Let's divide 76966 by 75
We want to divide 76966 by 75.

Moving on to step 1:
7 divided by 75 is 0 with a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 7 after subtracting 0 from 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 75

Going ahead to step 2:
76 divided by 75 is 1 with a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 75 away from 76, we end up with 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 75

Step 3:
The number 75 fits into 19 0 times, leaving a remainder of 19.
Write down 0 as next digit of the result. 
Result so far: 10.0
If we take 0 away from 19, we end up with 19.
Take the next digit (6) from the dividend and append it to 19, then repeat: 196 / 75

Let's proceed to step 4:
The number 75 fits into 196 2 times, leaving a remainder of 46.
The next digit of our result is 2. 
Result so far: 102.0
Subtract 150 from 196 to get 46.
Grab the next digit (6) from the dividend, add it to 46, then carry on: 466 / 75

Step 5:
If we divide 466 by 75, we get 6 and a remainder of 16.
The number 6 becomes the next digit in our result. 
Result so far: 1026.0
Deduct 450 from 466 and we're left 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 6:
If we divide 160 by 75, we get 2 and a remainder of 10.
Use 2 as the next digit of our solution. 
Result so far: 1026.2
Subtract 150 from 160 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.

Step 7:
75 can be fit into 100 1 times, resulting in a remainder of 25.
Use 1 as the next digit of our solution. 
Result so far: 1026.21
Subtracting 75 from 100 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
75 can be fit into 250 3 times, resulting in a remainder of 25.
The next digit of our result is 3. 
Result so far: 1026.213
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Advancing to step 9:
250 divided by 75 is 3 with a remainder of 25.
Use 3 as the next digit of our solution. 
Result so far: 1026.2133
If we take 225 away from 250, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 1026.2133 with a balance of 0.00025.