Question

What should be subtracted from $\left(\frac{3}{4}-\frac{2}{3}\right)$ to get $\frac{-1}{6}?$

Answer 1

$$\begin{gathered} \mathrm{Let}x\mathrm{be}\mathrm{subtracted}. \\ \therefore (\frac{3}{4}-\frac{2}{3})-x=\frac{-1}{6} \\ \Rightarrow (\frac{9}{12}-\frac{8}{12})-x=\frac{-1}{6} \\ \Rightarrow \left(\frac{9-8}{12}\right)-x=\frac{-1}{6} \\ \Rightarrow x=\frac{1}{12}-\frac{-1}{6} \\ \Rightarrow x=\frac{1}{12}-\frac{-2}{12} \\ \Rightarrow x=\frac{1-(-2)}{12} \\ \Rightarrow x=\frac{1+2}{12} \\ \Rightarrow x=\frac{3}{12} \\ \Rightarrow x=\frac{1}{4} \end{gathered}$$