To find out how much time Lily spent watching the movie, we first need to determine how long the movie was in hours.
The movie length is \(3\) and \(1/2\) hours, which can be converted to an improper fraction:
\[ 3 \frac{1}{2} = \frac{7}{2} \text{ hours} \]
Lily turned the movie off one-fourth of the way through, so we need to calculate one-fourth of the total time:
\[ \text{One-fourth of } \frac{7}{2} = \frac{1}{4} \times \frac{7}{2} = \frac{7}{8} \text{ hours} \]
Thus, the time Lily spent watching the movie is \(\frac{7}{8}\) of an hour.
Therefore, the answer is:
\[ \frac{7}{8} \text{ of an hour} \]
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