Question

Insert two rational numbers between:

(i) $\frac{3}{8}$ and $\frac{7}{12}$

(ii) $\frac{1}{3}$ and $\frac{1}{4}$

Answer 1

(i) $\frac{3}{8}$ and $\frac{7}{12}$

LCM of $8$ and $12$ is $24$. Therefore,

$\frac{3}{8}\times \frac{3}{3}=\frac{9}{24}$

$\frac{7}{12}\times \frac{2}{2}=\frac{14}{24}$

So, the required two rational numbers are $\frac{11}{24}$ and $\frac{13}{24}$

(ii) $\frac{1}{3}$ and $\frac{1}{4}$

$48$ is a common multiple of $3$ and $4$.Therefore,

$\frac{1}{3}\times \frac{16}{16}=\frac{16}{48}$

$\frac{1}{4}\times \frac{12}{12}=\frac{12}{48}$

So, the required two rational numbers are $\frac{13}{48}$ and $\frac{15}{48}$