Okay, we are tasked with adding 4379 and 5740. Let's begin!

Step 1: We'll start by adding the digits 9 & 0 in column 1 and get 9.

Step 2: We'll start by adding the digits 7 & 4 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 3 & 7 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 4 & 5 in column 4 and get 10.
We'll write down the last digit 0 and carry the 1 to the next column.

So, 4379 + 5740 = 10119.

