Simplify: \(\frac{3}{4} \div \frac{9}{4}of\frac{2}{3}\; - \frac{{\frac{1}{2} - \frac{1}{3}}}{{\frac{1}{2} + \frac{1}{3}}} \times 3\frac{1}{3} + \frac{5}{6}\)
Solution
Correct Answer: Option E
Given expression:
\(\frac{3}{4} \div \frac{9}{4}of\frac{2}{3} - \frac{{\frac{1}{2} - \frac{1}{3}}}{{\frac{1}{2} + \frac{1}{3}}} \times 3\frac{1}{3} + \frac{5}{6}\)
\(\begin{array}{l} = \frac{3}{4} \div \frac{3}{2}\; - \;\frac{{\frac{{3 - 2}}{6}}}{{\frac{{3 + 2}}{6}}} \times \frac{{3 \times 3 + 1}}{3} + \frac{5}{6}\\ = \frac{3}{4} \times \frac{2}{3}\; - \;\frac{{\frac{1}{6}}}{{\frac{5}{6}}} \times \frac{{10}}{3} + \frac{5}{6}\\ = \frac{1}{2}\; - \frac{1}{5} \times \frac{{10}}{3} + \frac{5}{6}\\ = \frac{1}{2}\; - \frac{2}{3} + \frac{5}{6}\\ = \frac{{3 - 4 + 5}}{6}\;\\ = \frac{4}{6} = \frac{2}{3} \end{array}\)
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