9556 ÷ 75 
We're looking to find how many times 75 goes into 9556.

On to step 1:
75 goes into 9 0 times with a remainder of 9.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 9 leaves us with 9.
Take the next digit (5) from the dividend and append it to 9, then repeat: 95 / 75

Advancing to step 2:
75 can be fit into 95 1 times, resulting in a remainder of 20.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 20 after subtracting 75 from 95.
Fetch the next digit (5) from the dividend, attach it to 20 and continue: 205 / 75

Moving on to step 3:
When dividing 205 by 75, we get 2 with a remainder of 55.
Put 2 as the next digit of the answer. 
Result so far: 12.0
If we take 150 away from 205, we end up with 55.
Bring next digit (6) of the dividend behind the 55 and repeat the process: 556 / 75

Advancing to step 4:
75 can be fit into 556 7 times, resulting in a remainder of 31.
Write down 7 as next digit of the result. 
Result so far: 127.0
If we take 525 away from 556, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 5:
310 divided by 75 is 4 with a remainder of 10.
Use 4 as the next digit of our solution. 
Result so far: 127.4
If we subtract 300 from 310, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 6:
75 can be fit into 100 1 times, resulting in a remainder of 25.
The number 1 becomes the next digit in our result. 
Result so far: 127.41
The remainder is 25 after subtracting 75 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 7:
250 divided by 75 is 3 with a remainder of 25.
Write down 3 as next digit of the result. 
Result so far: 127.413
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 8:
When dividing 250 by 75, we get 3 with a remainder of 25.
Use 3 as the next digit of our solution. 
Result so far: 127.4133
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Our division results in 127.4133 with a remaining 0.00025.