Find five rational numbers between \(\frac{3}{5} \) and \(\frac{4}{5} \).

There can be infinitely many rational numbers between \(\frac{3}{5} \) and \(\frac{4}{5} \) , one way to take them is

\(\frac{3}{5} = \frac{3×10}{5×10} = \frac{30}{50} \)
\(\frac{4}{5} = \frac{4×10}{5×10} = \frac{40}{50} \)

Therefore the rational number between \(\frac{30}{50} \) and \(\frac{40}{50} \) are

\(\frac{31}{50} ,\frac{32}{50} \frac{33}{50} ,\frac{34}{50} , \frac{35}{50} \)

Another way to find middle rational number between two number \(\frac{3}{5} \) and \(\frac{4}{5} \)is

\(\Rightarrow \) \(\frac{\frac{3}{5} + \frac{4}{5} }{2} \)
= \( \frac{\frac{7}{5} }{2} \)
= \(\frac{7}{10} \) .

As, \( \frac{3}{5} < \frac{7}{10} < \frac{4}{5} \) .

Now,a rational number between \(\frac{3}{5} \) and \(\frac{7}{10} \) is

\(\Rightarrow \)\(\frac{\frac{3}{5} + \frac{7}{10} }{2} \)
=\( \frac{\frac{13}{10} }{2} \)
= \(\frac{13}{20} \).

As, \(\frac{3}{5} < \frac{13}{20} < \frac{7}{10} < \frac{4}{5} \).

Similarly, \(\frac{25}{40} , \frac{27}{40} , \frac{15}{20} \) are rational numbers between \(\frac{3}{5} \) and \(\frac{4}{5} \).

Therefore, five rationals between numbers\(\frac{3}{5} \) and \(\frac{4}{5} \)are

\( \frac{25}{40} , \frac{13}{20} , \frac{27}{40} , \frac{7}{10} , \frac{15}{20} \).