To determine which of the given fractions equals 40%, we follow a systematic approach:
1. Understand 40%:
- First, we convert 40% into a fraction. Since percent means per hundred, 40% is equivalent to [tex]\(\frac{40}{100}\)[/tex].
- Simplify [tex]\(\frac{40}{100}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 20:
[tex]\[
\frac{40}{100} = \frac{40 \div 20}{100 \div 20} = \frac{2}{5}
\][/tex]
2. Compare the given fractions to [tex]\(\frac{2}{5}\)[/tex]:
- We are given the fractions [tex]\( \frac{1}{4} \)[/tex], [tex]\( \frac{2}{5} \)[/tex], [tex]\( \frac{4}{5} \)[/tex], and [tex]\( \frac{5}{2} \)[/tex].
3. Check each fraction:
- [tex]\( \frac{1}{4} \)[/tex]: This equals 0.25 or 25%, which is not 40%.
- [tex]\( \frac{2}{5} \)[/tex]: This equals 0.40 or 40%, which matches our target percentage.
- [tex]\( \frac{4}{5} \)[/tex]: This equals 0.80 or 80%, which is not 40%.
- [tex]\( \frac{5}{2} \)[/tex]: This equals 2.50 or 250%, which is not 40%.
4. Conclusion:
- Among the given fractions, [tex]\(\frac{2}{5}\)[/tex] is the one that equals 40%.
Therefore, the fraction that equals 40% is [tex]\( \frac{2}{5} \)[/tex], which corresponds to the second option in the list. Hence, the correct answer is:
[tex]\[
\boxed{2}
\][/tex]
