Okay, we are tasked with adding 7337 and 1829. Let's begin!

Step 1: We'll start by adding the digits 7 & 9 in column 1 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 3 & 2 in column 2 and get 6.

Step 3: We'll start by adding the digits 3 & 8 in column 3 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 7 & 1 in column 4 and get 9.

So, 7337 + 1829 = 9166.

