Determine the sum of two mixed numbers: 4.) $4 \frac{1}{2}+3 \frac{4}{5}$

Step 1 ：Convert each mixed number into an improper fraction. The first number, $4 \frac{1}{2}$, becomes $\frac{9}{2}$. The second number, $3 \frac{4}{5}$, becomes $\frac{19}{5}$.

Step 2 ：Add the two fractions together. $\frac{9}{2} + \frac{19}{5} = \frac{83}{10}$.

Step 3 ：Convert the result back into a mixed number. $\frac{83}{10}$ becomes $8 \frac{3}{10}$.

Step 4 ：Final Answer: The sum of $4 \frac{1}{2}$ and $3 \frac{4}{5}$ is \(\boxed{8 \frac{3}{10}}\).