Question

Find five rational numbers between $\frac{2}{5}$ and $\frac{3}{5}$

Answer 1

Since, We want five rational numbers, we write $\frac{2}{5}$ and $\frac{3}{5}$ .

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

$\frac{2\times 6}{5\times 6}=\frac{12}{30}$ and $\frac{3}{5}=\frac{3\times 6}{5\times 6}=\frac{18}{30}$

We know that, $13<14<15<16<17$

$\Rightarrow \frac{12}{30}<\frac{13}{30}<\frac{14}{30}<\frac{15}{30}<\frac{16}{30}<\frac{17}{30}<\frac{18}{30}$

Hence, $5$ rational numbers between $\frac{2}{5}$ and $\frac{3}{5}$ are:

$\Rightarrow \frac{13}{30},\frac{14}{30},\frac{15}{30},\frac{16}{30},\frac{17}{30}$ ans.