Let's divide 631639 by 9
Let's see how many times 9 fits into 631639.

On to step 1:
9 can be fit into 6 0 times, resulting in a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 9

Advancing to step 2:
9 goes into 63 7 times with a remainder of 0.
Put 7 as the next digit of the answer. 
Result so far: 7.0
The remainder is 0 after subtracting 63 from 63.
Grab the next digit (1) from the dividend, add it to 0, then carry on: 1 / 9

Advancing to step 3:
If we divide 1 by 9, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 70.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 9

On to step 4:
16 divided by 9 is 1 with a remainder of 7.
Write down 1 as next digit of the result. 
Result so far: 701.0
Deduct 9 from 16 and we're left with 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 9

Advancing to step 5:
73 divided by 9 is 8 with a remainder of 1.
Put 8 as the next digit of the answer. 
Result so far: 7018.0
If we subtract 72 from 73, we get 1.
Include the next digit (9) from the dividend after 1, then repeat: 19 / 9

Going ahead to step 6:
If we divide 19 by 9, we get 2 and a remainder of 1.
Write down 2 as next digit of the result. 
Result so far: 70182.0
Deduct 18 from 19 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

On to step 7:
If we divide 10 by 9, we get 1 and a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 70182.1
Subtract 9 from 10 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 8:
If we divide 10 by 9, we get 1 and a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 70182.11
Subtract 9 from 10 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The quotient of the division is 70182.11, and the remainder is 0.001.