513342 ÷ 7 
The aim is to understand the frequency of 7 in 513342.

Going ahead to step 1:
5 divided by 7 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 7

Going ahead to step 2:
The number 7 fits into 51 7 times, leaving a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Deduct 49 from 51 and we're left with 2.
Append the next digit (3) from the dividend to 2 and continue with: 23 / 7

Step 3:
If we divide 23 by 7, we get 3 and a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 73.0
Subtract 21 from 23 to get 2.
Fetch the next digit (3) from the dividend, attach it to 2 and continue: 23 / 7

Let's proceed to step 4:
If we divide 23 by 7, we get 3 and a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 733.0
Deduct 21 from 23 and we're left with 2.
Append the next digit (4) from the dividend to 2 and continue with: 24 / 7

Advancing to step 5:
7 can be fit into 24 3 times, resulting in a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 7333.0
Subtract 21 from 24 to get 3.
Append the next digit (2) from the dividend to 3 and continue with: 32 / 7

Going ahead to step 6:
7 goes into 32 4 times with a remainder of 4.
Record the quotient 4 as the next digit in the result. 
Result so far: 73334.0
If we take 28 away from 32, 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.

On to step 7:
If we divide 40 by 7, we get 5 and a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 73334.5
If we take 35 away from 40, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 8:
7 can be fit into 50 7 times, resulting in a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 73334.57
Subtracting 49 from 50 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 9:
10 divided by 7 is 1 with a remainder of 3.
The next digit of our result is 1. 
Result so far: 73334.571
If we take 7 away from 10, we end up 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.

Step 10:
7 goes into 30 4 times with a remainder of 2.
Put 4 as the next digit of the answer. 
Result so far: 73334.5714
The remainder is 2 after subtracting 28 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Moving on to step 11:
20 divided by 7 is 2 with a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 73334.57142
Deduct 14 from 20 and we're left with 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 12:
7 can be fit into 60 8 times, resulting in a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 73334.571428
Subtracting 56 from 60 leaves us 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.

On to step 13:
If we divide 40 by 7, we get 5 and a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 73334.5714285
The remainder is 5 after subtracting 35 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 14:
7 goes into 50 7 times with a remainder of 1.
The number 7 becomes the next digit in our result. 
Result so far: 73334.57142857
Subtracting 49 from 50 leaves us with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

After the division, we end up with 73334.57142857 and a remainder of 1e-09.