51513 ÷ 9 = 5723 R6
Alright, let's work through the division of 51513 by 9 step by step.

Step 1:
9 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 9

Step 2:
9 goes into 51 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 45 from 51 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: 57
Subtract 63 from 65 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 9

Step 4:
9 goes into 21 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 572
Subtract 18 from 21 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 9

Step 5:
9 goes into 33 3 times with a remainder of 6.
Write down 3 as next digit of of the result. 
Result so far: 5723
Subtract 27 from 33 to get 6.

The final result is 5723 with a remainder of 6.