10112 ÷ 9 
Our goal is to divide 10112 by 9.

Advancing to step 1:
The number 9 fits into 1 0 times, leaving a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Grab the next digit (0) from the dividend, add it to 1, then carry on: 10 / 9

Advancing to step 2:
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: 1.0
If we take 9 away from 10, we end up with 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 9

Moving on to step 3:
If we divide 11 by 9, we get 1 and a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 11.0
Subtract 9 from 11 to get 2.
Fetch the next digit (1) from the dividend, attach it to 2 and continue: 21 / 9

Let's proceed to step 4:
If we divide 21 by 9, we get 2 and a remainder of 3.
Put 2 as the next digit of the answer. 
Result so far: 112.0
Subtract 18 from 21 to get 3.
Fetch the next digit (2) from the dividend, attach it to 3 and continue: 32 / 9

Step 5:
If we divide 32 by 9, we get 3 and a remainder of 5.
The number 3 becomes the next digit in our result. 
Result so far: 1123.0
Deduct 27 from 32 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.

Step 6:
9 goes into 50 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 1123.5
If we subtract 45 from 50, 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.

Advancing to step 7:
9 can be fit into 50 5 times, resulting in a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 1123.55
Subtracting 45 from 50 leaves us 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 1123.55, and the remainder is 0.005.