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

Answer 1

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

(a)$-\frac{3}{10}=\frac{-18}{60}$

(b)$\frac{3}{10}=\frac{18}{60}$

(c)$-\frac{1}{4}=\frac{-15}{60}$

(d)$-\frac{7}{20}=\frac{-21}{60}$

$\frac{3}{10}=\frac{18}{60}>$ both the limits and it is a positive number as well.

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).