你吃饭了吗？ (Have you eaten?) is a traditional Chinese greeting, showing concern for the other person's well-being. It does not necessarily require a literal answer.
usage
饭 can mean either cooked rice specifically or a meal in general. 吃饭 means to eat (a meal), 做饭 means to cook, 早饭 / 午饭 / 晚饭 = breakfast / lunch / dinner.
Food radical on the left — the simplified side-form of 食 (eat, food). Marks 饭 firmly in the eating / cooked-grain family: 饭 is by default cooked rice, then any meal. Same radical in 饺 (dumpling), 饼 (cake), 饿 (hungry), 馆 (eatery), 馒 (steamed bun).
Right side 反 supplies the sound directly: fǎn → fàn with only a tone shift. Same phonetic anchors 板 (bǎn), 返 (fǎn), 贩 (fàn), 版 (bǎn) — the 反 cluster covers both b- and f- readings, a known labial split.
