We have numbers 77 and 1828. Let's start adding them together.

Step 1: We'll start by adding the digits 7 & 8 in column 1 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 7 & 2 in column 2 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 0 & 8 in column 3 and get 9.

Step 4: We'll start by adding the digits 0 & 1 in column 4 and get 1.

So, 77 + 1828 = 1905.

