75981 ÷ 7 
We want to figure out the number of times 75981 can be divided by 7.

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
If we subtract 7 from 7, we get 0.
Take the next digit (5) from the dividend and append it to 0, then repeat: 5 / 7

On to step 2:
The number 7 fits into 5 0 times, leaving a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 10.0
Subtracting 0 from 5 leaves us with 5.
Append the next digit (9) from the dividend to 5 and continue with: 59 / 7

Going ahead to step 3:
7 goes into 59 8 times with a remainder of 3.
Use 8 as the next digit of our solution. 
Result so far: 108.0
If we take 56 away from 59, we end up with 3.
Grab the next digit (8) from the dividend, add it to 3, then carry on: 38 / 7

On to step 4:
If we divide 38 by 7, we get 5 and a remainder of 3.
The number 5 becomes the next digit in our result. 
Result so far: 1085.0
Deduct 35 from 38 and we're left with 3.
Grab the next digit (1) from the dividend, add it to 3, then carry on: 31 / 7

Let's proceed to step 5:
7 goes into 31 4 times with a remainder of 3.
Record the quotient 4 as the next digit in the result. 
Result so far: 10854.0
Subtracting 28 from 31 leaves us 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.

On to step 6:
7 can be fit into 30 4 times, resulting in a remainder of 2.
Record the quotient 4 as the next digit in the result. 
Result so far: 10854.4
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.

Going ahead to step 7:
The number 7 fits into 20 2 times, leaving a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 10854.42
The remainder is 6 after subtracting 14 from 20.
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:
7 can be fit into 60 8 times, resulting in a remainder of 4.
The next digit of our result is 8. 
Result so far: 10854.428
If we subtract 56 from 60, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 9:
The number 7 fits into 40 5 times, leaving a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 10854.4285
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.

On to step 10:
If we divide 50 by 7, we get 7 and a remainder of 1.
Put 7 as the next digit of the answer. 
Result so far: 10854.42857
Subtract 49 from 50 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 11:
When dividing 10 by 7, we get 1 with a remainder of 3.
The next digit of our result is 1. 
Result so far: 10854.428571
If we subtract 7 from 10, we get 3.
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:
The number 7 fits into 30 4 times, leaving a remainder of 2.
Put 4 as the next digit of the answer. 
Result so far: 10854.4285714
Deduct 28 from 30 and we're left 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:
When dividing 20 by 7, we get 2 with a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 10854.42857142
If we take 14 away from 20, we end up 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.

The final outcome is 10854.42857142, with a leftover of 6e-09.