403 ÷ 9 = 44 R7
Alright, let's work through the division of 403 by 9 step by step.

Step 1:
9 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 9

Step 2:
9 goes into 40 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 36 from 40 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 9

Step 3:
9 goes into 43 4 times with a remainder of 7.
Write down 4 as next digit of of the result. 
Result so far: 44
Subtract 36 from 43 to get 7.

The final result is 44 with a remainder of 7.