In Human Resources, fraction can refer to the percentage of full-time a part-time employee works. So, for example, if an employee works 50% of the usual hours, their fraction is 50%. Positions which are filled by multiple employees at once can also be expressed by fractions > 100%. For example, if a position is budgeted as 150%, that means one 100% employee and one 50% employee can fill it at a time, or three 50% employees. In this sense, fraction is in units of full-time equivalent employees.
A faction – note spelling – is a splinter group or other smaller group within or previously associated with a larger group.
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