The value of \(\frac{3 \frac{2}{5} \div 5 \frac{2}{3} \text { of } \frac{1}{5}-\left(2 \frac{1}{4} \div \frac{2}{3} \text { of } \frac{9}{8}\right)}{(2.0 \overline{6} \div 0 . \overline{76}) \text { of } \frac{3}{5}+0.2}\) is: 

Given:

Expression: \(\frac{3 \frac{2}{5} \div 5 \frac{2}{3} \text { of } \frac{1}{5}-\left(2 \frac{1}{4} \div \frac{2}{3} \text { of } \frac{9}{8}\right)}{(2.0 \overline{6} \div 0 . \overline{76}) \text { of } \frac{3}{5}+0.2}\)

Formula Used:

Order of operations: BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction)

Conversion of mixed fractions to improper fractions: \(a \frac{b}{c} = \frac{ac + b}{c}\)

Calculation:

Numerator:

\(\frac{17}{5} \div (\frac{17}{3} \text{ of } \frac{1}{5}) - (\frac{9}{4} \div (\frac{2}{3} \text{ of } \frac{9}{8}))\)

= \(\frac{17}{5} \div (\frac{17}{3} \times \frac{1}{5}) - (\frac{9}{4} \div (\frac{2}{3} \times \frac{9}{8}))\)

= \(\frac{17}{5} \div \frac{17}{15} - (\frac{9}{4} \div \frac{18}{24})\)

= \(\frac{17}{5} \times \frac{15}{17} - (\frac{9}{4} \div \frac{3}{4})\)

= 3 - \((\frac{9}{4} \times \frac{4}{3})\)

= 3 - 3 = 0

Since numerator = 0, Value of extression = 0

∴ The correct answer is 0.