Question

Insert two fractions lying between :

$\frac{9}{7},1\frac{2}{3}$

Answer 1

If $\frac{a}{b},\frac{c}{d}$ are two fractions, then $\frac{a+c}{b+d}$ lies between these two fractions.

First fraction that lie between $\frac{9}{7},1\frac{2}{3}$

$$\begin{gathered} =\frac{9}{7},\frac{5}{3} \\ \Rightarrow \frac{9+5}{7+3}=\frac{14}{10} \end{gathered}$$

Second fraction that lie between $\frac{9}{7},\frac{14}{10}$

$\Rightarrow \frac{9+14}{7+10}=\frac{23}{17}$

Hence, the fractions lying between $\frac{9}{7},1\frac{2}{3}$ are $\frac{14}{10},\frac{23}{17}$.