We're dividing 31337 by 83 
We want to figure out the number of times 31337 can be divided by 83.

On to step 1:
The number 83 fits into 3 0 times, leaving a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Fetch the next digit (1) from the dividend, attach it to 3 and continue: 31 / 83

Advancing to step 2:
31 divided by 83 is 0 with a remainder of 31.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 31 and we're left with 31.
Append the next digit (3) from the dividend to 31 and continue with: 313 / 83

On to step 3:
When dividing 313 by 83, we get 3 with a remainder of 64.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we take 249 away from 313, we end up with 64.
Grab the next digit (3) from the dividend, add it to 64, then carry on: 643 / 83

Advancing to step 4:
643 divided by 83 is 7 with a remainder of 62.
Put 7 as the next digit of the answer. 
Result so far: 37.0
Deduct 581 from 643 and we're left with 62.
Grab the next digit (7) from the dividend, add it to 62, then carry on: 627 / 83

Going ahead to step 5:
83 goes into 627 7 times with a remainder of 46.
Put 7 as the next digit of the answer. 
Result so far: 377.0
If we take 581 away from 627, we end up with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 6:
When dividing 460 by 83, we get 5 with a remainder of 45.
Record the quotient 5 as the next digit in the result. 
Result so far: 377.5
If we subtract 415 from 460, we get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Moving on to step 7:
83 can be fit into 450 5 times, resulting in a remainder of 35.
Put 5 as the next digit of the answer. 
Result so far: 377.55
If we subtract 415 from 450, we get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Our division results in 377.55 with a remaining 0.035.