44349 ÷ 9 = 4927 R6
Alright, let's work through the division of 44349 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 (4) of the dividend behind the 4 and repeat the process: 44 / 9

Step 2:
9 goes into 44 4 times with a remainder of 8.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 36 from 44 to get 8.
Bring next digit (3) of the dividend behind the 8 and repeat the process: 83 / 9

Step 3:
9 goes into 83 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 49
Subtract 81 from 83 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 9

Step 4:
9 goes into 24 2 times with a remainder of 6.
Write down 2 as next digit of of the result. 
Result so far: 492
Subtract 18 from 24 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 9

Step 5:
9 goes into 69 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 4927
Subtract 63 from 69 to get 6.

The final result is 4927 with a remainder of 6.