15640 ÷ 9 = 1737 R7
Alright, let's work through the division of 15640 by 9 step by step.

Step 1:
9 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 9

Step 2:
9 goes into 15 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 9 from 15 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 9

Step 3:
9 goes into 66 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 17
Subtract 63 from 66 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 9

Step 4:
9 goes into 34 3 times with a remainder of 7.
Write down 3 as next digit of of the result. 
Result so far: 173
Subtract 27 from 34 to get 7.
Bring next digit (0) of the dividend behind the 7 and repeat the process: 70 / 9

Step 5:
9 goes into 70 7 times with a remainder of 7.
Write down 7 as next digit of of the result. 
Result so far: 1737
Subtract 63 from 70 to get 7.

The final result is 1737 with a remainder of 7.