Evaluate the following expression.

$$\left[ \frac{-4}{7} \div \frac{1}{12} \right] \div \left[ -\frac{4}{5} \times \left( (-2) - \left( -\frac{2}{7} \right) \right) \right]$$​

Correct option is A

Given:

​$$\left[ \frac{-4}{7} \div \frac{1}{12} \right] \div \left[ -\frac{4}{5} \times \left( (-2) - \left( -\frac{2}{7} \right) \right) \right]$$ 

Formula Used:

​$$\begin {array}{|c|c|} \hline \textbf{Operation preference wise} & \textbf{Symbol} \\ \hline Brackets &[],{}, () \\ \hline Orders, of & ² (power), √ (root) , of \\ \hline Division & ÷ \\ \hline Multiplication & × \\ \hline Addition & + \\ \hline Subtraction & - \\ \hline \end{array}$$​​

Solution:

$$\left[ \frac{-4}{7} \div \frac{1}{12} \right] \div \left[ -\frac{4}{5} \times \left( (-2) - \left( -\frac{2}{7} \right) \right) \right]\\ \ \\= \left[ \frac{-4}{7} \times 12 \right] \div \left[ -\frac{4}{5} \times \left( (-2) + \frac{2}{7} \right) \right]\\ \ \\= \left[ \frac{-4 \times 12}{7} \right] \div \left[ -\frac{4}{5} \times \left( -\frac{14}{7} + \frac{2}{7} \right) \right]\\ \ \\= \left[ \frac{-48}{7} \right] \div \left[ -\frac{4}{5} \times \left( -\frac{12}{7} \right) \right]\\ \ \\= \frac{-48}{7} \div \left( \frac{48}{35} \right)\\ \ \\= \frac{-48}{7} \times \frac{35}{48}\\ \ \\= -5$$​