\( \left. \begin{array} { r l l l l | l } { 9 } & { 6 } & { 4 } & { } & { 8 } \\ { + } & { 78 } & { 3 } & { 5 } & { } \\ \hline \end{array} \right. \)

To solve the addition problem presented in the format, we need to add the two numbers vertically. The numbers are: ``` 9648 + 7835 ``` Let's add them column by column, starting from the rightmost column: 1. **Rightmost column (units place)**: - \(8 + 5 = 13\) - Write down \(3\) and carry over \(1\). 2. **Second column (tens place)**: - \(4 + 3 + 1 = 8\) (adding the carry) - Write down \(8\). 3. **Third column (hundreds place)**: - \(6 + 8 = 14\) - Write down \(4\) and carry over \(1\). 4. **Fourth column (thousands place)**: - \(9 + 7 + 1 = 17\) (adding the carry) - Write down \(7\) and carry over \(1\). 5. **Final carry**: - Since there is a carry of \(1\), we write it down in the next column to the left. Putting it all together, we have: ``` 9648 + 7835 ------ 17483 ``` Thus, the sum of \(9648\) and \(7835\) is \(17483\).