Question

Insert three rational numbers between:

(i) $\frac{2}{5}$ and $\frac{3}{7}$

(ii) $\frac{4}{11}$ and $\frac{9}{16}$

Answer 1

(i) $\frac{2}{5}=\frac{14}{35}=\frac{140}{350}$

$\frac{3}{7}=\frac{15}{35}=\frac{150}{350}$

So, the three rational numbers are $\frac{141}{350}$, $\frac{142}{350}$ and $\frac{143}{350}$.

(ii) L.C.M. of 11 and 16 = 176

$\frac{4}{11}=\frac{64}{176}$

$\frac{9}{16}=\frac{99}{176}$

So, the three rational numbers are $\frac{65}{176}$, $\frac{66}{176}$ and $\frac{67}{176}$.