Factious - fractious

Beware a typographical error caused by omitting (or adding) an '-r-'. There are also errors caused by mis-reading '-n-' for '-u-' in both the words 'factious'/'faction' and 'fractious'/'fraction'. (This warning about typos, of course, applies to such derived words as the adjectives factional/fractional and the adverbs factionally/fractionally, etc.)

• Factious is an adjective meaning 'to do with [a] faction'; 'characterized by partisan dissent'.
  • Faction is a noun meaning 'an organized [sub-]group in religion or politics'; 'a party within a party', 'a group within a broader organization [such as a Church or a political party] which promotes an unorthodox view or policy'.

Don't confuse factious with factitious.

• The adjective Fractious is mostly used of children, although it may be used figuratively of adults whom one wants to characterize as childish. It means 'grumpy', 'cross', 'peevish', 'unruly', and denotes a characteristically stubborn and cross-grained behaviour in a small child.
  • The noun fraction is nowadays most commonly used to mean 'an arithmetical unit that is not an integer; one of those portions of a whole number that is expressed by an enumerator over [our convention is to use a straight line between them] a denominator. However, the word is sometimes used with much the same meaning as 'part', as in 'His contribution will cover only a (small) fraction of the cost'. This is the usual implication of the adjective fractional: the professional road cycling team Sky, for example, attributes much of its success to fractional improvements in small details.

The etymological, and archaic, meaning of fraction is 'a breaking'.

(OED records no such word as fractitious.)