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