The value of:
` 3/8 "of " 4/5 div 1 (1)/(5) + (3)/(7) " of" (7)/(12) div (1)/(40) "of" (2)/(5) - 3(2)/(3) div (11)/(30) "of" (2)/(3)`

Options

A. `10 (1)/(4)`
B. `2(1)/(4)`
C. `2 (1)/(2)`
D. `3 (1)/(3)`

Answer

To solve the expression step by step, we will follow the order of operations (BODMAS/BIDMAS rules).

### Given Expression:
\[ \frac{3}{8} \text{ of } \frac{4}{5} \div \frac{1}{5} + \frac{3}{7} \text{ of } \frac{7}{12} \div \left(\frac{1}{40} \text{ of } \frac{2}{5}\right) - \frac{3 \frac{2}{3}}{\frac{11}{30} \text{ of } \frac{2}{3}} \]

### Step 1: Solve each "of" operation
1. **Calculate** \(\frac{3}{8} \text{ of } \frac{4}{5}\):
\[ \frac{3}{8} \times \frac{4}{5} = \frac{3 \times 4}{8 \times 5} = \frac{12}{40} = \frac{3}{10} \]

2. **Calculate** \(\frac{3}{7} \text{ of } \frac{7}{12}\):
\[ \frac{3}{7} \times \frac{7}{12} = \frac{3 \times 7}{7 \times 12} = \frac{3}{12} = \frac{1}{4} \]

3. **Calculate** \(\frac{1}{40} \text{ of } \frac{2}{5}\):
\[ \frac{1}{40} \times \frac{2}{5} = \frac{1 \times 2}{40 \times 5} = \frac{2}{200} = \frac{1}{100} \]

4. **Calculate** \(\frac{11}{30} \text{ of } \frac{2}{3}\):
\[ \frac{11}{30} \times \frac{2}{3} = \frac{11 \times 2}{30 \times 3} = \frac{22}{90} = \frac{11}{45} \]

### Step 2: Substitute back into the expression
Now substituting these values back into the expression:
\[ \frac{3}{10} \div \frac{1}{5} + \frac{1}{4} \div \frac{1}{100} - \frac{3 \frac{2}{3}}{\frac{11}{45}} \]

### Step 3: Perform the divisions
1. **Calculate** \(\frac{3}{10} \div \frac{1}{5}\):
\[ \frac{3}{10} \times 5 = \frac{15}{10} = \frac{3}{2} \]

2. **Calculate** \(\frac{1}{4} \div \frac{1}{100}\):
\[ \frac{1}{4} \times 100 = \frac{100}{4} = 25 \]

3. **Convert** \(3 \frac{2}{3}\) to an improper fraction:
\[ 3 \frac{2}{3} = \frac{11}{3} \]
Now calculate \(\frac{11}{3} \div \frac{11}{45}\):
\[ \frac{11}{3} \times \frac{45}{11} = \frac{45}{3} = 15 \]

### Step 4: Substitute back into the expression
Now substituting these results back into the expression:
\[ \frac{3}{2} + 25 - 15 \]

### Step 5: Perform the addition and subtraction
1. **Calculate** \(\frac{3}{2} + 25\):
\[ 25 = \frac{50}{2} \quad \Rightarrow \quad \frac{3}{2} + \frac{50}{2} = \frac{53}{2} \]

2. **Calculate** \(\frac{53}{2} - 15\):
\[ 15 = \frac{30}{2} \quad \Rightarrow \quad \frac{53}{2} - \frac{30}{2} = \frac{23}{2} \]

### Final Result
The final result is:
\[ \frac{23}{2} \text{ or } 11 \frac{1}{2} \]