Improper means not right or not suitable for the occasion. Improper conduct, an improper question, improper use.
It is formal and belongs to rules and complaints: improper conduct, improper disclosure, improper use of funds. Applied to behaviour between people it carries a mild suggestion of the indecent, which is why improper suggestion is a fixed phrase. In mathematics, an improper fraction is one where the top is larger than the bottom, which is entirely respectable. Note impropriety, the noun.
1adjectiveimproperNot right or not suitable for the occasion.
“It would be improper for a judge to discuss the case with one side in private.”
2adjectivetopWith the top larger than the bottom, of a fraction.
“An improper fraction like nine over four is perfectly correct.”
improper is a quality of unsuitability.
Latin improprius is in- plus proprius, one's own or proper. Property, appropriate and proper come from the same ownership.
Latin
improprius — not proper
Middle French
impropre
English, today
improper
Built from
From Middle French impropre, from Latin improprius (“not proper”), from in- + proprius (“proper”). by surface analysis, en + im + proper.
Etymology from Wiktionary, CC BY-SA