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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

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