Okay, we are tasked with adding 614 and 903. Let's begin!

Step 1: We'll start by adding the digits 4 & 3 in column 1 and get 7.

Step 2: We'll start by adding the digits 1 & 0 in column 2 and get 1.

Step 3: We'll start by adding the digits 6 & 9 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

So, 614 + 903 = 1517.

