We're dividing 9255561 by 638 
The aim is to understand the frequency of 638 in 9255561.

Advancing to step 1:
When dividing 9 by 638, we get 0 with a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 9, we get 9.
Grab the next digit (2) from the dividend, add it to 9, then carry on: 92 / 638

On to step 2:
638 goes into 92 0 times with a remainder of 92.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 92 and we're left with 92.
Include the next digit (5) from the dividend after 92, then repeat: 925 / 638

Let's proceed to step 3:
When dividing 925 by 638, we get 1 with a remainder of 287.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 638 from 925 and we're left with 287.
Take the next digit (5) from the dividend and append it to 287, then repeat: 2875 / 638

Step 4:
When dividing 2875 by 638, we get 4 with a remainder of 323.
Put 4 as the next digit of the answer. 
Result so far: 14.0
Subtract 2552 from 2875 to get 323.
Fetch the next digit (5) from the dividend, attach it to 323 and continue: 3235 / 638

Step 5:
The number 638 fits into 3235 5 times, leaving a remainder of 45.
Use 5 as the next digit of our solution. 
Result so far: 145.0
If we take 3190 away from 3235, we end up with 45.
Fetch the next digit (6) from the dividend, attach it to 45 and continue: 456 / 638

Going ahead to step 6:
The number 638 fits into 456 0 times, leaving a remainder of 456.
Record the quotient 0 as the next digit in the result. 
Result so far: 1450.0
Subtract 0 from 456 to get 456.
Include the next digit (1) from the dividend after 456, then repeat: 4561 / 638

Going ahead to step 7:
The number 638 fits into 4561 7 times, leaving a remainder of 95.
The number 7 becomes the next digit in our result. 
Result so far: 14507.0
Subtracting 4466 from 4561 leaves us with 95.
Since there are no more digits in the dividend, we add a zero to the remainder making it 950, and continue the process.

Advancing to step 8:
The number 638 fits into 950 1 times, leaving a remainder of 312.
Put 1 as the next digit of the answer. 
Result so far: 14507.1
If we take 638 away from 950, we end up with 312.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3120, and continue the process.

Moving on to step 9:
638 goes into 3120 4 times with a remainder of 568.
Use 4 as the next digit of our solution. 
Result so far: 14507.14
Deduct 2552 from 3120 and we're left with 568.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5680, and continue the process.

Step 10:
When dividing 5680 by 638, we get 8 with a remainder of 576.
The next digit of our result is 8. 
Result so far: 14507.148
The remainder is 576 after subtracting 5104 from 5680.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5760, and continue the process.

Going ahead to step 11:
If we divide 5760 by 638, we get 9 and a remainder of 18.
Put 9 as the next digit of the answer. 
Result so far: 14507.1489
Subtract 5742 from 5760 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 12:
180 divided by 638 is 0 with a remainder of 180.
Use 0 as the next digit of our solution. 
Result so far: 14507.1489
If we subtract 0 from 180, we get 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1800, and continue the process.

Going ahead to step 13:
If we divide 1800 by 638, we get 2 and a remainder of 524.
The next digit of our result is 2. 
Result so far: 14507.148902
Subtract 1276 from 1800 to get 524.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5240, and continue the process.

Advancing to step 14:
When dividing 5240 by 638, we get 8 with a remainder of 136.
Use 8 as the next digit of our solution. 
Result so far: 14507.1489028
Subtracting 5104 from 5240 leaves us with 136.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1360, and continue the process.

Let's proceed to step 15:
1360 divided by 638 is 2 with a remainder of 84.
Use 2 as the next digit of our solution. 
Result so far: 14507.14890282
Subtract 1276 from 1360 to get 84.
Since there are no more digits in the dividend, we add a zero to the remainder making it 840, and continue the process.

After the division, we end up with 14507.14890282 and a remainder of 8.4e-08.