In a cheerful, happy, or carefree manner.
From 'gay' (Middle English meaning happy or carefree, from Old French 'gai') + '-ly' (adverb suffix). The adjective 'gay' originally had no sexual connotation and simply meant joyful.
Modern readers might not realize that Victorian and early 20th-century literature constantly uses 'gay' to mean happy—'the gay '90s' refers to the cheerful 1890s, a linguistic meaning shift that confuses students today.
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