55138 ÷ 7 = 7876 R6
Alright, let's work through the division of 55138 by 7 step by step.

Step 1:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 7

Step 2:
7 goes into 55 7 times with a remainder of 6.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 49 from 55 to get 6.
Bring next digit (1) of the dividend behind the 6 and repeat the process: 61 / 7

Step 3:
7 goes into 61 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 78
Subtract 56 from 61 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 7

Step 4:
7 goes into 53 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 787
Subtract 49 from 53 to get 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 7

Step 5:
7 goes into 48 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 7876
Subtract 42 from 48 to get 6.

The final result is 7876 with a remainder of 6.