Let's divide 13819 by 11
Our goal is to divide 13819 by 11.

Moving on to step 1:
The number 11 fits into 1 0 times, leaving a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 11

Going ahead to step 2:
13 divided by 11 is 1 with a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Subtract 11 from 13 to get 2.
Append the next digit (8) from the dividend to 2 and continue with: 28 / 11

On to step 3:
11 can be fit into 28 2 times, resulting in a remainder of 6.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Subtract 22 from 28 to get 6.
Take the next digit (1) from the dividend and append it to 6, then repeat: 61 / 11

Advancing to step 4:
11 can be fit into 61 5 times, resulting in a remainder of 6.
The next digit of our result is 5. 
Result so far: 125.0
The remainder is 6 after subtracting 55 from 61.
Append the next digit (9) from the dividend to 6 and continue with: 69 / 11

Let's proceed to step 5:
If we divide 69 by 11, we get 6 and a remainder of 3.
Put 6 as the next digit of the answer. 
Result so far: 1256.0
If we take 66 away from 69, we end up 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.

Moving on to step 6:
When dividing 30 by 11, we get 2 with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 1256.2
If we subtract 22 from 30, we get 8.
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 7:
11 can be fit into 80 7 times, resulting in a remainder of 3.
The number 7 becomes the next digit in our result. 
Result so far: 1256.27
If we subtract 77 from 80, 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.

Let's proceed to step 8:
The number 11 fits into 30 2 times, leaving a remainder of 8.
Write down 2 as next digit of the result. 
Result so far: 1256.272
The remainder is 8 after subtracting 22 from 30.
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 9:
The number 11 fits into 80 7 times, leaving a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 1256.2727
If we subtract 77 from 80, 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.

Step 10:
30 divided by 11 is 2 with a remainder of 8.
Use 2 as the next digit of our solution. 
Result so far: 1256.27272
Deduct 22 from 30 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 11:
11 can be fit into 80 7 times, resulting in a remainder of 3.
The next digit of our result is 7. 
Result so far: 1256.272727
The remainder is 3 after subtracting 77 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 12:
If we divide 30 by 11, we get 2 and a remainder of 8.
The next digit of our result is 2. 
Result so far: 1256.2727272
Deduct 22 from 30 and we're left with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 13:
When dividing 80 by 11, we get 7 with a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 1256.27272727
Subtracting 77 from 80 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.

The quotient of the division is 1256.27272727, and the remainder is 3e-09.