arithmetical vs arithmetic

arithmetical is not a noun while arithmetic is a noun.

Word	Noun	Adjective	Verb	Adverb
arithmetical	No	Yes	No	No
arithmetic	Yes	Yes	No	No

As adjectives, arithmetical and arithmetic are synonyms defined as:

arithmetical (noun)	arithmetic (noun)
	the branch of pure mathematics dealing with the theory of numerical calculations

arithmetical (adjective)	arithmetic (adjective)
relating to or involving arithmetic	relating to or involving arithmetic