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On this informational sign in ramen shop they use -i adjectives ending with め. I can understand plain かたい, 多い and such, but what purpose does ending an adjective in め serves?

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marked as duplicate by Chocolate May 13 at 0:44

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It's definition 17 on Jisho:

  1. somewhat; -ish

So, かため means on cooked a bit on the hard side, やわらかめ on cooked a bit on the soft side, etc

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