"%%" and "%/%" for the remainder and the quotient

In R, you can assign your own operators using %[characters]%. A trivial example:

'%p%' <- function(x, y){x^2 + y}

2 %p% 3 # result: 7

While I agree with BlueTrin that %% is pretty standard, I have a suspicion %/% may have something to do with the sort of operator definitions I showed above - perhaps it was easier to implement, and makes sense: %/% means do a special sort of division (integer division)

Have a look at the examples below for a clearer understanding of the differences between the different operators:

> # Floating Division:
> 5/2
[1] 2.5
> 
> # Integer Division:
> 5%/%2
[1] 2
> 
> # Remainder:
> 5%%2
[1] 1

I think it is because % has often be associated with the modulus operator in many programming languages.

It is the case, e.g., in C, C++, C# and Java, and many other languages which derive their syntax from C (C itself took it from B).