To me, "six times five" and "five times
six" are completely synonymous, not only mathematically but
commonsensically, as are "six multiplied by five" and "five multiplied
by six." But many English-Japanese dictionaries treat such pairs as
different. For example:|
Seven multiplied by two is [are, make(s)] fourteen. [≒ Two times seven is fourteen.] ７の２倍は１４です。(Favorite English-Japanese)Some dictionaries also claim that English is the opposite of Japanese in the interpretation of mathematical formulas:
Six times five is thirty. 5の6倍は30If "A times B" is synonymous only with "B multiplied by A," then some English-English dictionaries are defining "times" incorrectly:
times prep. multiplied by: two times four (Random House Webster's)Others ignore the order altogether:
times prep. used to indicate that a number is to be multiplied by another: Three times two is six. (Encarta World English)It seems that the Japanese dictionaries, influenced by the clear multiplicand/multiplier distiction in expressions of the form AのB倍, are trying to force a similar distinction on the English "A times B" and "A multiplied by B," when in fact the precedence relationship between A and B in such English expressions is obscure.
(July 15, 2003)
Today, I asked a colleague--a native speaker of British English in his fifties--about his interpretation of "three times seven" and "three multiplied by seven." Unlike me, he did perceive the expressions as being weighted in one direction, and he interpreted both as meaning "three repeated seven times," in other words, ３の７倍. The plot thickens.
(July 16, 2003)
Two comments came in today. First from Mark Spahn in the United States:
If forced to interpret "6 times 3" (i.e., to derive the mathematical meaning of "times" from an everyday meaning), I would understand it is 3を6回取る.Next, from a 32-year-old American working in Tokyo:
I find I am not quite sure where I stand.As the second correspondent points out, mathematically the result is the same. However, the positive integers are an abstraction of the real world, and when we use such numbers in day-to-day language it is sometimes unclear whether we are treating them as pure, abstract entities or as the objects whose quantities they represent. As mathematical abstractions "100 x 2" and "2 x 100" are identical, but one hundred boxes each containing two shoes is very different from two boxes each containing one hundred shoes.
When applied to boxes of shoes, the dictionaries say that, in Japanese, "100 x 2" means 100の２倍, or "two boxes each containing one hundred shoes." In English, I've now heard three different interpretations: "two boxes each containing one hundred shoes," "one hundred boxes each containing two shoes," and both (or either). And all of the English speakers have expressed some uncertainty about their interpretations.
I haven't yet looked into the meaning of かける, which Mark Spahn also mentioned.
(July 17, 2003)
A correspondent writes:
As a British English speaker in my twenties, I'd say that "six times five" slightly leans towards "six lots of five", and "five multiplied by six" more definitely does. However, I think your remark about boxes of shoes is something of a red herring, because I wouldn't use either of these expressions for anything other than representing a (more or less pure) mathematical construct. If I was trying to talk about shoes I'd say "five boxes of six shoes" or "five lots of six shoes" or something similar. I think the reason that there's no consensus about order in the 'times' and 'multiplied by' expressions is that they're only used when the order really doesn't matter.
(July 21, 2003)