-138 mod 116

This is sometimes confusing........many people think that the answer - at first blush - should be "22"...however.........n mod m refers to the difference beween "n" and the greatest multiple of "m"  that is less than or equal to "n" ......if "n" is multiple of "m"....then.....  n mod m  = 0

The greatest multiple of 116 that is  less than or equal to -138 is - 232....and the difference beween  -232 and - 138  is   94....so  -138 mod 116  = 94

-138 mod 116

$\begin{array}{|rcll|} \hline -138 \equiv x \pmod {116} \\ -138+116 \equiv x \pmod {116} \quad & | \quad 116 \pmod {116} = 0 \\ -22+116 \equiv x \pmod {116} \quad & | \quad 116 \pmod {116} = 0 \\ 94 \equiv x \pmod {116} \\\\ -138 \pmod {116} = 94 \pmod {116} = 94 \\ \hline \end{array}$