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) $\frac{5}{6}$
Solution:
(b) $\frac{-1}{12}$
Number between $\frac{-2}{3}$ and $\frac{1}{2}=\frac{1}{2} \times\left(\frac{-2}{3}+\frac{1}{2}\right)$
$=\frac{1}{2} \times\left(\frac{-2 \times 2}{3 \times 2}+\frac{1 \times 3}{2 \times 3}\right)$
$=\frac{1}{2} \times\left(\frac{-4}{6}+\frac{3}{6}\right)$
$=\frac{1}{2} \times\left(\frac{-4+3}{6}\right)$
$=\frac{-1}{12}$
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