To determine which movie theater sold out on a greater fraction of the nights it was open, we need to compare the fractions [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{14}{25}\)[/tex].
1. Express the fractions as decimals:
- For Greene Cinema, [tex]\(\frac{1}{2}\)[/tex] is converted into a decimal by performing the division: [tex]\(1 \div 2 = 0.5\)[/tex].
- For Perry Theater, [tex]\(\frac{14}{25}\)[/tex] is converted into a decimal by performing the division: [tex]\(14 \div 25 = 0.56\)[/tex].
2. Compare the decimal representations:
- The decimal for Greene Cinema is [tex]\(0.5\)[/tex].
- The decimal for Perry Theater is [tex]\(0.56\)[/tex].
3. Determine which decimal is greater:
- [tex]\(0.56\)[/tex] is greater than [tex]\(0.5\)[/tex].
Therefore, Perry Theater sold out on a greater fraction of the nights it was open, with a fraction of [tex]\(\frac{14}{25}\)[/tex] (or 0.56) compared to Greene Cinema's fraction of [tex]\(\frac{1}{2}\)[/tex] (or 0.5).
