To find the fraction of the pie that Lance ate, we start with the information given:
- There was initially half of the pie remaining, which we can denote as \( \frac{1}{2} \).
- After Lance eats a piece of pie, there is \( \frac{1}{6} \) of the whole pie remaining.
Let's denote the amount of pie Lance ate as \( x \).
According to the information provided:
\[ \frac{1}{2} - x = \frac{1}{6} \]
To solve for \( x \), we first convert \( \frac{1}{2} \) to a fraction with a common denominator with \( \frac{1}{6} \). The least common denominator for 2 and 6 is 6.
\[ \frac{1}{2} = \frac{3}{6} \]
Now we can rewrite the equation:
\[ \frac{3}{6} - x = \frac{1}{6} \]
Next, we solve for \( x \):
\[ x = \frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \]
So, Lance ate \( \frac{1}{3} \) of the whole pie.
Evaluating the options given:
- A. \( \frac{1}{3} \) of the whole pie
- B. \( \frac{1}{4} \) of the whole pie
- C. \( \frac{1}{5} \) of the whole pie
- D. \( \frac{1}{6} \) of the whole pie
None of the provided options correspond to \( \frac{1}{3} \), which means there might be some mistake in the options or interpretation of the question.
If we consider \( \frac{1}{3} \) as an alternative form, it would include fractions like \( \frac{2}{6} \) but since it doesn’t match any of the answer options, it appears that none of the listed answers are correct.
If you have any further instructions or clarifications, feel free to ask!