how can i find rational numbers between 4/6 and5/6

Dear Student,

Since the denominator of both fractions is same we will divide their sum by 2 to get the rational number.

$$\begin{gathered} \frac{{\displaystyle \frac{4}{6}+\frac{5}{6}}}{2} = \frac{{\displaystyle \frac{9}{6}}}{2} \\ = \frac{9}{6}\times \frac{1}{2} \\ = \frac{9}{12} \\ = \frac{3}{4} \\ So, \frac{{\displaystyle 4}}{{\displaystyle 6}}<\frac{{\displaystyle 3}}{{\displaystyle 4}}<\frac{{\displaystyle 5}}{{\displaystyle 6}} \\ To find another rational number , we can divide the sum of \frac{4}{6} and \frac{3}{4} by 2 \\ = \left(\frac{4}{6}+\frac{3}{4}\right) ÷ 2 \\ = \frac{17}{12}\times \frac{1}{2} \\ = \frac{17}{24} \\ In similar way we can find more rational numbers. \\ \mathit{H}\mathit{e}\mathit{n}\mathit{c}\mathit{e}\mathbf{,}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{r}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{a}\mathit{l}\mathbf{ }\mathit{n}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{s}\mathbf{ }\mathit{b}\mathit{e}\mathit{t}\mathit{w}\mathit{e}\mathit{e}\mathit{n}\mathbf{ }\frac{{\displaystyle \mathbf{4}}}{{\displaystyle \mathbf{6}}}\mathit{a}\mathit{n}\mathit{d}\mathbf{ }\frac{{\displaystyle \mathbf{5}}}{{\displaystyle \mathbf{6}}}\mathbf{ }\mathit{i}\mathit{s}\mathbf{ }\frac{\mathbf{3}}{\mathbf{4}}\mathbf{,}\frac{\mathbf{17}}{\mathbf{24}} \end{gathered}$$

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