To determine the largest fraction among [tex]\(\frac{5}{7}\)[/tex], [tex]\(\frac{13}{14}\)[/tex], and [tex]\(\frac{19}{21}\)[/tex], we need to compare the decimal values of each fraction.
1. Calculate the decimal value for [tex]\(\frac{5}{7}\)[/tex]:
[tex]\[
\frac{5}{7} \approx 0.7143
\][/tex]
2. Calculate the decimal value for [tex]\(\frac{13}{14}\)[/tex]:
[tex]\[
\frac{13}{14} \approx 0.9286
\][/tex]
3. Calculate the decimal value for [tex]\(\frac{19}{21}\)[/tex]:
[tex]\[
\frac{19}{21} \approx 0.9048
\][/tex]
Now, compare the decimal values calculated:
- [tex]\(\frac{5}{7} \approx 0.7143\)[/tex]
- [tex]\(\frac{13}{14} \approx 0.9286\)[/tex]
- [tex]\(\frac{19}{21} \approx 0.9048\)[/tex]
Among these, [tex]\(0.9286\)[/tex] is the largest decimal value, which corresponds to the fraction [tex]\(\frac{13}{14}\)[/tex].
Therefore, the largest fraction in the group is:
[tex]\[
\boxed{\frac{13}{14}}
\][/tex]
