Let's carefully analyze and solve the given problem step by step.
We are asked to find the product of two fractions: [tex]\( \frac{1}{6} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex].
When multiplying fractions, you multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
Here, both fractions are:
[tex]\[
\frac{1}{6} \text{ and } \frac{1}{2}
\][/tex]
Step 1: Multiply the numerators:
[tex]\( 1 \times 1 = 1 \)[/tex]
Step 2: Multiply the denominators:
[tex]\( 6 \times 2 = 12 \)[/tex]
Step 3: Combine the results from Step 1 and Step 2 to form the new fraction:
[tex]\[
\frac{1}{12}
\][/tex]
Thus, the product of [tex]\( \frac{1}{6} \)[/tex] and [tex]\( \frac{1}{2} \)[/tex] is [tex]\( \frac{1}{12} \)[/tex].
Reviewing the options, the correct choice is not listed, but based on the calculations the answer should be [tex]\( \frac{1}{12} \)[/tex].
