Question

Find any ten rational numbers between $-\frac{5}{6}$ and $\frac{5}{8}$.

Answer 1

Make denominators of both the fractions same:

Multiply first fraction by $\frac{4}{4}$.

$$\begin{gathered} \Rightarrow -\frac{5}{6}=-\frac{5}{6}\times \frac{4}{4} \\ =-\frac{20}{24} \end{gathered}$$

Multiply second fraction by $\frac{3}{3}$.

$$\begin{gathered} \Rightarrow \frac{5}{8}=\frac{5}{8}\times \frac{3}{3} \\ =\frac{15}{24} \end{gathered}$$

So,ten rational numbers are $-\frac{19}{24},-\frac{18}{24},-\frac{17}{24},-\frac{16}{24},-\frac{15}{24},-\frac{14}{24},-\frac{13}{24},-\frac{12}{24},-\frac{11}{24},-\frac{10}{24}$

Hence, ten rational numbers are $-\frac{19}{24},-\frac{18}{24},-\frac{17}{24},-\frac{16}{24},-\frac{15}{24},-\frac{14}{24},-\frac{13}{24},-\frac{12}{24},-\frac{11}{24},-\frac{10}{24}$.