965636 ÷ 9 
We're looking to find how many times 9 goes into 965636.

Going ahead to step 1:
When dividing 9 by 9, we get 1 with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
Deduct 9 from 9 and we're left with 0.
Fetch the next digit (6) from the dividend, attach it to 0 and continue: 6 / 9

Step 2:
If we divide 6 by 9, we get 0 and a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 10.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (5) from the dividend, add it to 6, then carry on: 65 / 9

Advancing to step 3:
If we divide 65 by 9, we get 7 and a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 107.0
Deduct 63 from 65 and we're left with 2.
Append the next digit (6) from the dividend to 2 and continue with: 26 / 9

Going ahead to step 4:
9 goes into 26 2 times with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 1072.0
If we take 18 away from 26, we end up with 8.
Bring next digit (3) of the dividend behind the 8 and repeat the process: 83 / 9

Moving on to step 5:
83 divided by 9 is 9 with a remainder of 2.
Use 9 as the next digit of our solution. 
Result so far: 10729.0
If we subtract 81 from 83, we get 2.
Fetch the next digit (6) from the dividend, attach it to 2 and continue: 26 / 9

On to step 6:
9 goes into 26 2 times with a remainder of 8.
Put 2 as the next digit of the answer. 
Result so far: 107292.0
If we take 18 away from 26, we end up with 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 7:
The number 9 fits into 80 8 times, leaving a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 107292.8
Subtracting 72 from 80 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Let's proceed to step 8:
80 divided by 9 is 8 with a remainder of 8.
The next digit of our result is 8. 
Result so far: 107292.88
If we take 72 away from 80, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

After the division, we end up with 107292.88 and a remainder of 0.008.