Question

What should be added to $\frac{-7}{8}$ so as to get $\frac{5}{9}?$

Answer 1

$$\begin{gathered} \mathrm{Let}x\mathrm{be}\mathrm{added}\mathrm{to}\frac{-7}{8}\mathrm{so}\mathrm{as}\mathrm{to}\mathrm{get}\frac{5}{9}. \\ \therefore x+\frac{-7}{8}=\frac{5}{9} \\ \Rightarrow x=\frac{5}{9}-\frac{-7}{8} \\ \Rightarrow x=\frac{40}{72}-\frac{-63}{72} \\ \Rightarrow x=\frac{40-(-63)}{72} \\ \Rightarrow x=\frac{40+63}{72}=\frac{103}{72} \end{gathered}$$