9669 ÷ 83 
The aim is to understand the frequency of 83 in 9669.

Let's proceed to step 1:
The number 83 fits into 9 0 times, leaving a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 9 leaves us with 9.
Fetch the next digit (6) from the dividend, attach it to 9 and continue: 96 / 83

Let's proceed to step 2:
96 divided by 83 is 1 with a remainder of 13.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 83 from 96, we get 13.
Include the next digit (6) from the dividend after 13, then repeat: 136 / 83

Let's proceed to step 3:
The number 83 fits into 136 1 times, leaving a remainder of 53.
The next digit of our result is 1. 
Result so far: 11.0
Deduct 83 from 136 and we're left with 53.
Include the next digit (9) from the dividend after 53, then repeat: 539 / 83

Step 4:
83 goes into 539 6 times with a remainder of 41.
Put 6 as the next digit of the answer. 
Result so far: 116.0
Deduct 498 from 539 and we're left with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

On to step 5:
The number 83 fits into 410 4 times, leaving a remainder of 78.
Put 4 as the next digit of the answer. 
Result so far: 116.4
The remainder is 78 after subtracting 332 from 410.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Step 6:
The number 83 fits into 780 9 times, leaving a remainder of 33.
The next digit of our result is 9. 
Result so far: 116.49
If we take 747 away from 780, we end up with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Advancing to step 7:
83 goes into 330 3 times with a remainder of 81.
The next digit of our result is 3. 
Result so far: 116.493
Deduct 249 from 330 and we're left with 81.
Since there are no more digits in the dividend, we add a zero to the remainder making it 810, and continue the process.

Let's proceed to step 8:
810 divided by 83 is 9 with a remainder of 63.
Write down 9 as next digit of the result. 
Result so far: 116.4939
Deduct 747 from 810 and we're left with 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Advancing to step 9:
630 divided by 83 is 7 with a remainder of 49.
Record the quotient 7 as the next digit in the result. 
Result so far: 116.49397
If we take 581 away from 630, we end up with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Advancing to step 10:
When dividing 490 by 83, we get 5 with a remainder of 75.
Use 5 as the next digit of our solution. 
Result so far: 116.493975
If we subtract 415 from 490, we get 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Step 11:
When dividing 750 by 83, we get 9 with a remainder of 3.
Put 9 as the next digit of the answer. 
Result so far: 116.4939759
Deduct 747 from 750 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 12:
When dividing 30 by 83, we get 0 with a remainder of 30.
Write down 0 as next digit of the result. 
Result so far: 116.4939759
If we subtract 0 from 30, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 116.4939759 with a balance of 3e-08.