501510 ÷ 45 
Let's see how many times 45 fits into 501510.

Going ahead to step 1:
If we divide 5 by 45, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Take the next digit (0) from the dividend and append it to 5, then repeat: 50 / 45

On to step 2:
If we divide 50 by 45, we get 1 and a remainder of 5.
The next digit of our result is 1. 
Result so far: 1.0
Subtract 45 from 50 to get 5.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 45

Advancing to step 3:
If we divide 51 by 45, we get 1 and a remainder of 6.
The next digit of our result is 1. 
Result so far: 11.0
If we take 45 away from 51, we end up with 6.
Take the next digit (5) from the dividend and append it to 6, then repeat: 65 / 45

Let's proceed to step 4:
If we divide 65 by 45, we get 1 and a remainder of 20.
Use 1 as the next digit of our solution. 
Result so far: 111.0
If we subtract 45 from 65, we get 20.
Fetch the next digit (1) from the dividend, attach it to 20 and continue: 201 / 45

Let's proceed to step 5:
201 divided by 45 is 4 with a remainder of 21.
The next digit of our result is 4. 
Result so far: 1114.0
Subtracting 180 from 201 leaves us with 21.
Grab the next digit (0) from the dividend, add it to 21, then carry on: 210 / 45

Step 6:
210 divided by 45 is 4 with a remainder of 30.
Write down 4 as next digit of the result. 
Result so far: 11144.0
If we subtract 180 from 210, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 7:
The number 45 fits into 300 6 times, leaving a remainder of 30.
The number 6 becomes the next digit in our result. 
Result so far: 11144.6
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.

Moving on to step 8:
The number 45 fits into 300 6 times, leaving a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 11144.66
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

The final result is 11144.66 with a remainder of 0.03.