What will come in place of the question mark (?) in the following questions?
`3 1/3 div 6 3/7 xx 1 1/ 2 xx (22)/7=?`

Options

A. `4 cdot 4`
B. `(22)/7`
C. `5/(22)`
D. None of these

Answer

To solve the expression \( 3 \frac{1}{3} \div 6 \frac{3}{7} \times 1 \frac{1}{2} \times \frac{22}{7} \), we will follow the order of operations (BODMAS/BIDMAS).

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions.

- \( 3 \frac{1}{3} = \frac{10}{3} \) (since \( 3 \times 3 + 1 = 10 \))
- \( 6 \frac{3}{7} = \frac{45}{7} \) (since \( 6 \times 7 + 3 = 45 \))
- \( 1 \frac{1}{2} = \frac{3}{2} \) (since \( 1 \times 2 + 1 = 3 \))

Now, we can rewrite the expression:
\[ \frac{10}{3} \div \frac{45}{7} \times \frac{3}{2} \times \frac{22}{7} \]

### Step 2: Perform Division
Next, we perform the division:
\[ \frac{10}{3} \div \frac{45}{7} = \frac{10}{3} \times \frac{7}{45} = \frac{10 \times 7}{3 \times 45} = \frac{70}{135} \]

### Step 3: Simplify the Fraction
Now, we simplify \( \frac{70}{135} \):
- The GCD of 70 and 135 is 5.
\[ \frac{70 \div 5}{135 \div 5} = \frac{14}{27} \]

### Step 4: Multiply by \( \frac{3}{2} \)
Now we multiply by \( \frac{3}{2} \):
\[ \frac{14}{27} \times \frac{3}{2} = \frac{14 \times 3}{27 \times 2} = \frac{42}{54} \]

### Step 5: Simplify the Result
Next, we simplify \( \frac{42}{54} \):
- The GCD of 42 and 54 is 6.
\[ \frac{42 \div 6}{54 \div 6} = \frac{7}{9} \]

### Step 6: Multiply by \( \frac{22}{7} \)
Finally, we multiply by \( \frac{22}{7} \):
\[ \frac{7}{9} \times \frac{22}{7} = \frac{7 \times 22}{9 \times 7} = \frac{22}{9} \]

### Conclusion
Thus, the final answer is:
\[ \frac{22}{9} \]