9444 ÷ 7 = 1349 R1
Alright, let's work through the division of 9444 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 (4) of the dividend behind the 2 and repeat the process: 24 / 7

Step 2:
7 goes into 24 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 21 from 24 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 7

Step 3:
7 goes into 34 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 134
Subtract 28 from 34 to get 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 7

Step 4:
7 goes into 64 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 1349
Subtract 63 from 64 to get 1.

The final result is 1349 with a remainder of 1.