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The problem asks how many video games Rory can play if each game lasts \(1 \frac{3}{4}\) hours, and he wants to play for 9 hours.

### Steps:
1. Convert the mixed fraction \(1 \frac{3}{4}\) to an improper fraction:
   \[
   1 \frac{3}{4} = \frac{7}{4}
   \]
   
2. To find how many games Rory can play, divide the total time (9 hours) by the time each game takes (\(\frac{7}{4}\) hours):
   \[
   \frac{9}{1} \div \frac{7}{4} = \frac{9}{1} \times \frac{4}{7} = \frac{36}{7}
   \]
   \[
   \frac{36}{7} = 5 \frac{1}{7}
   \]

So, Rory can play \(5 \frac{1}{7}\) games.

The correct answer is **D. 5 \(\frac{1}{7}\)**.

Would you like further details or have any questions? Here are five related questions to expand on this concept:

1. How would the solution change if Rory wanted to play for 12 hours?
2. What if each game lasted \(2 \frac{1}{2}\) hours? How many games could he play in 9 hours?
3. How do you convert a mixed number to an improper fraction?
4. If Rory wanted to play \(6\) games, how many hours would that take?
5. How do you simplify a division of fractions?

**Tip**: Always remember to invert and multiply when dividing fractions!

Rory is playing a video game in which each game lasts 1 3/4 hours. He wants to play for 9 hours today. How many games can he play?

Learn how to calculate how many games Rory can play if each game lasts 1 3/4 hours and he has 9 hours to play. This problem covers concepts like mixed number conversion to improper fractions and division of fractions. Suitable for Grades 6-8.

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