501413 ÷ 97 
The aim is to understand the frequency of 97 in 501413.

On to step 1:
The number 97 fits into 5 0 times, leaving a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 97

Advancing to step 2:
50 divided by 97 is 0 with a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 50, we get 50.
Grab the next digit (1) from the dividend, add it to 50, then carry on: 501 / 97

On to step 3:
When dividing 501 by 97, we get 5 with a remainder of 16.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 485 from 501 leaves us with 16.
Bring next digit (4) of the dividend behind the 16 and repeat the process: 164 / 97

Advancing to step 4:
164 divided by 97 is 1 with a remainder of 67.
The number 1 becomes the next digit in our result. 
Result so far: 51.0
Subtract 97 from 164 to get 67.
Bring next digit (1) of the dividend behind the 67 and repeat the process: 671 / 97

Let's proceed to step 5:
97 can be fit into 671 6 times, resulting in a remainder of 89.
Write down 6 as next digit of the result. 
Result so far: 516.0
If we subtract 582 from 671, we get 89.
Bring next digit (3) of the dividend behind the 89 and repeat the process: 893 / 97

Advancing to step 6:
97 goes into 893 9 times with a remainder of 20.
Record the quotient 9 as the next digit in the result. 
Result so far: 5169.0
Deduct 873 from 893 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Moving on to step 7:
The number 97 fits into 200 2 times, leaving a remainder of 6.
Put 2 as the next digit of the answer. 
Result so far: 5169.2
If we subtract 194 from 200, we 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 8:
The number 97 fits into 60 0 times, leaving a remainder of 60.
Use 0 as the next digit of our solution. 
Result so far: 5169.2
If we take 0 away from 60, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Step 9:
97 can be fit into 600 6 times, resulting in a remainder of 18.
Use 6 as the next digit of our solution. 
Result so far: 5169.206
Subtract 582 from 600 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.

Moving on to step 10:
97 goes into 180 1 times with a remainder of 83.
Record the quotient 1 as the next digit in the result. 
Result so far: 5169.2061
Subtracting 97 from 180 leaves us with 83.
Since there are no more digits in the dividend, we add a zero to the remainder making it 830, and continue the process.

Step 11:
830 divided by 97 is 8 with a remainder of 54.
The next digit of our result is 8. 
Result so far: 5169.20618
Subtracting 776 from 830 leaves us with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

On to step 12:
When dividing 540 by 97, we get 5 with a remainder of 55.
Record the quotient 5 as the next digit in the result. 
Result so far: 5169.206185
If we subtract 485 from 540, we get 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 13:
550 divided by 97 is 5 with a remainder of 65.
Put 5 as the next digit of the answer. 
Result so far: 5169.2061855
The remainder is 65 after subtracting 485 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

In conclusion, the division gives 5169.2061855 with a balance of 6.5e-07.