7824 ÷ 14 
We want to divide 7824 by 14.

Going ahead to step 1:
14 can be fit into 7 0 times, resulting in a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Append the next digit (8) from the dividend to 7 and continue with: 78 / 14

Moving on to step 2:
When dividing 78 by 14, we get 5 with a remainder of 8.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we subtract 70 from 78, we get 8.
Append the next digit (2) from the dividend to 8 and continue with: 82 / 14

Moving on to step 3:
The number 14 fits into 82 5 times, leaving a remainder of 12.
Put 5 as the next digit of the answer. 
Result so far: 55.0
If we take 70 away from 82, we end up with 12.
Append the next digit (4) from the dividend to 12 and continue with: 124 / 14

Step 4:
When dividing 124 by 14, we get 8 with a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 558.0
The remainder is 12 after subtracting 112 from 124.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 5:
14 can be fit into 120 8 times, resulting in a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 558.8
The remainder is 8 after subtracting 112 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 6:
14 goes into 80 5 times with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 558.85
Subtract 70 from 80 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.

On to step 7:
100 divided by 14 is 7 with a remainder of 2.
The number 7 becomes the next digit in our result. 
Result so far: 558.857
Subtracting 98 from 100 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.

Let's proceed to step 8:
When dividing 20 by 14, we get 1 with a remainder of 6.
Write down 1 as next digit of the result. 
Result so far: 558.8571
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.

On to step 9:
When dividing 60 by 14, we get 4 with a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 558.85714
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.

Let's proceed to step 10:
14 can be fit into 40 2 times, resulting in a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 558.857142
If we subtract 28 from 40, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 11:
120 divided by 14 is 8 with a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 558.8571428
The remainder is 8 after subtracting 112 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 12:
14 can be fit into 80 5 times, resulting in a remainder of 10.
Write down 5 as next digit of the result. 
Result so far: 558.85714285
Deduct 70 from 80 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The final outcome is 558.85714285, with a leftover of 1e-08.