Find ten rational numbers between


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


L. C.M of the denominator $s(2$ and 5$)$ is 10 .

We can write:

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

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

Since the integers between the numerators $(-4$ and 5$)$ of both the fractions are not sufficient, we will multiply the fractions by 2 .

$\therefore \frac{-4}{10}=\frac{-4 \times 2}{10 \times 2}=\frac{-8}{20}$

$\frac{5}{10}=\frac{5 \times 2}{10 \times 2}=\frac{10}{20}$

There are 17 integers between $-8$ and 10, which are $-7,-6,-5,-4 \ldots \ldots \ldots \ldots \ldots \ldots .8 .$ These can be written as:

$\frac{-7}{20}, \frac{-6}{20}, \frac{-5}{20}, \frac{-4}{20}, \frac{-3}{20}, \ldots \ldots \frac{8}{20}$ and $\frac{9}{20}$

We can take any 10 of these.

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