Question : The value of $\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$ is:
Option 1: $\frac{29}{6}$
Option 2: $\frac{17}{9}$
Option 3: $\frac{14}{3}$
Option 4: $\frac{49}{12}$
Correct Answer: $\frac{29}{6}$
Solution :
$\frac{2}{3} \div \frac{3}{10}$ of $\frac{4}{9}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$
= $\frac{2}{3} \div \frac{4}{30}-\frac{4}{5} \times 1 \frac{1}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$
= $\frac{2}{3} \div \frac{4}{30}-\frac{4}{5} \times \frac{10}{9} \div \frac{8}{15}+\frac{3}{4} \div \frac{1}{2}$
= $5-\frac{4}{5} \times \frac{50}{24} +\frac{3}{2}$
= $5- \frac{10}{6} +\frac{3}{2}$
= $5- \frac{1}{6}$
= $\frac{29}{6}$
Hence, the correct answer is $\frac{29}{6}$.
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