To find the smallest fraction among \(\frac{5}{7}\), \(\frac{4}{9}\), \(\frac{6}{11}\), \(\frac{2}{5}\) and \(\frac{3}{4}\), we compare their decimal values.
1. Calculate the decimal value of each fraction:
- \(\frac{5}{7} \approx 0.714\)
- \(\frac{4}{9} \approx 0.444\)
- \(\frac{6}{11} \approx 0.545\)
- \(\frac{2}{5} = 0.4\)
- \(\frac{3}{4} = 0.75\)
2. Compare the decimal values:
- \(0.714\) (for \(\frac{5}{7}\))
- \(0.444\) (for \(\frac{4}{9}\))
- \(0.545\) (for \(\frac{6}{11}\))
- \(0.4\) (for \(\frac{2}{5}\))
- \(0.75\) (for \(\frac{3}{4}\))
3. Determine the smallest value among these decimals:
- The smallest is \(0.4\).
Therefore, the smallest fraction among the given options is [tex]\(\frac{2}{5}\)[/tex].
