proportionately vs pro rata

proportionately and pro rata both are adverbs.

Word	Noun	Adjective	Verb	Adverb
proportionately	No	No	No	Yes
pro rata	No	No	No	Yes

As adverbs, proportionately and pro rata are synonyms defined as:

proportionately and pro rata: in a way that agrees in amount, magnitude or degree

proportionately (adverb)	pro rata (adverb)
to a proportionate degree	in a way that agrees in amount, magnitude or degree
in a way that is in correspondence among the constituents of another entity
in a way that agrees in amount, magnitude or degree