The phrase "year-and-a-half" is a modern English compound noun formed by combining the basic temporal unit "year" with the fractional unit "half" via the common conjunction "and" and the indefinite article "a". This construction follows a straightforward, literal pattern in English for specifying mixed units of time, similar to "two-and-a-half" or "hour-and-a-half". Its logic is purely additive and descriptive, directly summing the specified durations without metaphorical evolution. The phrase emerged naturally from the grammatical resources of English to meet the need for precise, colloquial expression of a common time interval.

This is a fixed compound phrase. Its components are common English words: 'year' (Old English 'gear', meaning a cycle of seasons), 'and' (Old English 'and', a conjunction), 'a' (Old English 'an', an indefinite article), 'half' (Old English 'healf', meaning one of two equal parts).