7638 ÷ 9 = 848 R6
Let's divide 7638 by 9.

Step 1:
9 goes into 7 0 times with a remainder of 7.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 7 to get 7.
Bring next digit (6) of the dividend behind the 7 and repeat the process: 76 / 9

Step 2:
9 goes into 76 8 times with a remainder of 4.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 72 from 76 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: 84
Subtract 36 from 43 to get 7.
Bring next digit (8) of the dividend behind the 7 and repeat the process: 78 / 9

Step 4:
9 goes into 78 8 times with a remainder of 6.
Write down 8 as next digit of of the result. 
Result so far: 848
Subtract 72 from 78 to get 6.

The final result is 848 with a remainder of 6.