9559 ÷ 7 = 1365 R4
Alright, let's work through the division of 9559 by 7 step by step.

Step 1:
7 goes into 9 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 9 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 7

Step 2:
7 goes into 25 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 21 from 25 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 7

Step 3:
7 goes into 45 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 136
Subtract 42 from 45 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 7

Step 4:
7 goes into 39 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 1365
Subtract 35 from 39 to get 4.

The final result is 1365 with a remainder of 4.