8758 ÷ 9 = 973 R1
Alright, let's work through the division of 8758 by 9 step by step.

Step 1:
9 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 8 to get 8.
Bring next digit (7) of the dividend behind the 8 and repeat the process: 87 / 9

Step 2:
9 goes into 87 9 times with a remainder of 6.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 81 from 87 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 9

Step 3:
9 goes into 65 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 97
Subtract 63 from 65 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 9

Step 4:
9 goes into 28 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 973
Subtract 27 from 28 to get 1.

The final result is 973 with a remainder of 1.