Question : What is the value of $\frac{5}{11}$ of $\frac{3}{7}+\frac{7}{11} \times \frac{55}{21}-\frac{8}{22} \div \frac{16}{33}$?
Option 1: $\frac{1088}{927}$
Option 2: $\frac{1027}{924}$
Option 3: $\frac{1811}{956}$
Option 4: $\frac{1029}{945}$
Correct Answer: $\frac{1027}{924}$
Solution :
$\frac{5}{11}$ of $\frac{3}{7}+\frac{7}{11} \times \frac{55}{21}-\frac{8}{22} \div \frac{16}{33}$
$=(\frac{5}{11}\times\frac{3}{7})+\frac{7}{11} \times \frac{55}{21}-\frac{8}{22} \div \frac{16}{33}$
$=\frac{15}{77}+\frac{7}{11} \times \frac{55}{21}-\frac{8}{22} \times \frac{33}{16}$
$=\frac{15}{77}+\frac{5}{3}-\frac{3}{4}$
$=\frac{180+1540-693}{924}$
$=\frac{1720-693}{924}$
$=\frac{1027}{924}$
Hence, the correct answer is $\frac{1027}{924}$.
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