Question

Find ten rational numbers between $\frac{-2}{5}$and $\frac{1}{2}$.

Answer 1

We know that there exists infinite rational numbers between two rational numbers. But to find any finite number of rational numbers among those infinite set, we have to follow the following procedure:-

Here the rational numbers are $\frac{-2}{5}$ and $\frac{1}{2}$

LCM of $5$ and $2$ is $10$

Therefore,

$\Rightarrow \frac{-2}{5}\times \frac{2}{2}=\frac{-4}{10}$ and

$\Rightarrow \frac{1}{2}\times \frac{5}{5}=\frac{5}{10}$

Now since we have to find $10$ rational numbers we multiply numerator and denominator of $\frac{-4}{10}$ and $\frac{5}{10}$ by $5$ as we cannot find the required number of rational numbers between $\frac{-4}{10}$ and $\frac{5}{10}$

Therefore,

$\Rightarrow \frac{-4}{10}\times \frac{5}{5}=\frac{-20}{50}$ and

$\Rightarrow \frac{5}{10}\times \frac{5}{5}=\frac{25}{50}$

Thus, $\frac{-20}{50},\frac{-19}{50},\frac{-18}{50},\frac{-17}{50},\frac{-16}{50},\frac{-15}{50},\frac{-14}{50},\frac{-13}{50},\frac{-12}{50},\frac{-11}{50},\frac{-10}{50},\frac{25}{50}$ are some of the $10$ rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$.