Question

Insert two fractions lying between :

$\frac{17}{12},\frac{5}{19}$

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 $\frac{17}{12},\frac{5}{19}$

$\Rightarrow \frac{17+5}{12+19}=\frac{22}{31}$

Second fraction that lie between $\frac{17}{12},\frac{22}{31}$

$\Rightarrow \frac{17+22}{12+31}=\frac{39}{43}$

Hence, the fractions lying between $\frac{17}{12},\frac{5}{19}$ are $\frac{22}{31},\frac{39}{43}$.