6938 ÷ 7 = 991 R1
Alright, let's work through the division of 6938 by 7 step by step.

Step 1:
7 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (9) of the dividend behind the 6 and repeat the process: 69 / 7

Step 2:
7 goes into 69 9 times with a remainder of 6.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 63 from 69 to get 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 7

Step 3:
7 goes into 63 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 99
Subtract 63 from 63 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 7

Step 4:
7 goes into 8 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 991
Subtract 7 from 8 to get 1.

The final result is 991 with a remainder of 1.