Finding the Largest Fraction

The question asks us to identify the largest fraction from the set: \(\frac{4}{9},\frac{5}{7},\frac{11}{13},\frac{13}{17}\). We can determine this by converting each fraction to a decimal and comparing the values.

Comparing Fractions Using Decimal Conversion

To compare these fractions effectively, we convert each one into its decimal representation. This allows for a direct numerical comparison.

Step 1: Convert Fractions to Decimals

We perform the division for each fraction:

• For \(\frac{4}{9}\): \(4 \div 9 = 0.444...\)
• For \(\frac{5}{7}\): \(5 \div 7 \approx 0.714...\)
• For \(\frac{11}{13}\): \(11 \div 13 \approx 0.846...\)
• For \(\frac{13}{17}\): \(13 \div 17 \approx 0.764...\)

Step 2: Tabulate Decimal Equivalents

The decimal values are listed below for easy comparison:

Step 3: Compare Decimal Values

By comparing the decimal values, we can order the fractions from smallest to largest:

The decimal values are \(0.444...\), \(0.714...\), \(0.846...\), and \(0.764...\).

Ordering these decimals in ascending order:

\(0.444... < 0.714... < 0.764... < 0.846...\)

This order corresponds to the fractions:

\(\frac{4}{9} < \frac{5}{7} < \frac{13}{17} < \frac{11}{13}\)

Conclusion

The largest decimal value obtained is \(0.846...\), which corresponds to the fraction \(\frac{11}{13}\). Therefore, \(\frac{11}{13}\) is the largest fraction among the given options.