Find two rational numbers lying between

Required number $=\frac{1}{2} \times\left(\frac{-1}{3}+\frac{1}{2}\right)$

$=\frac{1}{2} \times\left(\frac{-2+3}{6}\right)$

$=\frac{1}{2} \times \frac{1}{6}$

$=\frac{1}{12}$

$\frac{-1}{3}<\frac{1}{12}<\frac{1}{2}$

Rational number between $\frac{-1}{3}$ and $\frac{1}{12}$ :

$\frac{1}{2} \times\left(\frac{-1}{3}+\frac{1}{12}\right)$

$=\frac{1}{2} \times\left(\frac{1-4}{12}\right)$

$=\frac{1}{2} \times \frac{-3}{12}$

$=\frac{-3}{24}=\frac{-3 \div 3}{24 \div 3}$

$=\frac{-1}{8}$

Thus, $\frac{1}{12}$ and $\frac{-1}{8}$ are the two rational numbers between $\frac{-1}{3}$ and $\frac{1}{2}$.