We look at the division of 82525 by 97 
Our goal is to divide 82525 by 97.

Moving on to step 1:
If we divide 8 by 97, we get 0 and a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Bring next digit (2) of the dividend behind the 8 and repeat the process: 82 / 97

Going ahead to step 2:
The number 97 fits into 82 0 times, leaving a remainder of 82.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 82 to get 82.
Grab the next digit (5) from the dividend, add it to 82, then carry on: 825 / 97

Step 3:
If we divide 825 by 97, we get 8 and a remainder of 49.
Use 8 as the next digit of our solution. 
Result so far: 8.0
If we subtract 776 from 825, we get 49.
Append the next digit (2) from the dividend to 49 and continue with: 492 / 97

Going ahead to step 4:
If we divide 492 by 97, we get 5 and a remainder of 7.
Write down 5 as next digit of the result. 
Result so far: 85.0
Subtracting 485 from 492 leaves us with 7.
Include the next digit (5) from the dividend after 7, then repeat: 75 / 97

Let's proceed to step 5:
If we divide 75 by 97, we get 0 and a remainder of 75.
The next digit of our result is 0. 
Result so far: 850.0
Subtracting 0 from 75 leaves us with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Advancing to step 6:
The number 97 fits into 750 7 times, leaving a remainder of 71.
Put 7 as the next digit of the answer. 
Result so far: 850.7
If we subtract 679 from 750, we get 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Step 7:
The number 97 fits into 710 7 times, leaving a remainder of 31.
Record the quotient 7 as the next digit in the result. 
Result so far: 850.77
If we take 679 away from 710, 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.

The quotient of the division is 850.77, and the remainder is 0.031.