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Find ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$.
Given:
Given rational numbers are $\frac{-2}{5}$ and $\frac{1}{2}$.
To do:
We have to find ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$.
Solution:
LCM of 5 and 2 is 10.
$\frac{-2}{5}=\frac{-2\times2}{5\times2}$
$=\frac{-4}{10}$
$\frac{1}{2}=\frac{1\times5}{2\times5}$
$=\frac{5}{10}$
As we need 10 rational numbers between $\frac{-4}{10}$ and $\frac{5}{10}$, multiply both the fractions by $\frac{2}{2}$.
This implies,
$\frac{-4}{10}=\frac{-4}{10}\times\frac{2}{2}$
$=\frac{-8}{20}$
$\frac{5}{10}=\frac{5}{10}\times\frac{2}{2}$
$=\frac{10}{20}$
Therefore,
Ten rational numbers between $\frac{-2}{5}$ and $\frac{1}{2}$ are $\frac{-7}{20}, \frac{-6}{20}, ........,\frac{1}{20}, \frac{2}{20}$.
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