422035 ÷ 111 
Our goal is to divide 422035 by 111.

On to step 1:
4 divided by 111 is 0 with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 111

On to step 2:
42 divided by 111 is 0 with a remainder of 42.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 42, we get 42.
Grab the next digit (2) from the dividend, add it to 42, then carry on: 422 / 111

Moving on to step 3:
422 divided by 111 is 3 with a remainder of 89.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
If we subtract 333 from 422, we get 89.
Bring next digit (0) of the dividend behind the 89 and repeat the process: 890 / 111

On to step 4:
If we divide 890 by 111, we get 8 and a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 38.0
If we subtract 888 from 890, we get 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 111

Going ahead to step 5:
111 can be fit into 23 0 times, resulting in a remainder of 23.
The number 0 becomes the next digit in our result. 
Result so far: 380.0
Subtract 0 from 23 to get 23.
Grab the next digit (5) from the dividend, add it to 23, then carry on: 235 / 111

Let's proceed to step 6:
If we divide 235 by 111, we get 2 and a remainder of 13.
The next digit of our result is 2. 
Result so far: 3802.0
Subtract 222 from 235 to get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 7:
If we divide 130 by 111, we get 1 and a remainder of 19.
Put 1 as the next digit of the answer. 
Result so far: 3802.1
If we subtract 111 from 130, we get 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Step 8:
111 can be fit into 190 1 times, resulting in a remainder of 79.
Put 1 as the next digit of the answer. 
Result so far: 3802.11
If we subtract 111 from 190, we get 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

The quotient of the division is 3802.11, and the remainder is 0.079.