Question

Find two rational numbers lying between $\frac{-1}{3}\mathrm{and}\frac{1}{2}.$

Answer 1

$$\begin{gathered} \mathrm{Required}\mathrm{number}=\frac{1}{2}\times \left(\frac{-1}{3}+\frac{1}{2}\right) \\ =\frac{1}{2}\times \left(\frac{-2+3}{6}\right) \\ =\frac{1}{2}\times \frac{1}{6} \\ =\frac{1}{12} \\ \frac{-1}{3}<\frac{1}{12}<\frac{1}{2} \\ \mathrm{Rational}\mathrm{number}\mathrm{between}\frac{-1}{3}\mathrm{and}\frac{1}{12}: \\ \frac{1}{2}\times \left(\frac{-1}{3}+\frac{1}{12}\right) \\ =\frac{1}{2}\times \left(\frac{1-4}{12}\right) \\ =\frac{1}{2}\times \frac{-3}{12} \\ =\frac{-3}{24}=\frac{-3÷3}{24÷3} \\ =\frac{-1}{8} \\ \mathrm{Thus},\frac{1}{12}\mathrm{and}\frac{-1}{8}\mathrm{are}\mathrm{the}\mathrm{two}\mathrm{rational}\mathrm{numbers}\mathrm{between}\frac{-1}{3}\mathrm{and}\frac{1}{2}. \end{gathered}$$