To determine the smallest fraction from the list \(\frac{5}{7}, \frac{4}{9}, \frac{6}{11}, \frac{2}{5},\) and \(\frac{3}{4},\) follow these steps:
1. List the fractions:
- \(\frac{5}{7}\)
- \(\frac{4}{9}\)
- \(\frac{6}{11}\)
- \(\frac{2}{5}\)
- \(\frac{3}{4}\)
2. Understand the concept: We need to identify which fraction has the smallest value. A useful approach is to convert these fractions to decimal form or compare them directly.
3. Compare the fractions: Let's inspect and compare each fraction:
- \(\frac{5}{7} \approx 0.714\)
- \(\frac{4}{9} \approx 0.444\)
- \(\frac{6}{11} \approx 0.545\)
- \(\frac{2}{5} = 0.4\)
- \(\frac{3}{4} = 0.75\)
4. Determine the smallest fraction:
- From the decimal approximations:
- \(0.714\) (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 \(\frac{3}{4}\))
5. Identify the smallest decimal: Clearly, \(0.4\) is the smallest decimal value among these.
6. Conclusion: Therefore, the smallest fraction among them is \(\frac{2}{5}\), which is \(0.4\).
So, out of the fractions [tex]\(\frac{5}{7}, \frac{4}{9}, \frac{6}{11}, \frac{2}{5},\)[/tex] and [tex]\(\frac{3}{4},\)[/tex] the smallest fraction is [tex]\(\frac{2}{5}.\)[/tex]
