Question

Find five rational number between:
$\frac{1}{4}$ and $\frac{1}{2}$

Answer 1

$\frac{1}{4}$ and $\frac{1}{2}$
LCM of $4$ and $2$ is $4$.
$\Rightarrow \frac{1}{4}\times \frac{1}{1}=\frac{1}{4}$ and $\frac{1}{2}\times \frac{2}{2}=\frac{2}{4}$

Since, no integer exist between $1$ and $2$.

Again,

$\frac{1}{4}\times \frac{8}{8}=\frac{8}{32}$ and $\frac{2}{4}\times \frac{8}{8}=\frac{16}{32}$

Here, integers exist between $8$ and $16$ are,

$9,10,11,12,13,14$ and $15$.

Therefor, five rational numbers between

$\frac{1}{4}$ and $\frac{1}{2}$

$\frac{9}{32},\frac{10}{32},\frac{11}{32},\frac{12}{32},\frac{13}{32}.$

Note: There exist infinite many rational numbers between any two rational numbers.