388978 ÷ 75 
We're looking to find how many times 75 goes into 388978.

On to step 1:
If we divide 3 by 75, we get 0 and a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Grab the next digit (8) from the dividend, add it to 3, then carry on: 38 / 75

Going ahead to step 2:
The number 75 fits into 38 0 times, leaving a remainder of 38.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 38 after subtracting 0 from 38.
Grab the next digit (8) from the dividend, add it to 38, then carry on: 388 / 75

On to step 3:
75 can be fit into 388 5 times, resulting in a remainder of 13.
Record the quotient 5 as the next digit in the result. 
Result so far: 5.0
The remainder is 13 after subtracting 375 from 388.
Bring next digit (9) of the dividend behind the 13 and repeat the process: 139 / 75

Moving on to step 4:
139 divided by 75 is 1 with a remainder of 64.
Put 1 as the next digit of the answer. 
Result so far: 51.0
The remainder is 64 after subtracting 75 from 139.
Include the next digit (7) from the dividend after 64, then repeat: 647 / 75

Step 5:
The number 75 fits into 647 8 times, leaving a remainder of 47.
Use 8 as the next digit of our solution. 
Result so far: 518.0
The remainder is 47 after subtracting 600 from 647.
Take the next digit (8) from the dividend and append it to 47, then repeat: 478 / 75

Going ahead to step 6:
75 goes into 478 6 times with a remainder of 28.
Use 6 as the next digit of our solution. 
Result so far: 5186.0
If we take 450 away from 478, 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.

Advancing to step 7:
If we divide 280 by 75, we get 3 and a remainder of 55.
The number 3 becomes the next digit in our result. 
Result so far: 5186.3
If we take 225 away from 280, we end up with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Going ahead to step 8:
75 goes into 550 7 times with a remainder of 25.
Put 7 as the next digit of the answer. 
Result so far: 5186.37
Subtract 525 from 550 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.

Step 9:
If we divide 250 by 75, we get 3 and a remainder of 25.
Record the quotient 3 as the next digit in the result. 
Result so far: 5186.373
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.

Moving on to step 10:
75 can be fit into 250 3 times, resulting in a remainder of 25.
The next digit of our result is 3. 
Result so far: 5186.3733
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.

In conclusion, the division gives 5186.3733 with a balance of 0.00025.