What will come in place of the question-mark (2) in the following questions?
`12/19 xx 76/81 xx 3/8 =?`

Options

A. `4/9`
B. `2/7`
C. `4/7`
D. `2/9`

Answer

To solve the expression \( \frac{12}{19} \times \frac{76}{81} \times \frac{3}{8} \), we will follow these steps:

### Step 1: Write the expression
We start with the expression:
\[ \frac{12}{19} \times \frac{76}{81} \times \frac{3}{8} \]

### Step 2: Multiply the fractions
When multiplying fractions, we multiply the numerators together and the denominators together:
\[ \frac{12 \times 76 \times 3}{19 \times 81 \times 8} \]

### Step 3: Simplify before multiplying
We can simplify the fractions before multiplying to make calculations easier. We will look for common factors in the numerator and denominator.

- The number \(76\) can be factored as \(4 \times 19\).
- The number \(81\) can be factored as \(3 \times 27\).

Now, substituting these values in:
\[ \frac{12 \times (4 \times 19) \times 3}{19 \times (3 \times 27) \times 8} \]

### Step 4: Cancel out common factors
Now we can cancel out common factors:
- \(19\) in the numerator and denominator cancels out.
- \(3\) in the numerator and denominator cancels out.

This gives us:
\[ \frac{12 \times 4}{27 \times 8} \]

### Step 5: Calculate the remaining multiplication
Now we can multiply the remaining numbers:
- The numerator: \(12 \times 4 = 48\)
- The denominator: \(27 \times 8 = 216\)

So we have:
\[ \frac{48}{216} \]

### Step 6: Simplify the fraction
Now we simplify \( \frac{48}{216} \). We can divide both the numerator and denominator by their greatest common divisor (GCD), which is \(24\):
\[ \frac{48 \div 24}{216 \div 24} = \frac{2}{9} \]

### Final Answer
Thus, the final answer is:
\[ \frac{2}{9} \]

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