Question

find. three rational number between 1/4 and 1/2 using the average method ?

Answer 1

$$\begin{gathered} 3\mathrm{rational}\mathrm{numbers}\mathrm{between}\frac{1}{4}\mathrm{and}\frac{1}{2}\mathrm{is}: \\ \frac{\frac{1}{4}+\frac{1}{2}}{2}=\frac{1}{2}\left(\frac{1}{4}+\frac{1}{2}\right)=\frac{1}{2}\left(\frac{1+2}{4}\right)=\frac{1}{2}\times \frac{3}{4}=\frac{3}{8} \\ \frac{{\displaystyle \frac{1}{4}}+{\displaystyle \frac{3}{8}}}{2}=\frac{1}{2}\left(\frac{1}{4}+\frac{3}{8}\right)=\frac{1}{2}\left(\frac{2+3}{8}\right)=\frac{1}{2}\times \frac{5}{8}=\frac{5}{16} \\ \frac{{\displaystyle \frac{1}{2}}+{\displaystyle \frac{5}{16}}}{2}=\frac{1}{2}\left(\frac{1}{2}+\frac{5}{16}\right)=\frac{1}{2}\left(\frac{8+5}{16}\right)=\frac{1}{2}\times \frac{13}{16}=\frac{13}{32} \\ \mathrm{So}3\mathrm{required}\mathrm{numbers}\mathrm{are}\frac{3}{8},\frac{5}{16},\frac{13}{32} \end{gathered}$$