11135 divided by 31 
We want to figure out the number of times 11135 can be divided by 31.

On to step 1:
If we divide 1 by 31, we get 0 and a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Include the next digit (1) from the dividend after 1, then repeat: 11 / 31

On to step 2:
If we divide 11 by 31, we get 0 and a remainder of 11.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 11 to get 11.
Take the next digit (1) from the dividend and append it to 11, then repeat: 111 / 31

Going ahead to step 3:
111 divided by 31 is 3 with a remainder of 18.
Write down 3 as next digit of the result. 
Result so far: 3.0
Subtracting 93 from 111 leaves us with 18.
Include the next digit (3) from the dividend after 18, then repeat: 183 / 31

Let's proceed to step 4:
When dividing 183 by 31, we get 5 with a remainder of 28.
The next digit of our result is 5. 
Result so far: 35.0
If we subtract 155 from 183, we get 28.
Fetch the next digit (5) from the dividend, attach it to 28 and continue: 285 / 31

Let's proceed to step 5:
When dividing 285 by 31, we get 9 with a remainder of 6.
Record the quotient 9 as the next digit in the result. 
Result so far: 359.0
If we take 279 away from 285, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 6:
31 can be fit into 60 1 times, resulting in a remainder of 29.
The number 1 becomes the next digit in our result. 
Result so far: 359.1
Deduct 31 from 60 and we're left with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Going ahead to step 7:
If we divide 290 by 31, we get 9 and a remainder of 11.
Put 9 as the next digit of the answer. 
Result so far: 359.19
If we take 279 away from 290, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 8:
31 goes into 110 3 times with a remainder of 17.
The next digit of our result is 3. 
Result so far: 359.193
The remainder is 17 after subtracting 93 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Advancing to step 9:
31 can be fit into 170 5 times, resulting in a remainder of 15.
The number 5 becomes the next digit in our result. 
Result so far: 359.1935
The remainder is 15 after subtracting 155 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 10:
The number 31 fits into 150 4 times, leaving a remainder of 26.
The next digit of our result is 4. 
Result so far: 359.19354
Subtract 124 from 150 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Let's proceed to step 11:
31 goes into 260 8 times with a remainder of 12.
The number 8 becomes the next digit in our result. 
Result so far: 359.193548
Deduct 248 from 260 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 12:
120 divided by 31 is 3 with a remainder of 27.
The number 3 becomes the next digit in our result. 
Result so far: 359.1935483
Subtract 93 from 120 to get 27.
Since there are no more digits in the dividend, we add a zero to the remainder making it 270, and continue the process.

Step 13:
The number 31 fits into 270 8 times, leaving a remainder of 22.
Write down 8 as next digit of the result. 
Result so far: 359.19354838
If we take 248 away from 270, we end up with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

The final result is 359.19354838 with a remainder of 2.2e-08.