Let's solve this addition problem. We have 7778 and 825, and we need to add them together.

Step 1: We'll start by adding the digits 8 & 5 in column 1 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 2 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 7 & 8 in column 3 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 0 in column 4 and get 8.

So, 7778 + 825 = 8603.

