Question

Find four rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$

Answer 1

Since, We want five rational numbers, we write $\frac{3}{5}$ and $\frac{4}{5}$ .

So multiply in numerator and denominator by $5+1=6$ and we get,

$\frac{3\times 6}{5\times 6}=\frac{18}{30}$ and $\frac{4}{5}=\frac{4\times 6}{5\times 6}=\frac{24}{30}$

We know that, $19<20<21<22<23$

$\Rightarrow \frac{18}{30}<\frac{19}{30}<\frac{20}{30}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{24}{30}$

Hence, $5$ rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ are:

$\Rightarrow \frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30},\frac{23}{30}$ ans.