At Porgie's Arcade, $\frac{2}{5}$ of the games are animal games. Among the animal games, $\frac{5}{6}$ are role-playing games.

a) What fraction of the games at Porgie's Arcade are animal role-playing games? Write your answer as a fraction in simplest form.

b) If there are 300 games at Porgie's Arcade, how many are animal role-playing games?

To determine the fraction of animal role-playing games at Porgie's Arcade, we multiply the fraction of animal games (2/5) by the fraction that is role-playing (5/6) to get 1/3. For 300 games at the arcade, this equates to 100 animal role-playing games.

Explanation:

The student is asking about finding a specific fraction of a whole given two different fraction categories at Porgie's Arcade. To find the fraction of the games that are animal role-playing games, we multiply the fraction of games that are animal games by the fraction of animal games that are role-playing games.

Step-by-step calculation:

Multiply 2/5 (fraction of animal games) by 5/6 (fraction of those that are role-playing games).
The result is 2/5 * 5/6 = 10/30, which simplifies to 1/3.
1/3 of the games at Porgie's Arcade are animal role-playing games.
To find the number of games that are animal role-playing games when there are 300 games total, multiply 1/3 by 300.
The result is 1/3 * 300 = 100 games.

Therefore, if Porgie's Arcade has 300 games, 100 of them are animal role-playing games.