99114 ÷ 7 = 14159 R1
Alright, let's work through the division of 99114 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 (9) of the dividend behind the 2 and repeat the process: 29 / 7

Step 2:
7 goes into 29 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 14
Subtract 28 from 29 to get 1.
Bring next digit (1) of the dividend behind the 1 and repeat the process: 11 / 7

Step 3:
7 goes into 11 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 141
Subtract 7 from 11 to get 4.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 7

Step 4:
7 goes into 41 5 times with a remainder of 6.
Write down 5 as next digit of of the result. 
Result so far: 1415
Subtract 35 from 41 to get 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 7

Step 5:
7 goes into 64 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 14159
Subtract 63 from 64 to get 1.

The final result is 14159 with a remainder of 1.