Question 74

What is the value of
$$\frac{3}{4}  of  \left(\frac{1}{3} \div \frac{1}{2}\right) + \left(2 - \frac{2}{5}\right) \times \frac{3}{2} + \frac{2}{3}$$?

Solution

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

$$\frac{3}{4}\times(\frac{1}{3}\times\frac{2}{1}) + (\frac{10 - 2}{5})\times\frac{3}{2} + \frac{2}{3}$$

$$\frac{3}{4}\times\frac{2}{3} + \frac{8}{5}\times\frac{3}{2} + \frac{2}{3}$$

$$\frac{6}{12} + \frac{24}{10} + \frac{2}{3}$$

$$\frac{30 + 144 + 40}{60}$$

$$\frac{214}{60}$$ = $$\frac{107}{30}$$

Therefore option A is the answer.


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