Question

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

Answer 1

Compute the required numbers

Let us make the denominators the same, say $20$.

Thus,

$-\frac{2}{5}=-\frac{2\times 4}{5\times 4}=-\frac{8}{20}$

$\frac{1}{2}=\frac{1\times 10}{2\times 10}=\frac{10}{20}$

Ten rational numbers between $-\frac{2}{5}$ and $\frac{1}{2}$ is same as ten rational numbers between $-\frac{8}{20}$ and $\frac{10}{20}$.

We can find rational numbers between the two numbers by replacing the numerator by any integer between the lower and upper bounds (i.e., $-8$ and $10$).

Therefore, ten rational numbers between $-\frac{8}{20}$ and $\frac{10}{20}$ are $\frac{-7}{20}$, $\frac{-6}{20}$, $\frac{-5}{20}$, $\frac{-4}{20}$, $\frac{-3}{20}$, $\frac{1}{20}$, $\frac{3}{20}$, $\frac{5}{20}$, $\frac{7}{20}$ and $\frac{8}{20}$.