To find the fraction of students at Georgia Connections Academy (GACA) who participate in eSports, we can use the information given.
- Fraction of students in a club: \( \frac{2}{5} \)
- Fraction of club members in eSports: \( \frac{1}{4} \)
To find the fraction of the total student body that participates in eSports, we multiply these two fractions:
\[ \text{Fraction in eSports} = \left(\frac{2}{5}\right) \times \left(\frac{1}{4}\right) \]
Calculating this gives:
\[ \frac{2}{5} \times \frac{1}{4} = \frac{2 \times 1}{5 \times 4} = \frac{2}{20} = \frac{1}{10} \]
Thus, the fraction of the students at GACA that participate in eSports is \( \frac{1}{10} \).
The answer is \( \frac{1}{10} \).