821875 ÷ 11 
Our goal is to divide 821875 by 11.

Moving on to step 1:
When dividing 8 by 11, we get 0 with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 8 after subtracting 0 from 8.
Grab the next digit (2) from the dividend, add it to 8, then carry on: 82 / 11

On to step 2:
When dividing 82 by 11, we get 7 with a remainder of 5.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Subtract 77 from 82 to get 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 11

Step 3:
If we divide 51 by 11, we get 4 and a remainder of 7.
The number 4 becomes the next digit in our result. 
Result so far: 74.0
Deduct 44 from 51 and we're left with 7.
Append the next digit (8) from the dividend to 7 and continue with: 78 / 11

Moving on to step 4:
11 goes into 78 7 times with a remainder of 1.
Write down 7 as next digit of the result. 
Result so far: 747.0
Deduct 77 from 78 and we're left with 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 11

Advancing to step 5:
The number 11 fits into 17 1 times, leaving a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 7471.0
Subtracting 11 from 17 leaves us with 6.
Grab the next digit (5) from the dividend, add it to 6, then carry on: 65 / 11

Let's proceed to step 6:
When dividing 65 by 11, we get 5 with a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 74715.0
Subtract 55 from 65 to get 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 7:
100 divided by 11 is 9 with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 74715.9
Subtracting 99 from 100 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 8:
10 divided by 11 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 74715.9
If we take 0 away from 10, 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 9:
100 divided by 11 is 9 with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 74715.909
Deduct 99 from 100 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 10:
11 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 74715.909
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 11:
If we divide 100 by 11, we get 9 and a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 74715.90909
If we take 99 away from 100, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 12:
11 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 74715.90909
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 13:
The number 11 fits into 100 9 times, leaving a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 74715.9090909
If we take 99 away from 100, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 14:
When dividing 10 by 11, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 74715.9090909
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

After the division, we end up with 74715.9090909 and a remainder of 1e-08.