The value of `-7div[5+1div2-{4+(4 " of "2div4)+(4div4 " of "2)}]`is :

Options

A. a)`-7`
B. b)`-(7)/(2)`
C. c)14/5
D. d)`(7)/(2)`

Answer

To solve the expression \(-7 \div [5 + 1 \div 2 - \{4 + (4 \text{ of } 2 \div 4) + (4 \div 4 \text{ of } 2)\}]\), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Identify the innermost brackets and operations**:
We start with the expression inside the brackets:
\[ 4 + (4 \text{ of } 2 \div 4) + (4 \div 4 \text{ of } 2) \]

2. **Evaluate the "of" operations**:
The term "of" indicates multiplication. Thus, we rewrite:
\[ 4 + \left(\frac{4 \times 2}{4}\right) + \left(\frac{4}{4} \times 2\right) \]

3. **Simplify the multiplications**:
- For \(4 \times 2 \div 4\):
\[ \frac{4 \times 2}{4} = \frac{8}{4} = 2 \]
- For \(4 \div 4 \text{ of } 2\):
\[ \frac{4}{4} \times 2 = 1 \times 2 = 2 \]

4. **Combine the results**:
Now substituting back, we have:
\[ 4 + 2 + 2 = 8 \]

5. **Substitute back into the original expression**:
Now, we substitute this back into the original expression:
\[ -7 \div [5 + 1 \div 2 - 8] \]

6. **Evaluate \(1 \div 2\)**:
\[ 1 \div 2 = \frac{1}{2} \]

7. **Combine the terms inside the brackets**:
We now have:
\[ 5 + \frac{1}{2} - 8 \]
To combine these, convert \(5\) and \(-8\) into fractions with a common denominator:
\[ 5 = \frac{10}{2}, \quad -8 = -\frac{16}{2} \]
Therefore:
\[ \frac{10}{2} + \frac{1}{2} - \frac{16}{2} = \frac{10 + 1 - 16}{2} = \frac{-5}{2} \]

8. **Final division**:
Now we substitute back:
\[ -7 \div \left(-\frac{5}{2}\right) \]
Dividing by a negative fraction is the same as multiplying by its reciprocal:
\[ -7 \times \left(-\frac{2}{5}\right) = \frac{14}{5} \]

### Final Answer:
The value of the expression is \(\frac{14}{5}\).