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to cut into (a line, conversation, etc.); to force oneself into (e.g. a crowd); to wedge oneself into; to squeeze oneself into; to intrude on; to interrupt
to fall below (of stock prices, sales, etc.); to drop below
電車を待つ列に割込むのは非常に失礼な行為だ。
Cutting into a line waiting for a train is very rude.
急用のために会話に割込んでしまって申し訳ない。
Sorry for cutting into the conversation due to an urgent matter.
他の車が急に割込んできてひやりとした経験がある。
I've had a scary experience when another car suddenly cut in.