Maharashtra BoardEnglish MediumSTD 8MathsRational Numbers3 Marks
Question
Find two rational numbers lying between $\frac{-1}{3}$ and $\frac{1}{2}$.
✓
Answer
Required number $=\frac{1}{2}\times\Big(\frac{-1}{3}+\frac{1}{2}\Big)$
$=\frac{1}{2}\times\Big(\frac{-2+3}{6}\Big)$
$=\frac{1}{2}\times\frac{1}{6}$
$=\frac{1}{12}$
$\frac{-1}{3}<\frac{1}{12}<\frac{1}{2}$
Required number between $\frac{-1}{3}$ and $\frac{1}{2}$:
$=\frac{1}{2}\times\Big(\frac{-1}{3}+\frac{1}{12}\Big)$
$=\frac{1}{2}\times\Big(\frac{1-4}{12}\Big)$
$=\frac{1}{2}\times\Big(\frac{-3}{12}\Big)$
$=\frac{-3}{24}$
$=\frac{-3\div3}{24\div3}$
$=\frac{-1}{8}$
Thus, $\frac{1}{12}$ and $\frac{-1}{8}$ are two rational numbers between $\frac{-1}{3}$ and $\frac{1}{2}$.
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