815774 ÷ 9 
We want to divide 815774 by 9.

Going ahead to step 1:
The number 9 fits into 8 0 times, leaving a remainder of 8.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 8, we end up with 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 9

Advancing to step 2:
9 can be fit into 81 9 times, resulting in a remainder of 0.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
The remainder is 0 after subtracting 81 from 81.
Take the next digit (5) from the dividend and append it to 0, then repeat: 5 / 9

Moving on to step 3:
When dividing 5 by 9, we get 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 90.0
If we subtract 0 from 5, we get 5.
Grab the next digit (7) from the dividend, add it to 5, then carry on: 57 / 9

On to step 4:
9 can be fit into 57 6 times, resulting in a remainder of 3.
Put 6 as the next digit of the answer. 
Result so far: 906.0
Subtract 54 from 57 to get 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 9

Moving on to step 5:
37 divided by 9 is 4 with a remainder of 1.
Put 4 as the next digit of the answer. 
Result so far: 9064.0
Deduct 36 from 37 and we're left with 1.
Fetch the next digit (4) from the dividend, attach it to 1 and continue: 14 / 9

On to step 6:
The number 9 fits into 14 1 times, leaving a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 90641.0
If we subtract 9 from 14, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 7:
The number 9 fits into 50 5 times, leaving a remainder of 5.
The next digit of our result is 5. 
Result so far: 90641.5
The remainder is 5 after subtracting 45 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
If we divide 50 by 9, we get 5 and a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 90641.55
Deduct 45 from 50 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 90641.55, and the remainder is 0.005.