31825 ÷ 75 
We want to divide 31825 by 75.

On to step 1:
75 can be fit into 3 0 times, resulting in a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (1) from the dividend and append it to 3, then repeat: 31 / 75

Going ahead to step 2:
75 can be fit into 31 0 times, resulting in a remainder of 31.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 31, we end up with 31.
Include the next digit (8) from the dividend after 31, then repeat: 318 / 75

Moving on to step 3:
318 divided by 75 is 4 with a remainder of 18.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Subtract 300 from 318 to get 18.
Bring next digit (2) of the dividend behind the 18 and repeat the process: 182 / 75

On to step 4:
When dividing 182 by 75, we get 2 with a remainder of 32.
Use 2 as the next digit of our solution. 
Result so far: 42.0
If we take 150 away from 182, we end up with 32.
Include the next digit (5) from the dividend after 32, then repeat: 325 / 75

Step 5:
325 divided by 75 is 4 with a remainder of 25.
The next digit of our result is 4. 
Result so far: 424.0
If we take 300 away from 325, we end up 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.

On to step 6:
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: 424.3
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.

Step 7:
The number 75 fits into 250 3 times, leaving a remainder of 25.
Put 3 as the next digit of the answer. 
Result so far: 424.33
If we subtract 225 from 250, we 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.

The final outcome is 424.33, with a leftover of 0.025.