Multiply: `(3)/(4) xx (2)/( 9)`

Options

A. `(5)/(6)`
B. `(1)/(6)`
C. `(7)/(6)`
D. `(1)/(7)`

Answer

To solve the problem of multiplying the fractions \(\frac{3}{4}\) and \(\frac{2}{9}\), we can follow these steps:

### Step 1: Write down the fractions
We start with the two fractions:
\[ \frac{3}{4} \times \frac{2}{9} \]

### Step 2: Multiply the numerators
Next, we multiply the numerators (the top numbers) of the fractions:
\[ 3 \times 2 = 6 \]

### Step 3: Multiply the denominators
Now, we multiply the denominators (the bottom numbers) of the fractions:
\[ 4 \times 9 = 36 \]

### Step 4: Write the result as a fraction
We can now write the result of the multiplication as a single fraction:
\[ \frac{6}{36} \]

### Step 5: Simplify the fraction
Next, we simplify the fraction \(\frac{6}{36}\). We can do this by finding the greatest common divisor (GCD) of 6 and 36, which is 6. We divide both the numerator and the denominator by 6:
\[ \frac{6 \div 6}{36 \div 6} = \frac{1}{6} \]

### Final Answer
Thus, the final answer is:
\[ \frac{1}{6} \]

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