509765 ÷ 97 
The aim is to understand the frequency of 97 in 509765.

Moving on to step 1:
If we divide 5 by 97, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 97

Going ahead to step 2:
When dividing 50 by 97, we get 0 with a remainder of 50.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 50 to get 50.
Bring next digit (9) of the dividend behind the 50 and repeat the process: 509 / 97

Going ahead to step 3:
97 goes into 509 5 times with a remainder of 24.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtract 485 from 509 to get 24.
Bring next digit (7) of the dividend behind the 24 and repeat the process: 247 / 97

Moving on to step 4:
97 can be fit into 247 2 times, resulting in a remainder of 53.
Use 2 as the next digit of our solution. 
Result so far: 52.0
Subtracting 194 from 247 leaves us with 53.
Bring next digit (6) of the dividend behind the 53 and repeat the process: 536 / 97

Step 5:
97 can be fit into 536 5 times, resulting in a remainder of 51.
Record the quotient 5 as the next digit in the result. 
Result so far: 525.0
The remainder is 51 after subtracting 485 from 536.
Fetch the next digit (5) from the dividend, attach it to 51 and continue: 515 / 97

Advancing to step 6:
97 goes into 515 5 times with a remainder of 30.
Record the quotient 5 as the next digit in the result. 
Result so far: 5255.0
Subtract 485 from 515 to 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.

Let's proceed to step 7:
The number 97 fits into 300 3 times, leaving a remainder of 9.
The number 3 becomes the next digit in our result. 
Result so far: 5255.3
Subtracting 291 from 300 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 8:
97 can be fit into 90 0 times, resulting in a remainder of 90.
The number 0 becomes the next digit in our result. 
Result so far: 5255.3
The remainder is 90 after subtracting 0 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

Let's proceed to step 9:
900 divided by 97 is 9 with a remainder of 27.
The number 9 becomes the next digit in our result. 
Result so far: 5255.309
The remainder is 27 after subtracting 873 from 900.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

On to step 10:
The number 97 fits into 270 2 times, leaving a remainder of 76.
Record the quotient 2 as the next digit in the result. 
Result so far: 5255.3092
Subtract 194 from 270 to get 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Step 11:
97 goes into 760 7 times with a remainder of 81.
Use 7 as the next digit of our solution. 
Result so far: 5255.30927
If we take 679 away from 760, we end up 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 12:
810 divided by 97 is 8 with a remainder of 34.
Record the quotient 8 as the next digit in the result. 
Result so far: 5255.309278
Deduct 776 from 810 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 13:
If we divide 340 by 97, we get 3 and a remainder of 49.
Put 3 as the next digit of the answer. 
Result so far: 5255.3092783
If we take 291 away from 340, 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.

On to step 14:
490 divided by 97 is 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 5255.30927835
If we subtract 485 from 490, 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.

In conclusion, the division gives 5255.30927835 with a balance of 5e-09.