Okay, we are tasked with adding 9198 and 8829. Let's begin!

Step 1: We'll start by adding the digits 8 & 9 in column 1 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 2 in column 2 and get 12.
We'll write down the last digit 2 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 8 in column 3 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 9 & 8 in column 4 and get 18.
We'll write down the last digit 8 and carry the 1 to the next column.

So, 9198 + 8829 = 18027.

