109824 divided by 87 
We want to figure out the number of times 109824 can be divided by 87.

Advancing to step 1:
87 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 87

Going ahead to step 2:
When dividing 10 by 87, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Include the next digit (9) from the dividend after 10, then repeat: 109 / 87

Let's proceed to step 3:
87 can be fit into 109 1 times, resulting in a remainder of 22.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 87 from 109 leaves us with 22.
Include the next digit (8) from the dividend after 22, then repeat: 228 / 87

Step 4:
The number 87 fits into 228 2 times, leaving a remainder of 54.
The number 2 becomes the next digit in our result. 
Result so far: 12.0
The remainder is 54 after subtracting 174 from 228.
Grab the next digit (2) from the dividend, add it to 54, then carry on: 542 / 87

On to step 5:
542 divided by 87 is 6 with a remainder of 20.
Use 6 as the next digit of our solution. 
Result so far: 126.0
Deduct 522 from 542 and we're left with 20.
Fetch the next digit (4) from the dividend, attach it to 20 and continue: 204 / 87

Let's proceed to step 6:
When dividing 204 by 87, we get 2 with a remainder of 30.
The next digit of our result is 2. 
Result so far: 1262.0
Subtracting 174 from 204 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 7:
300 divided by 87 is 3 with a remainder of 39.
Write down 3 as next digit of the result. 
Result so far: 1262.3
Subtracting 261 from 300 leaves us with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Let's proceed to step 8:
If we divide 390 by 87, we get 4 and a remainder of 42.
Record the quotient 4 as the next digit in the result. 
Result so far: 1262.34
Deduct 348 from 390 and we're left with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Step 9:
If we divide 420 by 87, we get 4 and a remainder of 72.
Record the quotient 4 as the next digit in the result. 
Result so far: 1262.344
The remainder is 72 after subtracting 348 from 420.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

In conclusion, the division gives 1262.344 with a balance of 0.0072.