Okay, we are tasked with adding 9735 and 9100. Let's begin!

Step 1: We'll start by adding the digits 5 & 0 in column 1 and get 5.

Step 2: We'll start by adding the digits 3 & 0 in column 2 and get 3.

Step 3: We'll start by adding the digits 7 & 1 in column 3 and get 8.

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

So, 9735 + 9100 = 18835.

