Question

Choose the rational number which lie between rational numbers $-\frac{2}{5}$ and $-\frac{1}{5}$.

• A. $-\frac{1}{4}$
• B. $-\frac{3}{10}$
• C. $\frac{3}{10}$
• D. $-\frac{7}{20}$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $-\frac{1}{4}$
B $-\frac{3}{10}$
D $-\frac{7}{20}$

Let $p$ be a rational number between $-\frac{2}{5}$ and $-\frac{1}{5}$

$p=\frac{-\frac{2}{5}+(-\frac{1}{5})}{2}=-\frac{3}{10}$

Let $m$ be an another rational number between $-\frac{2}{5}$ and $-\frac{3}{10}$

$m=\frac{-\frac{2}{5}+(-\frac{3}{10})}{2}=-\frac{7}{20}$

Let $q$ be an another rational number between $-\frac{1}{5}$ and $-\frac{3}{10}$

$q=\frac{-\frac{1}{5}+(-\frac{3}{10})}{2}=-\frac{1}{4}$

Hence, required rational numbers between $(-\frac{2}{5})$ and $(-\frac{1}{5})$ are $(-\frac{3}{10}),(-\frac{7}{20}),(-\frac{1}{4})$

For a rational number to lie between $\frac{-2}{5}$ and $\frac{-1}{5}$,it should be less than $\frac{-1}{5}$ and greater than $\frac{-2}{5}$.
Now,$\frac{3}{10}$ is not less than $\frac{-1}{5}$.
So,$\frac{3}{10}$ does not lie between $\frac{-1}{5}$ and $\frac{-2}{5}$.