Question

Mark (✓) against the correct answer
What should be subtracted from $\frac{-2}{3}$ to get $\frac{3}{4}?$
(a) $\frac{-11}{12}$
(b) $\frac{-13}{12}$
(c) $\frac{-5}{4}$
(d) $\frac{-17}{12}$

Answer 1

(d) $\frac{-17}{12}$

Let the number be $x$.
Now,

$$\begin{gathered} \frac{-2}{3}-x=\frac{3}{4} \\ \Rightarrow -1\times \left(\frac{2}{3}+x\right)=\frac{3}{4} \\ \Rightarrow \frac{2}{3}+x=\frac{-3}{4} \\ \Rightarrow x=\frac{-3}{4}+\left(\mathrm{Additive}\mathrm{inverse}\mathrm{of}{\displaystyle \frac{2}{3}}\right)\Rightarrow x=\frac{-3}{4}+\left({\displaystyle \frac{-2}{3}}\right)\Rightarrow x=\frac{-3}{4}+\frac{-2}{3}\Rightarrow x=\frac{-3\times 3}{4\times 3}+\frac{-2\times 4}{3\times 4}\Rightarrow x\frac{-9}{12}+\frac{-8}{12}\Rightarrow x=\frac{-17}{12} \end{gathered}$$