80513 ÷ 9 = 8945 R8
Alright, let's work through the division of 80513 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 (0) of the dividend behind the 8 and repeat the process: 80 / 9

Step 2:
9 goes into 80 8 times with a remainder of 8.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 72 from 80 to get 8.
Bring next digit (5) of the dividend behind the 8 and repeat the process: 85 / 9

Step 3:
9 goes into 85 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 89
Subtract 81 from 85 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 9

Step 4:
9 goes into 41 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 894
Subtract 36 from 41 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 9

Step 5:
9 goes into 53 5 times with a remainder of 8.
Write down 5 as next digit of of the result. 
Result so far: 8945
Subtract 45 from 53 to get 8.

The final result is 8945 with a remainder of 8.