Choose the rational number which does not lie between
Question:

Choose the rational number which does not lie between $-\frac{2}{3}$ and $-\frac{1}{5}$.

(a) $-\frac{3}{10}$

(b) $\frac{3}{10}$

(c) $-\frac{1}{4}$

(d) $-\frac{7}{20}$

Solution:

We have, $-\frac{2}{3}=-\frac{2 \times 20}{3 \times 20}=-\frac{40}{60}$ and $-\frac{1}{5}=-\frac{1 \times 12}{5 \times 12}=-\frac{12}{60}$

And $,-\frac{3}{10}=-\frac{3 \times 6}{10 \times 6}=-\frac{18}{60}, \frac{3}{10}=\frac{3 \times 6}{10 \times 6}=\frac{18}{60},-\frac{1}{4}=-\frac{1 \times 15}{4 \times 15}=-\frac{15}{60}$, and $-\frac{7}{20}=-\frac{7 \times 3}{20 \times 3}=-\frac{21}{60}$

Since, $-\frac{40}{60}\left(=-\frac{2}{3}\right)<-\frac{21}{60}\left(=-\frac{7}{20}\right)<-\frac{18}{60}\left(=-\frac{3}{10}\right)<-\frac{15}{60}\left(=-\frac{1}{4}\right)<-\frac{12}{60}\left(=-\frac{1}{5}\right)<\frac{18}{60}\left(=\frac{3}{10}\right)$

So, the rational number which does not lie between $-\frac{2}{3}$ and $-\frac{1}{5}$ is $\frac{3}{10}$.

Hence, the correct option is (b).