11791 ÷ 9 = 1310 R1
Alright, let's work through the division of 11791 by 9 step by step.

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

Step 2:
9 goes into 11 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 9 from 11 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 9

Step 3:
9 goes into 27 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 27 from 27 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: 131
Subtract 9 from 9 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 9

Step 5:
9 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 1310
Subtract 0 from 1 to get 1.

The final result is 1310 with a remainder of 1.