The value of `8 div [ ( 9-5) div { ( 4 div 2 " of "4 ) - ( 8 div 8 " of " 15 ) + ( 4 xx 2 div 8 ) } ]` is `:`

Options

A. 15/43
B. 32/23
C. 43/15
D. 23/32

Answer

To solve the expression \( 8 \div \left[ (9-5) \div \left\{ \left( \frac{4}{2} \text{ of } 4 \right) - \left( \frac{8}{8} \text{ of } 15 \right) + \left( \frac{4 \times 2}{8} \right) \right\} \right] \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Evaluate the innermost brackets**:
- Start with \( 9 - 5 \):
\[ 9 - 5 = 4 \]
- So the expression now looks like:
\[ 8 \div \left[ 4 \div \left\{ \left( \frac{4}{2} \text{ of } 4 \right) - \left( \frac{8}{8} \text{ of } 15 \right) + \left( \frac{4 \times 2}{8} \right) \right\} \right] \]

2. **Evaluate the "of" operations**:
- Calculate \( \frac{4}{2} \text{ of } 4 \):
\[ \frac{4}{2} \times 4 = 2 \times 4 = 8 \]
- Calculate \( \frac{8}{8} \text{ of } 15 \):
\[ \frac{8}{8} \times 15 = 1 \times 15 = 15 \]
- Calculate \( \frac{4 \times 2}{8} \):
\[ \frac{4 \times 2}{8} = \frac{8}{8} = 1 \]
- Substitute these values back into the expression:
\[ 8 \div \left[ 4 \div \left\{ 8 - 15 + 1 \right\} \right] \]

3. **Simplify the curly brackets**:
- Now calculate \( 8 - 15 + 1 \):
\[ 8 - 15 = -7 \quad \text{and} \quad -7 + 1 = -6 \]
- Update the expression:
\[ 8 \div \left[ 4 \div (-6) \right] \]

4. **Evaluate the division**:
- Calculate \( 4 \div (-6) \):
\[ 4 \div (-6) = -\frac{2}{3} \]
- Now substitute this back into the expression:
\[ 8 \div \left( -\frac{2}{3} \right) \]

5. **Final division**:
- Dividing by a fraction is the same as multiplying by its reciprocal:
\[ 8 \div \left( -\frac{2}{3} \right) = 8 \times \left( -\frac{3}{2} \right) = -12 \]

### Final Answer:
The value of the expression is \( -12 \).