Question 70

Simplify the following expression:
$$\left(\frac{3}{4}-\frac{1}{4}\div\frac{1}{4}  \text{of}  \frac{2}{5}\right)\div\left(\frac{3}{4}\div\frac{2}{3}  \text{of}  \frac{3}{5}\right)$$

Solution

$$\left(\frac{3}{4}-\frac{1}{4}\div\frac{1}{4}  \text{of}  \frac{2}{5}\right)\div\left(\frac{3}{4}\div\frac{2}{3}  \text{of}  \frac{3}{5}\right)$$

= $$\left(\frac{3}{4}-\frac{1}{4}\div\frac{2}{20}\right)\div\left(\frac{3}{4}\div\frac{6}{15}\right)$$

= $$\left(\frac{3}{4}-\frac{1}{4}\times\frac{20}{2}\right)\div\left(\frac{3}{4}\times\frac{15}{6}\right)$$

= $$\left(\frac{3}{4}-\frac{5}{2}\right)\div\left(\frac{15}{8}\right)$$

= $$\left(\frac{3-10}{4}\right)\div\left(\frac{15}{8}\right)$$

= $$\left(\frac{-7}{4}\right)\div\left(\frac{15}{8}\right)$$

= $$\left(\frac{-7}{4}\right)\times\left(\frac{8}{15}\right)$$

= $$-\frac{14}{15}$$

Hence, the correct answer is Option D


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