We're dividing 135565 by 30 
We want to figure out the number of times 135565 can be divided by 30.

Step 1:
When dividing 1 by 30, we get 0 with 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.
Append the next digit (3) from the dividend to 1 and continue with: 13 / 30

Going ahead to step 2:
30 goes into 13 0 times with a remainder of 13.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 13 after subtracting 0 from 13.
Grab the next digit (5) from the dividend, add it to 13, then carry on: 135 / 30

Advancing to step 3:
30 can be fit into 135 4 times, resulting in a remainder of 15.
The next digit of our result is 4. 
Result so far: 4.0
Subtracting 120 from 135 leaves us with 15.
Include the next digit (5) from the dividend after 15, then repeat: 155 / 30

Let's proceed to step 4:
155 divided by 30 is 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 45.0
Subtracting 150 from 155 leaves us with 5.
Include the next digit (6) from the dividend after 5, then repeat: 56 / 30

Going ahead to step 5:
30 goes into 56 1 times with a remainder of 26.
Write down 1 as next digit of the result. 
Result so far: 451.0
If we take 30 away from 56, we end up with 26.
Include the next digit (5) from the dividend after 26, then repeat: 265 / 30

Step 6:
30 goes into 265 8 times with a remainder of 25.
The number 8 becomes the next digit in our result. 
Result so far: 4518.0
The remainder is 25 after subtracting 240 from 265.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 7:
When dividing 250 by 30, we get 8 with a remainder of 10.
The next digit of our result is 8. 
Result so far: 4518.8
Subtracting 240 from 250 leaves us 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.

On to step 8:
If we divide 100 by 30, we get 3 and a remainder of 10.
The number 3 becomes the next digit in our result. 
Result so far: 4518.83
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 9:
If we divide 100 by 30, we get 3 and a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 4518.833
If we subtract 90 from 100, we 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.

After the division, we end up with 4518.833 and a remainder of 0.001.