We're dividing 559635 by 44 
We want to figure out the number of times 559635 can be divided by 44.

On to step 1:
The number 44 fits into 5 0 times, leaving a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Grab the next digit (5) from the dividend, add it to 5, then carry on: 55 / 44

Moving on to step 2:
44 goes into 55 1 times with a remainder of 11.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 44 away from 55, we end up with 11.
Fetch the next digit (9) from the dividend, attach it to 11 and continue: 119 / 44

Let's proceed to step 3:
44 can be fit into 119 2 times, resulting in a remainder of 31.
Write down 2 as next digit of the result. 
Result so far: 12.0
Subtract 88 from 119 to get 31.
Grab the next digit (6) from the dividend, add it to 31, then carry on: 316 / 44

Going ahead to step 4:
316 divided by 44 is 7 with a remainder of 8.
Record the quotient 7 as the next digit in the result. 
Result so far: 127.0
If we take 308 away from 316, we end up with 8.
Append the next digit (3) from the dividend to 8 and continue with: 83 / 44

On to step 5:
44 goes into 83 1 times with a remainder of 39.
The next digit of our result is 1. 
Result so far: 1271.0
If we subtract 44 from 83, we get 39.
Append the next digit (5) from the dividend to 39 and continue with: 395 / 44

Going ahead to step 6:
44 can be fit into 395 8 times, resulting in a remainder of 43.
Put 8 as the next digit of the answer. 
Result so far: 12718.0
Deduct 352 from 395 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Let's proceed to step 7:
If we divide 430 by 44, we get 9 and a remainder of 34.
Record the quotient 9 as the next digit in the result. 
Result so far: 12718.9
Subtracting 396 from 430 leaves us with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 8:
When dividing 340 by 44, we get 7 with a remainder of 32.
Use 7 as the next digit of our solution. 
Result so far: 12718.97
Subtract 308 from 340 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Step 9:
44 can be fit into 320 7 times, resulting in a remainder of 12.
Record the quotient 7 as the next digit in the result. 
Result so far: 12718.977
If we subtract 308 from 320, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

The final result is 12718.977 with a remainder of 0.0012.