We look at the division of 111531 by 45 
We want to figure out the number of times 111531 can be divided by 45.

Step 1:
The number 45 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 45

On to step 2:
45 can be fit into 11 0 times, resulting in a remainder of 11.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 11, we end up with 11.
Bring next digit (1) of the dividend behind the 11 and repeat the process: 111 / 45

Let's proceed to step 3:
If we divide 111 by 45, we get 2 and a remainder of 21.
The next digit of our result is 2. 
Result so far: 2.0
Deduct 90 from 111 and we're left with 21.
Fetch the next digit (5) from the dividend, attach it to 21 and continue: 215 / 45

On to step 4:
If we divide 215 by 45, we get 4 and a remainder of 35.
The next digit of our result is 4. 
Result so far: 24.0
Subtracting 180 from 215 leaves us with 35.
Bring next digit (3) of the dividend behind the 35 and repeat the process: 353 / 45

Going ahead to step 5:
If we divide 353 by 45, we get 7 and a remainder of 38.
Write down 7 as next digit of the result. 
Result so far: 247.0
Subtract 315 from 353 to get 38.
Append the next digit (1) from the dividend to 38 and continue with: 381 / 45

Let's proceed to step 6:
45 can be fit into 381 8 times, resulting in a remainder of 21.
Put 8 as the next digit of the answer. 
Result so far: 2478.0
If we subtract 360 from 381, we get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 7:
When dividing 210 by 45, we get 4 with a remainder of 30.
Put 4 as the next digit of the answer. 
Result so far: 2478.4
If we take 180 away from 210, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 8:
45 can be fit into 300 6 times, resulting in a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 2478.46
Deduct 270 from 300 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 9:
When dividing 300 by 45, we get 6 with a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 2478.466
If we take 270 away from 300, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Our division results in 2478.466 with a remaining 0.003.