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そして、調べた77の海岸のうち60%で、砂が全部なくなる可能性があることがわかりました。
In 60% of the 77 coasts investigated, it is understood that there is a possibility that all the sand will be lost.

I'm a bit confused by the 調べた77の海岸のうち60%で part. I'm assuming it means "in 60% of the 77 coasts investigated", but I'm uncomfortable with the lack of particle between うち and 60%. How do the following differ:

77の海岸のうち60%で
77の海岸のうちの60%で this one feels ungrammatical to me
77の海岸の60%で

Maybe I'm trying to join 77の海岸のうち and 60% into a single phrase when I shouldn't. Perhaps the correct answer is "Among the 77 coasts investigated, in 60% of them ...". Could I write 77の海岸のうち、それの60%で with the same meaning as the original?

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  • 77の海岸のうち60%で
  • 77の海岸のうちの60%で
  • 77の海岸の60%で

These all mean the same thing, and they are interchangeable. うち is basically a noun, but it can form an adverbial phrase or clause without another particle, just as 時, 中 can 場合 can do so.

From 明鏡国語辞典:

うち

⑩㋑ 問題とする数値がある範囲の中から選ばれたことを表す。
「仲間のうち二人が合格した」「定価のうち(の)二割を内金として払う」「三人残ったうちの一人が犯人だ」

うち is often optional, but it can remove an ambiguity from a sentence. For example, 友達の2人 means either "the two friends (mentioned in the conversation)" or "two of the (many) friends" depending on the context. 友達のうちの2人 only means the latter.

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