Okay, we are tasked with adding 510 and 9797. Let's begin!

Step 1: We'll start by adding the digits 0 & 7 in column 1 and get 7.

Step 2: We'll start by adding the digits 1 & 9 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 5 & 7 in column 3 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 0 & 9 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 510 + 9797 = 10307.

