合理
ごうり · gouri · JLPT N2 · noun
rational number
⚖️ 合 fit + 理 reason = reason that fits, so rational
合 means join or fit, and 理 means reason or principle. Together they describe a judgment that fits sound reasoning.
合 — 乛 (lid/roof) + 口 (mouth)
Originally a pictograph of a lidded vessel — a cover (亼) closing over an opening (口) — giving the core sense of 'come together, join, fit.' From 'fit/match' it extended to 'combine, unite, agree' and to measure-word uses. The reading hé reflects this 'joining' meaning.
理 — jade radical 玉/王 + village 里 (phonetic)
理 is a semantic-phonetic compound: the jade radical 王 (玉) on the left signals meaning, while 里 on the right gives the sound. It originally meant the natural veins or grain in a piece of jade, then extended to 'pattern,' 'order,' 'principle,' and finally the modern senses 'reason' and 'to manage.'