We're dividing 10697 by 11 
The aim is to understand the frequency of 11 in 10697.

Let's proceed to step 1:
11 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
Subtracting 0 from 1 leaves us with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 11

Step 2:
If we divide 10 by 11, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 11

Going ahead to step 3:
11 can be fit into 106 9 times, resulting in a remainder of 7.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
The remainder is 7 after subtracting 99 from 106.
Append the next digit (9) from the dividend to 7 and continue with: 79 / 11

Let's proceed to step 4:
If we divide 79 by 11, we get 7 and a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 97.0
Deduct 77 from 79 and we're left with 2.
Append the next digit (7) from the dividend to 2 and continue with: 27 / 11

Advancing to step 5:
11 goes into 27 2 times with a remainder of 5.
Write down 2 as next digit of the result. 
Result so far: 972.0
Subtracting 22 from 27 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 6:
50 divided by 11 is 4 with a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 972.4
Subtracting 44 from 50 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 7:
The number 11 fits into 60 5 times, leaving a remainder of 5.
The next digit of our result is 5. 
Result so far: 972.45
Subtracting 55 from 60 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 8:
11 can be fit into 50 4 times, resulting in a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 972.454
Subtract 44 from 50 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 9:
When dividing 60 by 11, we get 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 972.4545
Subtract 55 from 60 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 10:
11 can be fit into 50 4 times, resulting in a remainder of 6.
The next digit of our result is 4. 
Result so far: 972.45454
The remainder is 6 after subtracting 44 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 11:
The number 11 fits into 60 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 972.454545
If we subtract 55 from 60, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 12:
The number 11 fits into 50 4 times, leaving a remainder of 6.
The next digit of our result is 4. 
Result so far: 972.4545454
Subtract 44 from 50 to get 6.
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 13:
When dividing 60 by 11, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 972.45454545
Subtract 55 from 60 to get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 972.45454545, and the remainder is 5e-09.