The value of `4 xx2 div `3of `12-3div2 (2-3) xx 2+3 div 2` of 3 is:

Options

A. `59/18`
B. `13/18`
C. `67/18`
D. `23/6`

Answer

To solve the expression \( 4 \times 2 \div 3 \text{ of } 12 - 3 \div 2 (2 - 3) \times 2 + 3 \div 2 \text{ of } 3 \), we will follow the order of operations, often referred to as BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution

1. **Evaluate the brackets**:
\[ 2 - 3 = -1 \]
So, the expression now becomes:
\[ 4 \times 2 \div 3 \text{ of } 12 - 3 \div 2 \times (-1) \times 2 + 3 \div 2 \text{ of } 3 \]

2. **Evaluate the "of" (which means multiplication)**:
- For \( 3 \text{ of } 12 \):
\[ 3 \text{ of } 12 = 3 \times 12 = 36 \]
- For \( 3 \text{ of } 3 \):
\[ 3 \text{ of } 3 = 3 \times 3 = 9 \]
Now the expression is:
\[ 4 \times 2 \div 36 - 3 \div 2 \times (-1) \times 2 + 9 \]

3. **Evaluate the division and multiplication from left to right**:
- For \( 4 \times 2 \div 36 \):
\[ 4 \times 2 = 8 \quad \Rightarrow \quad 8 \div 36 = \frac{8}{36} = \frac{2}{9} \]
- For \( 3 \div 2 \times (-1) \times 2 \):
\[ 3 \div 2 = \frac{3}{2} \quad \Rightarrow \quad \frac{3}{2} \times (-1) = -\frac{3}{2} \quad \Rightarrow \quad -\frac{3}{2} \times 2 = -3 \]
Now the expression is:
\[ \frac{2}{9} - 3 + 9 \]

4. **Combine the terms**:
- First, convert \( -3 \) to a fraction with a denominator of 9:
\[ -3 = -\frac{27}{9} \]
- Now, combine:
\[ \frac{2}{9} - \frac{27}{9} + \frac{81}{9} = \frac{2 - 27 + 81}{9} = \frac{56}{9} \]

5. **Final result**:
The value of the expression is:
\[ \frac{56}{9} \]