Question

By what rational number should we multiply $\frac{-15}{56}$ to get $\frac{-5}{7}$?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}\mathrm{x}. \\ \mathrm{Now}, \\ \mathrm{x}\times \frac{-15}{56}=\frac{-5}{7} \\ \Rightarrow \mathrm{x}=\frac{-5}{7}÷\frac{-15}{56} \\ \Rightarrow \mathrm{x}=\frac{-5}{7}\times \frac{56}{-15} \\ \Rightarrow \mathrm{x}=\frac{280}{105} \\ \Rightarrow \mathrm{x}=\frac{280÷5}{105÷5} \\ \Rightarrow \mathrm{x}=\frac{56}{21} \\ \Rightarrow \mathrm{x}=\frac{56÷7}{21÷7} \\ \Rightarrow \mathrm{x}=\frac{8}{3} \end{gathered}$$