The value of `2 xx 3 div "2 of 3" xx 2 div (4 + 4 xx 4 div "4 of 4" - 4 div 4 xx 4)` is :

Options

A. 8
B. 1
C. 4
D. 2

Answer

To solve the expression \(2 \times 3 \div "2 \text{ of } 3" \times 2 \div (4 + 4 \times 4 \div "4 \text{ of } 4" - 4 \div 4 \times 4)\), we will follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:

1. **Interpret "of" as multiplication**:
- The term "2 of 3" means \(2 \times 3 = 6\).
- The term "4 of 4" means \(4 \times 4 = 16\).

So, we can rewrite the expression:
\[ 2 \times 3 \div 6 \times 2 \div (4 + 4 \times 4 \div 16 - 4 \div 4 \times 4) \]

2. **Calculate the inner expression**:
- Start with \(4 + 4 \times 4 \div 16 - 4 \div 4 \times 4\).
- Calculate \(4 \times 4 = 16\).
- Then, \(16 \div 16 = 1\).
- Now, calculate \(4 \div 4 = 1\) and then \(1 \times 4 = 4\).
- Substitute back into the expression:
\[ 4 + 1 - 4 \]
- This simplifies to \(4 + 1 = 5\) and \(5 - 4 = 1\).

3. **Substitute back into the main expression**:
- Now we have:
\[ 2 \times 3 \div 6 \times 2 \div 1 \]

4. **Perform the operations from left to right**:
- First, calculate \(2 \times 3 = 6\).
- Then, \(6 \div 6 = 1\).
- Next, \(1 \times 2 = 2\).
- Finally, \(2 \div 1 = 2\).

5. **Final Result**:
- The value of the entire expression is \(2\).

### Final Answer:
\[ \text{The value is } 2. \]