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For example, what is the difference between 減少(する) and 削減(する)? Would prefer an answer in English.

And also which one is more correct? この株価は3年前からずっと減少している or この株価は3年前からずっと削減している

Also, are there other ways to say reduce or decrease?

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減少する is usually used as an intransitive verb and means "get smaller in volume/number". For example, 日本の人口は、減少している (The population of Japan is getting smaller).

削減する is a transitive verb and means "cut", "reduce", "curtail". For example, 多くの会社は、人件費を削減したいにちがいない (Many companies must want to reduce labor cost).

下落 and 下がる are appropriate for prices, so この株価は3年前からずっと下落している is natural.

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    この辺に説明がありますが、 less (とその原形である little や、仲間の few) は通常限定用法のみで使います。 – naruto May 15 '17 at 18:03
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I believe that 減少 is used to denote something simply getting quantitatively smaller (like weight or money) while 削減 implies some getting-rid-of or cutting. In the sentence you gave the thing that is decreasing is a stock price, from which you can't really cut or remove, it just changes in size on its own so 減少 is probably more appropriate. If it were something like employees at a company being laid-off, perhaps 削減 would be better.

  • 消える and 削減する use different kanjis. 削 is used in verbs such as 削る(けずる). – みっち May 15 '17 at 17:27
  • Oh whoops! My mistake. Thanks for pointing that out. – tcallred May 15 '17 at 17:30
  • I think I still stand by 減少 being a better choice, though, because 削減 still invokes the image of voluntarily cutting something down like time spent on something, budgets, or employee count while 減少 is more like something decreasing on it's own accord. – tcallred May 15 '17 at 17:40

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