How to use "mod" related words in technical paper？ Modular reduction is a widely used arithmetic operation. I found many "mod" related words such as 


modulo
modulus
modular


Can anyone explains the difference among these words?  Please give examples or idioms.
A modular operation is an operation done modulo some modulus.


"modular" is an adjective: modular inverse, modular operation, modular reduction, ...
"modulo" is indeed the Latin ablative of modulus, and that makes it an adverb: I walk modulo $n$, just like I walk fast.
"modulus" is a noun: the number $n$ is the modulus that you would use in some system.