We look at the division of 11590 by 45 
Let's see how many times 45 fits into 11590.

Moving on to step 1:
The number 45 fits into 1 0 times, leaving a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 45

Going ahead to step 2:
If we divide 11 by 45, we get 0 and a remainder of 11.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 11, we end up with 11.
Include the next digit (5) from the dividend after 11, then repeat: 115 / 45

Step 3:
If we divide 115 by 45, we get 2 and a remainder of 25.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Deduct 90 from 115 and we're left with 25.
Take the next digit (9) from the dividend and append it to 25, then repeat: 259 / 45

Step 4:
259 divided by 45 is 5 with a remainder of 34.
Write down 5 as next digit of the result. 
Result so far: 25.0
Subtracting 225 from 259 leaves us with 34.
Take the next digit (0) from the dividend and append it to 34, then repeat: 340 / 45

On to step 5:
45 can be fit into 340 7 times, resulting in a remainder of 25.
The next digit of our result is 7. 
Result so far: 257.0
If we take 315 away from 340, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 6:
The number 45 fits into 250 5 times, leaving a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 257.5
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 7:
250 divided by 45 is 5 with a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 257.55
Subtracting 225 from 250 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The quotient of the division is 257.55, and the remainder is 0.025.