19119 ÷ 38 
We want to figure out the number of times 19119 can be divided by 38.

Step 1:
1 divided by 38 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Append the next digit (9) from the dividend to 1 and continue with: 19 / 38

Step 2:
38 goes into 19 0 times with a remainder of 19.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 19, we end up with 19.
Fetch the next digit (1) from the dividend, attach it to 19 and continue: 191 / 38

On to step 3:
When dividing 191 by 38, we get 5 with a remainder of 1.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtract 190 from 191 to get 1.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 38

Step 4:
11 divided by 38 is 0 with a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 50.0
The remainder is 11 after subtracting 0 from 11.
Grab the next digit (9) from the dividend, add it to 11, then carry on: 119 / 38

Step 5:
38 goes into 119 3 times with a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 503.0
If we subtract 114 from 119, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 6:
38 can be fit into 50 1 times, resulting in a remainder of 12.
The next digit of our result is 1. 
Result so far: 503.1
Subtract 38 from 50 to 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.

Moving on to step 7:
The number 38 fits into 120 3 times, leaving a remainder of 6.
The next digit of our result is 3. 
Result so far: 503.13
If we subtract 114 from 120, 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.

Let's proceed to step 8:
38 goes into 60 1 times with a remainder of 22.
Record the quotient 1 as the next digit in the result. 
Result so far: 503.131
Subtract 38 from 60 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 9:
If we divide 220 by 38, we get 5 and a remainder of 30.
Write down 5 as next digit of the result. 
Result so far: 503.1315
If we take 190 away from 220, we end up 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.

Let's proceed to step 10:
If we divide 300 by 38, we get 7 and a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 503.13157
The remainder is 34 after subtracting 266 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Step 11:
When dividing 340 by 38, we get 8 with a remainder of 36.
The number 8 becomes the next digit in our result. 
Result so far: 503.131578
The remainder is 36 after subtracting 304 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 12:
38 goes into 360 9 times with a remainder of 18.
Write down 9 as next digit of the result. 
Result so far: 503.1315789
If we take 342 away from 360, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 13:
The number 38 fits into 180 4 times, leaving a remainder of 28.
The number 4 becomes the next digit in our result. 
Result so far: 503.13157894
Subtract 152 from 180 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

After the division, we end up with 503.13157894 and a remainder of 2.8e-08.