35981 ÷ 9 
The aim is to understand the frequency of 9 in 35981.

Advancing to step 1:
When dividing 3 by 9, we get 0 with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Take the next digit (5) from the dividend and append it to 3, then repeat: 35 / 9

Going ahead to step 2:
The number 9 fits into 35 3 times, leaving a remainder of 8.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Subtract 27 from 35 to get 8.
Fetch the next digit (9) from the dividend, attach it to 8 and continue: 89 / 9

On to step 3:
When dividing 89 by 9, we get 9 with a remainder of 8.
Put 9 as the next digit of the answer. 
Result so far: 39.0
Deduct 81 from 89 and we're left with 8.
Take the next digit (8) from the dividend and append it to 8, then repeat: 88 / 9

Advancing to step 4:
9 goes into 88 9 times with a remainder of 7.
Put 9 as the next digit of the answer. 
Result so far: 399.0
Subtracting 81 from 88 leaves us with 7.
Bring next digit (1) of the dividend behind the 7 and repeat the process: 71 / 9

On to step 5:
71 divided by 9 is 7 with a remainder of 8.
The number 7 becomes the next digit in our result. 
Result so far: 3997.0
Deduct 63 from 71 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 6:
When dividing 80 by 9, we get 8 with a remainder of 8.
Put 8 as the next digit of the answer. 
Result so far: 3997.8
Subtracting 72 from 80 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 7:
9 can be fit into 80 8 times, resulting in a remainder of 8.
Use 8 as the next digit of our solution. 
Result so far: 3997.88
Subtracting 72 from 80 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The quotient of the division is 3997.88, and the remainder is 0.008.