Alright, let's solve this problem step by step. We have 7638 and 5530 and we're adding them together.

Step 1: We'll start by adding the digits 8 & 0 in column 1 and get 8.

Step 2: We'll start by adding the digits 3 & 3 in column 2 and get 6.

Step 3: We'll start by adding the digits 6 & 5 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 5 in column 4 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

So, 7638 + 5530 = 13168.

