Okay, let's tackle this math problem. We're starting with 83098 and subtracting 11827.

Step 1: We'll start by subtracting the digit 7 and the borrow 0 from 8 in column 1 and get 1.
1 is the first digit of our result.

Step 2: We'll start by subtracting the digit 2 and the borrow 0 from 9 in column 2 and get 7.
7 is the next digit of our result.

Step 3: We'll start by subtracting the digit 8 and the borrow 0 from 0 in column 3 and get -8.
We add -8 to 10 and get 2 as the next digit of the result.

Step 4: We'll start by subtracting the digit 1 and the borrow 1 from 3 in column 4 and get 1.
1 is the next digit of our result.

Step 5: We'll start by subtracting the digit 1 and the borrow 0 from 8 in column 5 and get 7.
7 is the next digit of our result.

So, 83098 - 11827 = 71271.