745663 ÷ 9 
Our goal is to divide 745663 by 9.

On to step 1:
When dividing 7 by 9, we get 0 with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Bring next digit (4) of the dividend behind the 7 and repeat the process: 74 / 9

Step 2:
The number 9 fits into 74 8 times, leaving a remainder of 2.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
Subtracting 72 from 74 leaves us with 2.
Append the next digit (5) from the dividend to 2 and continue with: 25 / 9

On to step 3:
If we divide 25 by 9, we get 2 and a remainder of 7.
Write down 2 as next digit of the result. 
Result so far: 82.0
Subtracting 18 from 25 leaves us with 7.
Take the next digit (6) from the dividend and append it to 7, then repeat: 76 / 9

Going ahead to step 4:
76 divided by 9 is 8 with a remainder of 4.
Put 8 as the next digit of the answer. 
Result so far: 828.0
Subtracting 72 from 76 leaves us with 4.
Include the next digit (6) from the dividend after 4, then repeat: 46 / 9

Let's proceed to step 5:
If we divide 46 by 9, we get 5 and a remainder of 1.
The next digit of our result is 5. 
Result so far: 8285.0
Subtracting 45 from 46 leaves us with 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 9

On to step 6:
When dividing 13 by 9, we get 1 with a remainder of 4.
The number 1 becomes the next digit in our result. 
Result so far: 82851.0
Subtract 9 from 13 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 7:
When dividing 40 by 9, we get 4 with a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 82851.4
If we subtract 36 from 40, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 8:
9 can be fit into 40 4 times, resulting in a remainder of 4.
The number 4 becomes the next digit in our result. 
Result so far: 82851.44
Deduct 36 from 40 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

In conclusion, the division gives 82851.44 with a balance of 0.004.