We have numbers 9581 and 7029. Let's start adding them together.

Step 1: We'll start by adding the digits 1 & 9 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 8 & 2 in column 2 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 5 & 0 in column 3 and get 6.

Step 4: We'll start by adding the digits 9 & 7 in column 4 and get 16.
We'll write down the last digit 6 and carry the 1 to the next column.

So, 9581 + 7029 = 16610.

