Question

By what rational number should $\frac{-8}{39}$ be multiplied to obtain $\frac{1}{26}$?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}\mathrm{x}. \\ \mathrm{Now}, \\ \mathrm{x}\times \frac{-8}{39}=\frac{1}{26} \\ \Rightarrow \mathrm{x}=\frac{1}{26}÷\frac{-8}{39} \\ \Rightarrow \mathrm{x}=\frac{1}{26}\times \frac{39}{-8} \\ \Rightarrow \mathrm{x}=\frac{39}{-208} \\ \Rightarrow \mathrm{x}=\frac{39\times -1}{-208\times -1} \\ \Rightarrow \mathrm{x}=\frac{-39}{208} \\ \Rightarrow \mathrm{x}=\frac{-39÷13}{208÷13} \\ \Rightarrow \mathrm{x}=\frac{-3}{16} \end{gathered}$$