What should come in place of the question mark (?) in the following questions ?
`(3)/(7) div (9)/(14) xx (6)/(11) = ?`

Options

A. `(5)/(22)`
B. `(9)/(11)`
C. `(4)/(11)`
D. `(7)/(22)`

Answer

To solve the equation \((\frac{3}{7}) \div (\frac{9}{14}) \times (\frac{6}{11}) = ?\), we will follow the order of operations, starting with the division.

### Step 1: Rewrite the division as multiplication by the reciprocal
The division of fractions can be rewritten as multiplication by the reciprocal. Therefore, we have:
\[ \frac{3}{7} \div \frac{9}{14} = \frac{3}{7} \times \frac{14}{9} \]

### Step 2: Multiply the fractions
Now we can multiply the fractions:
\[ \frac{3 \times 14}{7 \times 9} \]

### Step 3: Simplify the multiplication
Now we can simplify this expression. First, we can cancel out common factors:
- \(14\) and \(7\) can be simplified: \(14 \div 7 = 2\)
- So, we have:
\[ \frac{3 \times 2}{1 \times 9} = \frac{6}{9} \]

### Step 4: Further simplify \(\frac{6}{9}\)
Now, we can simplify \(\frac{6}{9}\):
\[ \frac{6}{9} = \frac{2}{3} \]

### Step 5: Multiply by the next fraction
Next, we multiply this result by \(\frac{6}{11}\):
\[ \frac{2}{3} \times \frac{6}{11} = \frac{2 \times 6}{3 \times 11} = \frac{12}{33} \]

### Step 6: Simplify \(\frac{12}{33}\)
Now, we can simplify \(\frac{12}{33}\):
- The greatest common divisor (GCD) of \(12\) and \(33\) is \(3\).
- So, we simplify:
\[ \frac{12 \div 3}{33 \div 3} = \frac{4}{11} \]

### Final Answer
Thus, the answer is:
\[ \frac{4}{11} \]

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