555319 ÷ 44 
Our goal is to divide 555319 by 44.

Step 1:
44 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 44

Advancing to step 2:
When dividing 55 by 44, we get 1 with a remainder of 11.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 44 from 55 and we're left with 11.
Bring next digit (5) of the dividend behind the 11 and repeat the process: 115 / 44

Let's proceed to step 3:
44 can be fit into 115 2 times, resulting in a remainder of 27.
Put 2 as the next digit of the answer. 
Result so far: 12.0
If we subtract 88 from 115, we get 27.
Append the next digit (3) from the dividend to 27 and continue with: 273 / 44

On to step 4:
The number 44 fits into 273 6 times, leaving a remainder of 9.
Use 6 as the next digit of our solution. 
Result so far: 126.0
Subtract 264 from 273 to get 9.
Include the next digit (1) from the dividend after 9, then repeat: 91 / 44

Moving on to step 5:
44 can be fit into 91 2 times, resulting in a remainder of 3.
The number 2 becomes the next digit in our result. 
Result so far: 1262.0
If we subtract 88 from 91, we get 3.
Include the next digit (9) from the dividend after 3, then repeat: 39 / 44

On to step 6:
The number 44 fits into 39 0 times, leaving a remainder of 39.
Write down 0 as next digit of the result. 
Result so far: 12620.0
Deduct 0 from 39 and we're left with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Let's proceed to step 7:
44 goes into 390 8 times with a remainder of 38.
Record the quotient 8 as the next digit in the result. 
Result so far: 12620.8
Deduct 352 from 390 and we're left with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Step 8:
44 can be fit into 380 8 times, resulting in a remainder of 28.
Use 8 as the next digit of our solution. 
Result so far: 12620.88
If we take 352 away from 380, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

After the division, we end up with 12620.88 and a remainder of 0.028.