501 ÷ 9 = 55 R6
We're going to perform division on 501 with 9 as the divisor.

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 (0) of the dividend behind the 5 and repeat the process: 50 / 9

Step 2:
9 goes into 50 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 45 from 50 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 9

Step 3:
9 goes into 51 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 55
Subtract 45 from 51 to get 6.

The final result is 55 with a remainder of 6.