11509 ÷ 7 = 1644 R1
Alright, let's work through the division of 11509 by 7 step by step.

Step 1:
7 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 (1) of the dividend behind the 1 and repeat the process: 11 / 7

Step 2:
7 goes into 11 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 11 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: 16
Subtract 42 from 45 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 7

Step 4:
7 goes into 30 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 164
Subtract 28 from 30 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 7

Step 5:
7 goes into 29 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 1644
Subtract 28 from 29 to get 1.

The final result is 1644 with a remainder of 1.