515663 ÷ 75 
Our goal is to divide 515663 by 75.

Advancing to step 1:
5 divided by 75 is 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 75

On to step 2:
The number 75 fits into 51 0 times, leaving a remainder of 51.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Append the next digit (5) from the dividend to 51 and continue with: 515 / 75

Let's proceed to step 3:
75 goes into 515 6 times with a remainder of 65.
The number 6 becomes the next digit in our result. 
Result so far: 6.0
If we subtract 450 from 515, we get 65.
Append the next digit (6) from the dividend to 65 and continue with: 656 / 75

Moving on to step 4:
The number 75 fits into 656 8 times, leaving a remainder of 56.
Record the quotient 8 as the next digit in the result. 
Result so far: 68.0
If we subtract 600 from 656, we get 56.
Append the next digit (6) from the dividend to 56 and continue with: 566 / 75

Step 5:
When dividing 566 by 75, we get 7 with a remainder of 41.
Use 7 as the next digit of our solution. 
Result so far: 687.0
Subtract 525 from 566 to get 41.
Bring next digit (3) of the dividend behind the 41 and repeat the process: 413 / 75

Going ahead to step 6:
If we divide 413 by 75, we get 5 and a remainder of 38.
Write down 5 as next digit of the result. 
Result so far: 6875.0
Subtracting 375 from 413 leaves us 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.

Going ahead to step 7:
When dividing 380 by 75, we get 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 6875.5
Deduct 375 from 380 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
75 can be fit into 50 0 times, resulting in a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 6875.5
If we take 0 away from 50, we end up with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

On to step 9:
If we divide 500 by 75, we get 6 and a remainder of 50.
Use 6 as the next digit of our solution. 
Result so far: 6875.506
Subtract 450 from 500 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 10:
The number 75 fits into 500 6 times, leaving a remainder of 50.
Write down 6 as next digit of the result. 
Result so far: 6875.5066
Deduct 450 from 500 and we're left with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

In conclusion, the division gives 6875.5066 with a balance of 0.0005.