\frac{49}{7} }{2} \)
= \(\frac{7}{2} \).

As,\(\frac{ 21}{7} < \frac{7}{2} < \frac{28}{7} \).


Rational no. between\(\frac{21}{7} \) and \(\frac{7}{2} \) will become

\(\Rightarrow \) \(\frac{\frac{21}{7} + \frac{7}{2} }{2} \)
= \(\frac{\frac{91}{14} }{2} \)
= \(\frac{91}{28} \) .

As,\(\frac{21}{7} < \frac{91}{28} < \frac{7}{2} < \frac{28}{7} \).


Similarly, the other group of rational numbers between 3 and 4 will become

\(\frac{175}{56} , \frac{91}{28} , \frac{7}{2} , \frac{203}{56} , \frac{105}{28} , \frac{217}{56} \) .