The value of `500 -: 3/8 " of " 2/3 -: [ 5/3 " of "300 + 7 1/2 -: 5 1/2 xx 1100]` is

Options

A. 5
B. 10
C. 4
D. 1

Answer

To solve the expression \( 500 \div \frac{3}{8} \text{ of } \frac{2}{3} \div \left[ \frac{5}{3} \text{ of } 300 + \frac{7}{2} \div \frac{5}{2} \times 1100 \right] \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate the expression inside the brackets**:
\[ \frac{5}{3} \text{ of } 300 + \frac{7}{2} \div \frac{5}{2} \times 1100 \]

- First, calculate \( \frac{5}{3} \text{ of } 300 \):
\[ \frac{5}{3} \times 300 = \frac{1500}{3} = 500 \]

- Next, calculate \( \frac{7}{2} \div \frac{5}{2} \):
\[ \frac{7}{2} \div \frac{5}{2} = \frac{7}{2} \times \frac{2}{5} = \frac{7}{5} \]

- Now, multiply \( \frac{7}{5} \) by 1100:
\[ \frac{7}{5} \times 1100 = \frac{7700}{5} = 1540 \]

- Combine the results:
\[ 500 + 1540 = 2040 \]

2. **Substituting back into the main expression**:
\[ 500 \div \frac{3}{8} \text{ of } \frac{2}{3} \div 2040 \]

3. **Calculate \( \frac{3}{8} \text{ of } \frac{2}{3} \)**:
\[ \frac{3}{8} \times \frac{2}{3} = \frac{6}{24} = \frac{1}{4} \]

4. **Now substitute this back into the expression**:
\[ 500 \div \frac{1}{4} \div 2040 \]

5. **Calculate \( 500 \div \frac{1}{4} \)**:
\[ 500 \div \frac{1}{4} = 500 \times 4 = 2000 \]

6. **Finally, calculate \( 2000 \div 2040 \)**:
\[ 2000 \div 2040 = \frac{2000}{2040} = \frac{200}{204} = \frac{100}{102} = \frac{50}{51} \]

### Final Answer:
The value of the expression is \( \frac{50}{51} \).