Let's solve this addition problem. We have 8727 and 8824, and we need to add them together.

Step 1: We'll start by adding the digits 7 & 4 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 2 & 2 in column 2 and get 5.

Step 3: We'll start by adding the digits 7 & 8 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 8 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 8727 + 8824 = 17551.

