We have numbers 1497 and 644. Let's start adding them together.

Step 1: We'll start by adding the digits 7 & 4 in column 1 and get 11.
We'll write down the last digit 1 and carry the 1 to the next column.

Step 2: We'll start by adding the digits 9 & 4 in column 2 and get 14.
We'll write down the last digit 4 and carry the 1 to the next column.

Step 3: We'll start by adding the digits 4 & 6 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 1 & 0 in column 4 and get 2.

So, 1497 + 644 = 2141.

