Question

Mark the correct alternative in each of the following:

$\frac{5}{4}-\frac{7}{6}-\frac{-2}{3}=$

(a) $\frac{3}{4}$ (b) $-\frac{3}{4}$ (c) $\frac{-7}{12}$ (d) $\frac{7}{12}$

Answer 1

$$\begin{gathered} \frac{5}{4}-\frac{7}{6}-\frac{-2}{3} \\ =\frac{5}{4}+\left(\frac{-7}{6}\right)+\frac{2}{3}\left[-\left(\frac{-2}{3}\right)=\frac{2}{3}\right] \\ =\frac{5\times 3+\left(-7\right)\times 2+2\times 4}{12}\left(\mathrm{LCM}\mathrm{of}3,4\mathrm{and}6=12\right) \\ =\frac{15-14+8}{12} \\ =\frac{9}{12} \end{gathered}$$

$$\begin{gathered} =\frac{9÷3}{12÷3}\left(\mathrm{Dividing}\mathrm{numerator}\mathrm{and}\mathrm{denominator}\mathrm{by}3\right) \\ =\frac{3}{4} \end{gathered}$$

Hence, the correct answer is option (a).