Question

Insert two fractions lying between :

$\frac{5}{12}and3\frac{1}{4}$

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 $\frac{5}{12},3\frac{1}{4}$

$=\frac{5}{12},\frac{13}{4}$

$\Rightarrow \frac{5+13}{12+4}=\frac{18}{16}$

Second fraction that lie between $\frac{5}{12},\frac{18}{16}$

$\Rightarrow \frac{5+18}{12+16}=\frac{23}{28}$

Hence, the fractions lying between $\frac{5}{12},3\frac{1}{4}$ are $\frac{18}{16},\frac{23}{28}$.