In your class, [tex]\frac{2}{5}[/tex] of the students play checkers. Of the students who play checkers, [tex]\frac{5}{6}[/tex] also play chess. If there are 30 students in the class, how many play both checkers and chess?

In a class of 30 students, 12 students play checkers based on the given fraction ⅖. The number of students who play both checkers and chess is 10, as derived from the provided fraction ⅚ of the checker-players.

Explanation:

The problem deals with the application of fractions in a real life situation - the distribution of students in a class that play two different games.

First, we find out how many students play checkers. According to the question, ⅖ of the students in the class play checkers. In a class of 30 students, you multiply the total number of students by the fraction that plays checkers. So, 30 students times ⅖ equals 12 students play checkers.

The next step is to find out how many of those students also play chess. The problem states that ⅚ of the students who play checkers also play chess. This means we multiply the number of students who play checkers by the fraction that also play chess; which is 12 students times ⅚ equals 10 students.

So, 10 students out of the total 30 in the class play both checkers and chess.

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