The value of `13/2 [ 15 -: 3/5 " of " 1/2 + 76 + 1 1/2 xx 4 1/2 -: 3 1/4]` is :

Options

A. 832.5
B. 732.5
C. 832
D. 830.5

Answer

To solve the expression \( \frac{13}{2} \left[ \frac{15}{\frac{3}{5}} \text{ of } \frac{1}{2} + 76 + \frac{3}{2} \times \frac{9}{2} - \frac{3}{4} \right] \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Calculate \( \frac{15}{\frac{3}{5}} \)**:
\[ \frac{15}{\frac{3}{5}} = 15 \times \frac{5}{3} = \frac{75}{3} = 25 \]

**Hint**: To divide by a fraction, multiply by its reciprocal.

2. **Calculate \( 25 \text{ of } \frac{1}{2} \)**:
\[ 25 \text{ of } \frac{1}{2} = 25 \times \frac{1}{2} = \frac{25}{2} = 12.5 \]

**Hint**: "Of" in mathematics often means multiplication.

3. **Calculate \( \frac{3}{2} \times \frac{9}{2} \)**:
\[ \frac{3}{2} \times \frac{9}{2} = \frac{27}{4} = 6.75 \]

**Hint**: Multiply the numerators and the denominators separately.

4. **Combine all parts inside the brackets**:
\[ 12.5 + 76 + 6.75 - \frac{3}{4} \]
First, convert \( \frac{3}{4} \) to decimal:
\[ \frac{3}{4} = 0.75 \]
Now, calculate:
\[ 12.5 + 76 + 6.75 - 0.75 = 12.5 + 76 + 6 = 94.5 \]

**Hint**: When adding or subtracting decimals, align them properly.

5. **Now calculate the entire expression**:
\[ \frac{13}{2} \times 94.5 \]
First, calculate \( \frac{13 \times 94.5}{2} \):
\[ 13 \times 94.5 = 1228.5 \]
Then divide by 2:
\[ \frac{1228.5}{2} = 614.25 \]

**Hint**: Multiplication before division when both operations are present.

### Final Answer:
The value of the expression is \( 614.25 \).