9991 ÷ 2 = 4995 R1
Alright, let's work through the division of 9991 by 2 step by step.

Step 1:
2 goes into 9 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 8 from 9 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 2

Step 2:
2 goes into 19 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 49
Subtract 18 from 19 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 2

Step 3:
2 goes into 19 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 499
Subtract 18 from 19 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 2

Step 4:
2 goes into 11 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 4995
Subtract 10 from 11 to get 1.

The final result is 4995 with a remainder of 1.