Oh my word Faction, Fraction

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Faction is a group within a large group (political party, movement) that have different ideas and opinions than the rest of the group; a dissentient group in a political party; dissension in an organization. Feud (long angry fight) is the quintessence of the factions. Faction is derived from the French word ‘factio’. Its variants are factional (adjective), and factitiousness (noun).

Another meaning of faction is a book, film, play that is based on real events as the basis for a fictional narrative, for fictional dramatization. When something or someone is inclined to be faction, it is described as factious (adjective), factiously (adverb) and factiousness (noun).

Fraction is a number that is not a whole number such as ½, .5, 1/3, ⅓, .33; fraction is a small part, piece, amount; a portion of a mixture in chemistry such as fractional distillation, fractional crystallization.
Fractional is an adjective meaning relating to fraction: very slight, incomplete, separation of parts of a mixture.

“For all its idiosyncrasies, English is said to have a fewer of the awkward consonant clusters and singsong tonal variations that make other languages so difficult to master. In Cantonese, hae means ‘yes’. But with a fractional change of pitch, it also describes the female pudenda.”–Mother Tongue: The Story of the English Language by Bill Bryson

The variants of fraction the noun are fractionalize (fractionalise, verb) and fractionally (adverb). But fractionate, verb, means to break up something into parts; separate something by fractional distillation.
Fractious is adjective meaning someone who is irritable, peevish, disruption of peace. The variants in this sense are fractiously (adverb) and fractiousness (noun).

Note the difference between factious (factional, characterized or inclined to faction) and fractious (unruly, peevish). There are factional politics in the Indian electoral arena that causes fractiousness to a section of the society.