To add the fractions \( \frac{11}{5} \) and \( \frac{13}{4} \), we first need a common denominator. The least common multiple of the denominators 5 and 4 is 20.
Now, convert each fraction to have a denominator of 20:
\[ \frac{11}{5} = \frac{11 \times 4}{5 \times 4} = \frac{44}{20} \]
\[ \frac{13}{4} = \frac{13 \times 5}{4 \times 5} = \frac{65}{20} \]
Now, we can add the two fractions:
\[ \frac{44}{20} + \frac{65}{20} = \frac{44 + 65}{20} = \frac{109}{20} \]
So, \( \frac{11}{5} + \frac{13}{4} = \frac{109}{20} \).
If you want to express this as a mixed number:
\[ \frac{109}{20} = 5 \frac{9}{20} \]
Thus, the final answer is \( \frac{109}{20} \) or \( 5 \frac{9}{20} \).
