Question

Find 10 rational numbers between $\frac{-3}{4}\mathrm{and}\frac{5}{6}.$

Answer 1

$$\begin{gathered} \mathrm{LCM}\mathrm{of}4\mathrm{and}6\mathrm{is}12. \\ \mathrm{Now}, \\ \frac{-3}{4}=\frac{-3\times 3}{4\times 3}=\frac{-9}{12} \\ \mathrm{And}, \\ \frac{5}{6}=\frac{5\times 2}{6\times 2}=\frac{10}{12} \\ \mathrm{Rational}\mathrm{numbers}\mathrm{lying}\mathrm{between}\frac{-3}{4}\mathrm{and}\frac{5}{6}: \\ \frac{-8}{12},\frac{-7}{12},\frac{-6}{12},\frac{-5}{12},\frac{-4}{12},...\frac{1}{12},\frac{2}{12},\frac{3}{12},\frac{4}{12},\frac{5}{12},\frac{6}{12},\frac{7}{12},\frac{8}{12},\frac{9}{12} \end{gathered}$$

We can take any 10 out of these.