Question

Find ten rational numbers between $-\frac{2}{5}$ and $\frac{1}{7}$

Answer 1

Find the rational numbers

A number that can be expressed as $\raisebox{1ex}{$p$}\!\left/ \!\raisebox{-1ex}{$q$}\right.$, where $q$ is not equal to zero is called a rational number.

Given numbers are $-\frac{2}{5}$ and $\frac{1}{7}$.

LCM of denominators is $5\times 7=35$

We convert the given fractions into like fractions.

So $-\frac{2}{5}=-\frac{14}{35}$

and, $\frac{1}{7}=\frac{5}{35}$

The rational numbers between $-\frac{14}{35}$ and $\frac{5}{35}$ are $-\frac{13}{35},-\frac{12}{35},-\frac{11}{35},-\frac{10}{35},-\frac{9}{35},-\frac{8}{35},-\frac{7}{35},-\frac{6}{35},-\frac{5}{35},-\frac{4}{35}$

Hence, the rational numbers between $-\frac{14}{35}$ and $\frac{5}{35}$ are $-\frac{13}{35},-\frac{12}{35},-\frac{11}{35},-\frac{10}{35},-\frac{9}{35},-\frac{8}{35},-\frac{7}{35},-\frac{6}{35},-\frac{5}{35},-\frac{4}{35}$