Simplify the following expression.

$3\frac{1}{5}\text{ of }2\frac{3}{4}÷\frac{11}{3}+(2\frac{1}{5}÷1\frac{2}{5}\text{ of }1\frac{3}{7}-2\frac{1}{3})$

The correct answer is $1\frac{1}{6}$.

To simplify the given numerical expression, we follow the standard order of operations (BODMAS / PEMDAS rule: Brackets, Of, Division, Multiplication, Addition, and Subtraction). Note that the operation 'of' represents multiplication and takes precedence over regular division and multiplication.

The given expression is:

$3\frac{1}{5}\text{ of }2\frac{3}{4}÷\frac{11}{3}+(2\frac{1}{5}÷1\frac{2}{5}\text{ of }1\frac{3}{7}-2\frac{1}{3})$

Step 1: Convert all mixed fractions into improper fractions.
$3\frac{1}{5}=\frac{16}{5}$
$2\frac{3}{4}=\frac{11}{4}$
$2\frac{1}{5}=\frac{11}{5}$
$1\frac{2}{5}=\frac{7}{5}$
$1\frac{3}{7}=\frac{10}{7}$
$2\frac{1}{3}=\frac{7}{3}$

Step 2: Simplify the expression outside the bracket.
First, evaluate the 'of' operation:
$\frac{16}{5}\text{ of }\frac{11}{4}=\frac{16}{5}\times \frac{11}{4}=\frac{44}{5}$
Next, divide this result by $\frac{11}{3}$:
$\frac{44}{5}÷\frac{11}{3}=\frac{44}{5}\times \frac{3}{11}=\frac{12}{5}$

Step 3: Simplify the expression inside the bracket.
The expression inside the bracket is:
$(\frac{11}{5}÷\frac{7}{5}\text{ of }\frac{10}{7}-\frac{7}{3})$
First, evaluate the 'of' operation inside the bracket:
$\frac{7}{5}\text{ of }\frac{10}{7}=\frac{7}{5}\times \frac{10}{7}=2$
Next, perform the division:
$\frac{11}{5}÷2=\frac{11}{10}$
Now perform the subtraction:
$\frac{11}{10}-\frac{7}{3}=\frac{33-70}{30}=-\frac{37}{30}$

Step 4: Combine the results from Step 2 and Step 3.
$\frac{12}{5}+(-\frac{37}{30})=\frac{12}{5}-\frac{37}{30}$
Convert to a common denominator of 30:
$\frac{72-37}{30}=\frac{35}{30}=\frac{7}{6}=1\frac{1}{6}$

Thus, the final simplified answer is $1\frac{1}{6}$.