Question

A rational number between $\frac{-2}{3}$ and $\frac{1}{2}$ is
(a) $\frac{-1}{6}$
(b) $\frac{-1}{12}$
(c) $\frac{-5}{6}$
(d) $\frac{5}{6}$

Answer 1

(b) $\frac{-1}{12}$

$$\begin{gathered} \mathrm{Number}\mathrm{between}\frac{-2}{3}\mathrm{and}\frac{1}{2}=\frac{1}{2}\times \left(\frac{-2}{3}+\frac{1}{2}\right) \\ =\frac{1}{2}\times \left(\frac{-2\times 2}{3\times 2}+\frac{1\times 3}{2\times 3}\right) \\ =\frac{1}{2}\times \left(\frac{-4}{6}+\frac{3}{6}\right) \\ =\frac{1}{2}\times \left(\frac{-4+3}{6}\right) \\ =\frac{-1}{12} \end{gathered}$$