409666 ÷ 43 
Our goal is to divide 409666 by 43.

Step 1:
43 can be fit into 4 0 times, resulting in a remainder of 4.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 4 leaves us with 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 43

Let's proceed to step 2:
When dividing 40 by 43, we get 0 with a remainder of 40.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 40, we get 40.
Bring next digit (9) of the dividend behind the 40 and repeat the process: 409 / 43

Going ahead to step 3:
409 divided by 43 is 9 with a remainder of 22.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
If we take 387 away from 409, we end up with 22.
Fetch the next digit (6) from the dividend, attach it to 22 and continue: 226 / 43

On to step 4:
226 divided by 43 is 5 with a remainder of 11.
The number 5 becomes the next digit in our result. 
Result so far: 95.0
If we subtract 215 from 226, we get 11.
Include the next digit (6) from the dividend after 11, then repeat: 116 / 43

Advancing to step 5:
If we divide 116 by 43, we get 2 and a remainder of 30.
Use 2 as the next digit of our solution. 
Result so far: 952.0
If we subtract 86 from 116, we get 30.
Grab the next digit (6) from the dividend, add it to 30, then carry on: 306 / 43

Advancing to step 6:
43 can be fit into 306 7 times, resulting in a remainder of 5.
The number 7 becomes the next digit in our result. 
Result so far: 9527.0
The remainder is 5 after subtracting 301 from 306.
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 7:
The number 43 fits into 50 1 times, leaving a remainder of 7.
Use 1 as the next digit of our solution. 
Result so far: 9527.1
Subtract 43 from 50 to get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 8:
When dividing 70 by 43, we get 1 with a remainder of 27.
Use 1 as the next digit of our solution. 
Result so far: 9527.11
Subtract 43 from 70 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

In conclusion, the division gives 9527.11 with a balance of 0.027.