Question : The value of $\frac{2}{3}-\frac{5}{6} \times \frac{4}{5} \div \frac{4}{3}+\frac{1}{2}$ is:
Option 1: $\frac{2}{3}$
Option 2: $\frac{2}{5}$
Option 3: $-\frac{11}{60}$
Option 4: $0$
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Correct Answer: $\frac{2}{3}$
Solution :
Given: $\frac{2}{3}-\frac{5}{6} \times \frac{4}{5} \div \frac{4}{3}+\frac{1}{2}$
= $\frac{2}{3}-\frac{5}{6} \times \frac{4}{5} \times \frac{3}{4}+\frac{1}{2}$
= $\frac{2}{3}-\frac{5}{6} \times \frac{3}{5}+\frac{1}{2}$
= $\frac{2}{3}- \frac{1}{2}+\frac{1}{2}$
= $\frac{2}{3}$
Hence, the correct answer is $\frac{2}{3}$.
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