Question : The value of $\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}+\left(2 \div 2\right.$ of $\left.\frac{1}{2}\right)$ is:
Option 1: $\frac{7}{2}$
Option 2: $3$
Option 3: $5$
Option 4: $\frac{9}{4}$
Correct Answer: $5$
Solution :
Given: $\left(5 \frac{1}{4} \div \frac{3}{7}\right.$ of $\left.\frac{1}{2}\right) \div\left(5 \frac{1}{9}-7 \frac{7}{8} \div 9 \frac{9}{20}\right) \times \frac{11}{21}+\left(2 \div 2\right.$ of $\left.\frac{1}{2}\right)$
= $(\frac{21}{4} \div (\frac{3}{7}\times\frac{1}{2})) \div( \frac{46}{9}-\frac{63}{8} \div \frac{189}{20}) \times \frac{11}{21}+(2 \div (2\times\frac{1}{2}))$
= $(\frac{21}{4} \times \frac{14}{3}) \div( \frac{46}{9}-\frac{63}{8} \times \frac{20}{189}) \times \frac{11}{21}+2$
= $(\frac{21}{4} \times \frac{14}{3}) \div( \frac{46}{9}-\frac{5}{6}) \times \frac{11}{21}+2$
= $\frac{49}{2} \div\frac{77}{18} \times \frac{11}{21}+2$
= $\frac{49}{2} \times\frac{18}{77} \times \frac{11}{21}+2$
= $\frac{49}{2} \times\frac{18}{77} \times \frac{11}{21}+2$
= $3 + 2$
= $5$
Hence, the correct answer is $5$.
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