We're dividing 13634 by 9 
We're looking to find how many times 9 goes into 13634.

Going ahead to step 1:
The number 9 fits into 1 0 times, leaving a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 9

Step 2:
The number 9 fits into 13 1 times, leaving a remainder of 4.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 9 from 13 to get 4.
Take the next digit (6) from the dividend and append it to 4, then repeat: 46 / 9

Advancing to step 3:
If we divide 46 by 9, we get 5 and a remainder of 1.
Record the quotient 5 as the next digit in the result. 
Result so far: 15.0
The remainder is 1 after subtracting 45 from 46.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 9

Step 4:
9 goes into 13 1 times with a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 151.0
If we take 9 away from 13, we end up with 4.
Fetch the next digit (4) from the dividend, attach it to 4 and continue: 44 / 9

Going ahead to step 5:
If we divide 44 by 9, we get 4 and a remainder of 8.
Record the quotient 4 as the next digit in the result. 
Result so far: 1514.0
If we subtract 36 from 44, 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 6:
80 divided by 9 is 8 with a remainder of 8.
The next digit of our result is 8. 
Result so far: 1514.8
The remainder is 8 after subtracting 72 from 80.
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:
The number 9 fits into 80 8 times, leaving a remainder of 8.
Use 8 as the next digit of our solution. 
Result so far: 1514.88
The remainder is 8 after subtracting 72 from 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

The quotient of the division is 1514.88, and the remainder is 0.008.