To simplify \( \frac{1}{6} \div \frac{1}{3} \), we can multiply by the reciprocal of the second fraction.
\[ \frac{1}{6} \div \frac{1}{3} = \frac{1}{6} \times \frac{3}{1} \]
Now, perform the multiplication:
\[ = \frac{1 \times 3}{6 \times 1} = \frac{3}{6} \]
Now, simplify \( \frac{3}{6} \):
\[ \frac{3}{6} = \frac{1}{2} \]
Since \( \frac{1}{2} \) is not one of the answer choices (A to D), it's possible that my interpretation of the input text is incorrect. Let me check that one more time:
You are asking to simplify \( \frac{1}{6} \div \frac{1}{3} \) which I have calculated correctly to be \( \frac{1}{2} \).
However, none of the options listed (A. \( \frac{1}{48} \), B. \( \frac{16}{3} \), C. \( \frac{3}{16} \), D. \( 5 \frac{1}{3} \)) corresponds to this answer.
Please clarify the numbers or operation if I missed something!