9757 ÷ 9 = 1084 R1
Let's divide 9757 by 9.

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 (7) of the dividend behind the 0 and repeat the process: 7 / 9

Step 2:
9 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 7 to get 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 9

Step 3:
9 goes into 75 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 108
Subtract 72 from 75 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 9

Step 4:
9 goes into 37 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 1084
Subtract 36 from 37 to get 1.

The final result is 1084 with a remainder of 1.