5511 ÷ 9 = 612 R3
Alright, let's work through the division of 5511 by 9 step by step.

Step 1:
9 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 9

Step 2:
9 goes into 55 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 54 from 55 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 9

Step 3:
9 goes into 11 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 61
Subtract 9 from 11 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 9

Step 4:
9 goes into 21 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 612
Subtract 18 from 21 to get 3.

The final result is 612 with a remainder of 3.