9999 ÷ 9 = 1111 R0
Alright, let's work through the division of 9999 by 9 step by step.

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

Step 2:
9 goes into 9 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 9 from 9 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 9

Step 3:
9 goes into 9 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 111
Subtract 9 from 9 to get 0.
Bring next digit (9) of the dividend behind the 0 and repeat the process: 9 / 9

Step 4:
9 goes into 9 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1111
Subtract 9 from 9 to get 0.

The final result is 1111 with a remainder of 0.