9565 ÷ 18 
We want to figure out the number of times 9565 can be divided by 18.

On to step 1:
9 divided by 18 is 0 with a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 9 leaves us with 9.
Take the next digit (5) from the dividend and append it to 9, then repeat: 95 / 18

On to step 2:
The number 18 fits into 95 5 times, leaving a remainder of 5.
The next digit of our result is 5. 
Result so far: 5.0
If we subtract 90 from 95, we get 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 18

Moving on to step 3:
The number 18 fits into 56 3 times, leaving a remainder of 2.
Write down 3 as next digit of the result. 
Result so far: 53.0
Deduct 54 from 56 and we're left with 2.
Grab the next digit (5) from the dividend, add it to 2, then carry on: 25 / 18

Advancing to step 4:
When dividing 25 by 18, we get 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 531.0
If we subtract 18 from 25, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 5:
The number 18 fits into 70 3 times, leaving a remainder of 16.
Write down 3 as next digit of the result. 
Result so far: 531.3
Subtract 54 from 70 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Going ahead to step 6:
The number 18 fits into 160 8 times, leaving a remainder of 16.
Record the quotient 8 as the next digit in the result. 
Result so far: 531.38
Subtracting 144 from 160 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Advancing to step 7:
If we divide 160 by 18, we get 8 and a remainder of 16.
Put 8 as the next digit of the answer. 
Result so far: 531.388
Subtracting 144 from 160 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

The final outcome is 531.388, with a leftover of 0.0016.