Solve Fraction Multiplication: 1/6 × 2/3 Step-by-Step

To solve the problem, we will calculate the product of the fractions $\frac{1}{6}$ and $\frac{2}{3}$ using the standard method for multiplying fractions.

Step 1: Multiply the numerators.
The numerators are 1 and 2. Thus, the product of the numerators is $1 \times 2 = 2$.

Step 2: Multiply the denominators.
The denominators are 6 and 3. Thus, the product of the denominators is $6 \times 3 = 18$.

Step 3: Form the resulting fraction from the products obtained in the previous steps.
This gives us the fraction $\frac{2}{18}$.

Step 4: Simplify the fraction.
To simplify $\frac{2}{18}$, find the greatest common divisor (GCD) of 2 and 18, which is 2. Divide both the numerator and the denominator by their GCD:
$\frac{2 \div 2}{18 \div 2} = \frac{1}{9}$

Therefore, the simplified result of $\frac{1}{6} \times \frac{2}{3}$ is $\frac{1}{9}$.

We compare this result with the multiple-choice options and confirm that the correct answer is:

$\frac{1}{9}$