Question

Find 5 rational number between $\frac{-4}{5}$ and $\frac{-2}{3}$

Answer 1

$5$ rational numbers between $\frac{-4}{5},\frac{-2}{3}$ are as follows:-

$\frac{\frac{-4}{5}+\frac{-2}{3}}{2}=\frac{-12-10}{15}\times \frac{1}{2}=\frac{-22}{15}\times \frac{-11}{15}$

$between$$\frac{-4}{5},\frac{-11}{15}\frac{\frac{-4}{5}+\frac{-11}{15}}{2}=\frac{-12-11}{15}\times \frac{1}{2}=\frac{-33}{30}=\frac{-11}{10}$

between $\frac{-4}{5},\frac{-11}{10}\frac{\frac{-8-11}{10}}{2}=\frac{-19}{10}\times \frac{1}{2}=\frac{-19}{20}$

between $\frac{-11}{10},\frac{-19}{20}\frac{\frac{-11}{10}+\frac{-19}{20}}{2}=\frac{-22-19}{20}\times \frac{1}{2}=\frac{-41}{20}\times \frac{1}{2}=\frac{-41}{40}$

between $\frac{-11}{15},\frac{-11}{10}\frac{\frac{-11}{15}+\frac{-11}{10}}{2}=\frac{-22-33}{30}\times \frac{1}{2}=\frac{-55}{30\times 2}=\frac{-11}{12}$

$\therefore 5$ rational numbers are

$\frac{-11}{15},\frac{-11}{10},\frac{-19}{20},\frac{-41}{40},\frac{-11}{12}$