501112 ÷ 42 
The aim is to understand the frequency of 42 in 501112.

Advancing to step 1:
When dividing 5 by 42, we get 0 with a remainder of 5.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Grab the next digit (0) from the dividend, add it to 5, then carry on: 50 / 42

Step 2:
If we divide 50 by 42, we get 1 and a remainder of 8.
The next digit of our result is 1. 
Result so far: 1.0
The remainder is 8 after subtracting 42 from 50.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 42

Advancing to step 3:
If we divide 81 by 42, we get 1 and a remainder of 39.
Record the quotient 1 as the next digit in the result. 
Result so far: 11.0
The remainder is 39 after subtracting 42 from 81.
Grab the next digit (1) from the dividend, add it to 39, then carry on: 391 / 42

Going ahead to step 4:
391 divided by 42 is 9 with a remainder of 13.
The next digit of our result is 9. 
Result so far: 119.0
Subtract 378 from 391 to get 13.
Grab the next digit (1) from the dividend, add it to 13, then carry on: 131 / 42

Moving on to step 5:
42 can be fit into 131 3 times, resulting in a remainder of 5.
The next digit of our result is 3. 
Result so far: 1193.0
If we take 126 away from 131, we end up with 5.
Grab the next digit (2) from the dividend, add it to 5, then carry on: 52 / 42

Advancing to step 6:
The number 42 fits into 52 1 times, leaving a remainder of 10.
Put 1 as the next digit of the answer. 
Result so far: 11931.0
The remainder is 10 after subtracting 42 from 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 7:
The number 42 fits into 100 2 times, leaving a remainder of 16.
Use 2 as the next digit of our solution. 
Result so far: 11931.2
If we subtract 84 from 100, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 8:
160 divided by 42 is 3 with a remainder of 34.
Use 3 as the next digit of our solution. 
Result so far: 11931.23
The remainder is 34 after subtracting 126 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Moving on to step 9:
When dividing 340 by 42, we get 8 with a remainder of 4.
Use 8 as the next digit of our solution. 
Result so far: 11931.238
If we take 336 away from 340, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 10:
If we divide 40 by 42, we get 0 and a remainder of 40.
The next digit of our result is 0. 
Result so far: 11931.238
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 11:
If we divide 400 by 42, we get 9 and a remainder of 22.
The number 9 becomes the next digit in our result. 
Result so far: 11931.23809
The remainder is 22 after subtracting 378 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Going ahead to step 12:
42 can be fit into 220 5 times, resulting in a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 11931.238095
Subtract 210 from 220 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 13:
When dividing 100 by 42, we get 2 with a remainder of 16.
Use 2 as the next digit of our solution. 
Result so far: 11931.2380952
If we take 84 away from 100, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

On to step 14:
42 can be fit into 160 3 times, resulting in a remainder of 34.
Put 3 as the next digit of the answer. 
Result so far: 11931.23809523
The remainder is 34 after subtracting 126 from 160.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

In conclusion, the division gives 11931.23809523 with a balance of 3.4e-08.