The value of `7div[5+1div2-{4+("4 of "2div4)+(5 div5" of "2)}]` is

Options

A. `7/2`
B. 7
C. `-(7)/(2)`
D. `-7`

Answer

To solve the expression \( 7 \div \left[ 5 + \frac{1}{2} - \left( 4 + \left( 4 \text{ of } \frac{2}{4} \right) + \left( \frac{5}{5} \text{ of } 2 \right) \right) \right] \), we will follow these steps:

### Step 1: Simplify the innermost expressions
First, we need to simplify the terms inside the parentheses.

1. Calculate \( 4 \text{ of } \frac{2}{4} \):
- This means \( 4 \times \frac{2}{4} = 4 \times 0.5 = 2 \).

2. Calculate \( \frac{5}{5} \text{ of } 2 \):
- This means \( 1 \times 2 = 2 \).

Now, we can rewrite the expression:
\[ 7 \div \left[ 5 + \frac{1}{2} - \left( 4 + 2 + 2 \right) \right] \]

### Step 2: Combine the values inside the brackets
Next, we simplify the expression inside the brackets:
- Calculate \( 4 + 2 + 2 = 8 \).

Now, the expression becomes:
\[ 7 \div \left[ 5 + \frac{1}{2} - 8 \right] \]

### Step 3: Simplify \( 5 + \frac{1}{2} - 8 \)
Now, we simplify \( 5 + \frac{1}{2} \):
- Convert \( 5 \) to a fraction: \( 5 = \frac{10}{2} \).
- So, \( 5 + \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \).

Now, substitute this back into the expression:
\[ 7 \div \left[ \frac{11}{2} - 8 \right] \]

### Step 4: Convert \( 8 \) to a fraction and simplify
Convert \( 8 \) to a fraction:
- \( 8 = \frac{16}{2} \).

Now, we have:
\[ 7 \div \left[ \frac{11}{2} - \frac{16}{2} \right] = 7 \div \left[ \frac{11 - 16}{2} \right] = 7 \div \left[ \frac{-5}{2} \right] \]

### Step 5: Divide by a fraction
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ 7 \div \left[ \frac{-5}{2} \right] = 7 \times \left( \frac{-2}{5} \right) = \frac{-14}{5} \]

### Final Answer
The value of the expression is:
\[ \frac{-14}{5} \]