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"By August, prices had declined by roughly one-third from their 1860 peak. "

If the price at 1860 was x, does that mean prices have become (1/3)*x or (2/3)*x ?

I know one-third means 1/3.

I just don't know how to interpret "decline by"

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    Declined by means decreased by. The price is (2/3)*x where x is the beginning price, the amount of the decline is (1/3)*x
    – Peter
    Jan 23, 2016 at 22:19

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Decline with amounts or values means to become lesser, often slowly and with a connotation that it's not a good thing that it's becoming lesser.

A by prepositional phrase is used when you want to express "how much did X do" with most verbs.

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