Basic Arithmetic Operations

##Equals

({}[{}]<(())>){((<{}{}>))}{}

##Not Equals

({}[{}](<()>)){{}{}(<(())>)}{}

##Addition

({}{})

##Subtraction

([{}]{})

##Multiplication (Positive only)

({}<>)({<({}[()])><>({})<>}{}<><{}>)

(courtesy of Stack Exchange user MegaTom)

##Multiplication

([({})])<>((<(())>))<>{({}<({}()<(([{}])<>)>)<>>)<>({}<>)}{}{}<>{}{}{({}<>{})<>{}}{(<><>)}{}{}<>

##Integer Division (Positive only)

(<({}(<>))>)<>{({}[()])<>(({}()[({}<({}())>)])){{}(<({}({}<({}[()])>))>)}{}<>}{}<>{}{}({}<>)

##Integer Division

(()()){({}[()]<([([({})](<()>))](<>())){({}())<>}{}<>{}{}<>(({})){{}{}<>(<(())>)}{}(({})<>)<>{(<{}([{}])>)}{}({}<>)<>({}<><({}<>)>)>)}{}(<({}(<>))>)<>{({}[()])<>(({}()[({}<({}())>)])){{}(<({}({}<({}[()])>))>)}{}<>}{}<>{}{}({}<>)<>(({}{}[(())])){{}{}(((<{}>)))}{}{}{(<{}<>([{}])><>)}{}<>

##Modulo (Positive only)

({}(<()>)){({}[()]<(({}()[({})])){{}(<({}({}))>)}{}>)}({}{}<{}>)

(courtesy of Stack Exchange user Dennis)

##Factorial

({}<(())>){(({}<>)[()]<({<({}[()])><>({})<>}{}<><{}>)>)}{}

(courtesy of Stack Exchange user Mega Tom)