Okay, we are tasked with adding 1253 and 9587. Let's begin!

Step 1: We'll start by adding the digits 3 & 7 in column 1 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 5 & 8 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 2 & 5 in column 3 and get 8.

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

So, 1253 + 9587 = 10840.

