25031 ÷ 9 = 2781 R2
Alright, let's work through the division of 25031 by 9 step by step.

Step 1:
9 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 9

Step 2:
9 goes into 25 2 times with a remainder of 7.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 18 from 25 to get 7.
Bring next digit (0) of the dividend behind the 7 and repeat the process: 70 / 9

Step 3:
9 goes into 70 7 times with a remainder of 7.
Write down 7 as next digit of of the result. 
Result so far: 27
Subtract 63 from 70 to get 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 9

Step 4:
9 goes into 73 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 278
Subtract 72 from 73 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 9

Step 5:
9 goes into 11 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 2781
Subtract 9 from 11 to get 2.

The final result is 2781 with a remainder of 2.