Okay, we are tasked with adding 871 and 7682. Let's begin!

Step 1: We'll start by adding the digits 1 & 2 in column 1 and get 3.

Step 2: We'll start by adding the digits 7 & 8 in column 2 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 8 & 6 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 0 & 7 in column 4 and get 8.

So, 871 + 7682 = 8553.

