125031 ÷ 25 
Our goal is to divide 125031 by 25.

On to step 1:
25 can be fit into 1 0 times, resulting in a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Grab the next digit (2) from the dividend, add it to 1, then carry on: 12 / 25

Going ahead to step 2:
When dividing 12 by 25, we get 0 with a remainder of 12.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 12 to get 12.
Grab the next digit (5) from the dividend, add it to 12, then carry on: 125 / 25

Moving on to step 3:
When dividing 125 by 25, we get 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 5.0
Subtract 125 from 125 to get 0.
Append the next digit (0) from the dividend to 0 and continue with: 0 / 25

On to step 4:
When dividing 0 by 25, we get 0 with a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 50.0
If we subtract 0 from 0, we get 0.
Take the next digit (3) from the dividend and append it to 0, then repeat: 3 / 25

Going ahead to step 5:
If we divide 3 by 25, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 500.0
The remainder is 3 after subtracting 0 from 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 25

Going ahead to step 6:
31 divided by 25 is 1 with a remainder of 6.
The next digit of our result is 1. 
Result so far: 5001.0
The remainder is 6 after subtracting 25 from 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 7:
25 can be fit into 60 2 times, resulting in a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 5001.2
If we take 50 away from 60, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
When dividing 100 by 25, we get 4 with a remainder of 0.
The next digit of our result is 4. 
Result so far: 5001.24
Deduct 100 from 100 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 9:
0 divided by 25 is 0 with a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 5001.24
The remainder is 0 after subtracting 0 from 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 10:
If we divide 0 by 25, we get 0 and a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 5001.24
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 5001.24 with a balance of 0.0.