55518 ÷ 9 = 6168 R6
Alright, let's work through the division of 55518 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 (5) of the dividend behind the 1 and repeat the process: 15 / 9

Step 3:
9 goes into 15 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 61
Subtract 9 from 15 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 9

Step 4:
9 goes into 61 6 times with a remainder of 7.
Write down 6 as next digit of of the result. 
Result so far: 616
Subtract 54 from 61 to get 7.
Bring next digit (8) of the dividend behind the 7 and repeat the process: 78 / 9

Step 5:
9 goes into 78 8 times with a remainder of 6.
Write down 8 as next digit of of the result. 
Result so far: 6168
Subtract 72 from 78 to get 6.

The final result is 6168 with a remainder of 6.