Question

Write $5$ rational numbers between $\frac{3}{5}$ and $\frac{6}{5}$.

Answer 1

$\frac{3}{5}=\frac{3\times 6}{5\times 6}=\frac{18}{30}$

$\frac{6}{5}=\frac{6\times 6}{5\times 6}=\frac{36}{30}$

we know that

$18<22<23<26<30<34<36$

$\Rightarrow \frac{18}{30}<\frac{22}{30}<\frac{23}{30}<\frac{26}{30}<\frac{30}{30}<\frac{34}{30}<\frac{36}{30}$

Hence 5 rational numbers between $\frac{3}{5},\frac{6}{5}$ are

$\frac{22}{30},\frac{23}{30},\frac{26}{30},\frac{30}{30},\frac{34}{30}$