9791 ÷ 7 = 1398 R5
Alright, let's work through the division of 9791 by 7 step by step.

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

Step 2:
7 goes into 27 3 times with a remainder of 6.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 21 from 27 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 7

Step 3:
7 goes into 69 9 times with a remainder of 6.
Write down 9 as next digit of of the result. 
Result so far: 139
Subtract 63 from 69 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 7

Step 4:
7 goes into 61 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 1398
Subtract 56 from 61 to get 5.

The final result is 1398 with a remainder of 5.