Alright, let's solve this problem step by step. We have 635 and 404 and we're adding them together.

Step 1: We'll start by adding the digits 5 & 4 in column 1 and get 9.

Step 2: We'll start by adding the digits 3 & 0 in column 2 and get 3.

Step 3: We'll start by adding the digits 6 & 4 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 635 + 404 = 1039.

