We're dividing 559988 by 61 
We're looking to find how many times 61 goes into 559988.

Step 1:
The number 61 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (5) from the dividend and append it to 5, then repeat: 55 / 61

Step 2:
When dividing 55 by 61, we get 0 with a remainder of 55.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 55, we get 55.
Include the next digit (9) from the dividend after 55, then repeat: 559 / 61

On to step 3:
559 divided by 61 is 9 with a remainder of 10.
Use 9 as the next digit of our solution. 
Result so far: 9.0
The remainder is 10 after subtracting 549 from 559.
Include the next digit (9) from the dividend after 10, then repeat: 109 / 61

Advancing to step 4:
The number 61 fits into 109 1 times, leaving a remainder of 48.
Record the quotient 1 as the next digit in the result. 
Result so far: 91.0
The remainder is 48 after subtracting 61 from 109.
Bring next digit (8) of the dividend behind the 48 and repeat the process: 488 / 61

On to step 5:
488 divided by 61 is 8 with a remainder of 0.
Put 8 as the next digit of the answer. 
Result so far: 918.0
Subtracting 488 from 488 leaves us with 0.
Grab the next digit (8) from the dividend, add it to 0, then carry on: 8 / 61

Let's proceed to step 6:
The number 61 fits into 8 0 times, leaving a remainder of 8.
The next digit of our result is 0. 
Result so far: 9180.0
Subtract 0 from 8 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 7:
80 divided by 61 is 1 with a remainder of 19.
Write down 1 as next digit of the result. 
Result so far: 9180.1
If we subtract 61 from 80, we get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Let's proceed to step 8:
190 divided by 61 is 3 with a remainder of 7.
The number 3 becomes the next digit in our result. 
Result so far: 9180.13
Deduct 183 from 190 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 9:
61 can be fit into 70 1 times, resulting in a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 9180.131
If we take 61 away from 70, we end up with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

On to step 10:
61 goes into 90 1 times with a remainder of 29.
Write down 1 as next digit of the result. 
Result so far: 9180.1311
Subtracting 61 from 90 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

The quotient of the division is 9180.1311, and the remainder is 0.00029.