Question : The value of $6 \frac{8}{15}÷\frac{7}{9}$ of $\left(1 \frac{1}{10}+5 \frac{1}{5}\right)+\frac{2}{5}÷7 \frac{1}{5}$ is:
Option 1: $\frac{25}{16}$
Option 2: $\frac{5}{14}$
Option 3: $\frac{25}{18}$
Option 4: $\frac{5}{18}$
Correct Answer: $\frac{25}{18}$
Solution :
$6 \frac{8}{15}÷\frac{7}{9}$ of $\left(1 \frac{1}{10}+5 \frac{1}{5}\right)+\frac{2}{5}÷7 \frac{1}{5}$
= $\frac{98}{15}÷\frac{7}{9}$ of $\left( \frac{11}{10}+ \frac{26}{5}\right)+\frac{2}{5}÷\frac{36}{5}$
= $\frac{98}{15}÷(\frac{7}{9}\times\frac{63}{10})+\frac{2}{5}÷\frac{36}{5}$
= $\frac{98}{15}×\frac{10}{49}+\frac{2}{5}×\frac{5}{36}$
= $\frac{4}{3}+\frac{1}{18}$
= $\frac{25}{18}$
Hence, the correct answer is $\frac{25}{18}$.
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