Okay, we are tasked with adding 9191 and 5440. Let's begin!

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

Step 2: We'll start by adding the digits 9 & 4 in column 2 and get 13.
We'll write down the last digit 3 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 1 & 4 in column 3 and get 6.

Step 4: We'll start by adding the digits 9 & 5 in column 4 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

So, 9191 + 5440 = 14631.

