Question

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

Answer 1

LCM of $5,3=15$

$\Rightarrow \frac{3}{5}=\frac{3\times 3}{5\times 3}=\frac{9}{15}$

And

$\frac{2}{3}=\frac{2\times 5}{3\times 5}=\frac{10}{15}$

Multiplying numerator and denominator by $6$ we get

$\Rightarrow \frac{9\times 6}{15\times 6}=\frac{54}{90}$

$\Rightarrow \frac{10\times 6}{15\times 6}=\frac{60}{90}$

Hence the five rational numbers between $\frac{54}{90}$ and $\frac{60}{90}$ are:

$\frac{55}{90},\frac{56}{90},\frac{57}{90},\frac{58}{90},\frac{59}{90}$.