787978 divided by 7 
The aim is to understand the frequency of 7 in 787978.

On to step 1:
7 can be fit into 7 1 times, resulting in a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 7 from 7 and we're left with 0.
Grab the next digit (8) from the dividend, add it to 0, then carry on: 8 / 7

On to step 2:
7 goes into 8 1 times with a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 11.0
If we take 7 away from 8, we end up with 1.
Fetch the next digit (7) from the dividend, attach it to 1 and continue: 17 / 7

On to step 3:
If we divide 17 by 7, we get 2 and a remainder of 3.
The number 2 becomes the next digit in our result. 
Result so far: 112.0
Subtracting 14 from 17 leaves us with 3.
Take the next digit (9) from the dividend and append it to 3, then repeat: 39 / 7

Advancing to step 4:
7 can be fit into 39 5 times, resulting in a remainder of 4.
Write down 5 as next digit of the result. 
Result so far: 1125.0
Subtract 35 from 39 to get 4.
Take the next digit (7) from the dividend and append it to 4, then repeat: 47 / 7

Step 5:
When dividing 47 by 7, we get 6 with a remainder of 5.
Record the quotient 6 as the next digit in the result. 
Result so far: 11256.0
Subtract 42 from 47 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 7

Advancing to step 6:
When dividing 58 by 7, we get 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 112568.0
If we take 56 away from 58, we end up with 2.
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 7:
If we divide 20 by 7, we get 2 and a remainder of 6.
Record the quotient 2 as the next digit in the result. 
Result so far: 112568.2
Subtract 14 from 20 to 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.

Moving on to step 8:
The number 7 fits into 60 8 times, leaving a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 112568.28
If we take 56 away from 60, 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.

Going ahead to step 9:
If we divide 40 by 7, we get 5 and a remainder of 5.
Use 5 as the next digit of our solution. 
Result so far: 112568.285
Subtract 35 from 40 to 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.

Moving on to step 10:
If we divide 50 by 7, we get 7 and a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 112568.2857
The remainder is 1 after subtracting 49 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 11:
The number 7 fits into 10 1 times, leaving a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 112568.28571
The remainder is 3 after subtracting 7 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 12:
If we divide 30 by 7, we get 4 and a remainder of 2.
The next digit of our result is 4. 
Result so far: 112568.285714
Subtracting 28 from 30 leaves us with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 13:
7 goes into 20 2 times with a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 112568.2857142
If we subtract 14 from 20, 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.

Going ahead to step 14:
7 goes into 60 8 times with a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 112568.28571428
Deduct 56 from 60 and we're left 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.

The final outcome is 112568.28571428, with a leftover of 4e-09.