The value of
`3div18` of `3xx6+21xx6 div 18-3div2+3-3div9` of `3xx9` is :

Options

A. `(29)/(6)`
B. `(41)/(9)`
C. `(47)/(6)`
D. `(35)/(9)`

Answer

To solve the expression \( \frac{3}{18} \) of \( 3 \times 6 + \frac{21 \times 6}{18} - \frac{3}{2} + 3 - \frac{3}{9} \) of \( 3 \times 9 \), we will follow the order of operations (BODMAS/BIDMAS).

### Step-by-Step Solution:

1. **Identify the expression**:
We need to evaluate:
\[ \frac{3}{18} \text{ of } \left( 3 \times 6 + \frac{21 \times 6}{18} - \frac{3}{2} + 3 - \frac{3}{9} \text{ of } (3 \times 9) \right) \]

2. **Calculate \( 3 \times 6 \)**:
\[ 3 \times 6 = 18 \]

3. **Calculate \( 21 \times 6 \)**:
\[ 21 \times 6 = 126 \]

4. **Divide \( 126 \) by \( 18 \)**:
\[ \frac{126}{18} = 7 \]

5. **Calculate \( 3 \times 9 \)**:
\[ 3 \times 9 = 27 \]

6. **Divide \( 3 \) by \( 9 \)**:
\[ \frac{3}{9} = \frac{1}{3} \]

7. **Substituting the values back into the expression**:
Now we substitute these values back into the expression:
\[ 18 + 7 - \frac{3}{2} + 3 - \frac{1}{3} \]

8. **Combine the constants**:
Combine \( 18 + 7 + 3 = 28 \):
\[ 28 - \frac{3}{2} - \frac{1}{3} \]

9. **Finding a common denominator**:
The common denominator for \( 2 \) and \( 3 \) is \( 6 \). Rewrite the fractions:
\[ \frac{3}{2} = \frac{9}{6}, \quad \frac{1}{3} = \frac{2}{6} \]

10. **Substituting back**:
Substitute back into the expression:
\[ 28 - \frac{9}{6} - \frac{2}{6} = 28 - \frac{11}{6} \]

11. **Convert \( 28 \) to a fraction**:
Convert \( 28 \) to have a denominator of \( 6 \):
\[ 28 = \frac{168}{6} \]

12. **Final subtraction**:
Now perform the subtraction:
\[ \frac{168}{6} - \frac{11}{6} = \frac{157}{6} \]

13. **Multiply by \( \frac{3}{18} \)**:
Now we need to find \( \frac{3}{18} \) of \( \frac{157}{6} \):
\[ \frac{3}{18} = \frac{1}{6} \]
Therefore:
\[ \frac{1}{6} \times \frac{157}{6} = \frac{157}{36} \]

### Final Answer:
The value of the expression is:
\[ \frac{157}{36} \]