The value of `6xx2div3" of "12-3div2xx(2-3)xx2+3div2" of "3` is :

Options

A. `17/6`
B. `23/6`
C. `19/6`
D. `13/6`

Answer

To solve the expression \( 6 \times 2 \div 3 \) of \( 12 - 3 \div 2 \times (2 - 3) \times 2 + 3 \div 2 \) of \( 3 \), we will follow the order of operations, commonly known as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Evaluate the Brackets**:
- Calculate \( (2 - 3) \):
\[ 2 - 3 = -1 \]
- Now substitute this back into the expression:
\[ 6 \times 2 \div 3 \text{ of } 12 - 3 \div 2 \times (-1) \times 2 + 3 \div 2 \text{ of } 3 \]

2. **Rewrite the Expression**:
- The expression now looks like:
\[ 6 \times 2 \div 3 \text{ of } 12 - 3 \div 2 \times (-1) \times 2 + 3 \div 2 \text{ of } 3 \]

3. **Evaluate the Division and Multiplication**:
- Calculate \( 3 \div 2 \):
\[ 3 \div 2 = 1.5 \]
- Substitute this back:
\[ 6 \times 2 \div 3 \text{ of } 12 - 1.5 \times (-1) \times 2 + 1.5 \text{ of } 3 \]

4. **Calculate \( 6 \times 2 \div 3 \)**:
- First, \( 6 \times 2 = 12 \)
- Then, \( 12 \div 3 = 4 \)
- So, we have:
\[ 4 \text{ of } 12 - 1.5 \times (-1) \times 2 + 1.5 \text{ of } 3 \]

5. **Calculate \( 4 \text{ of } 12 \)**:
- This is \( 4 \times 12 = 48 \).

6. **Calculate \( 1.5 \times (-1) \times 2 \)**:
- First, \( 1.5 \times (-1) = -1.5 \)
- Then, \( -1.5 \times 2 = -3 \).

7. **Calculate \( 1.5 \text{ of } 3 \)**:
- This is \( 1.5 \times 3 = 4.5 \).

8. **Combine All Parts**:
- Now substitute back:
\[ 48 - (-3) + 4.5 \]
- This simplifies to:
\[ 48 + 3 + 4.5 = 55.5 \]

9. **Final Calculation**:
- Convert \( 55.5 \) to a fraction:
\[ 55.5 = \frac{111}{2} \]

### Final Answer:
The value of the expression is \( \frac{111}{2} \).