Lexical Leavings

by Tom Gally

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30
（［参考］6×5＝30の読み方; 日本人はこの式を「6の5倍」と解するが英米人は逆） (新グローバル英和辞典)
If "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)

times prep. multiplied by: eleven times four is forty-four (New Oxford American)
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)

time 24. a. (plural) (used as a multiplicative word in phrasal combinations expressing how many instances of a quantity or factor are taken together: four times five) (Macquarie)
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.

At first, my gut reaction was to agree with your British colleague that, in fact, six times/multiplied by five means "take a group of six units, five times".  So, this would be equivalent to the Japanese 6の5倍.

But then, upon further reflection, there are expressions like "two times the fun", which could be argued that "the fun" replaces a number (or take fun, two times).  With such logic, "6 times 5" would mean take 5, 6 times, or 5の6倍.  This strikes me as an older usage perhaps?

That said, the end result is entirely the same "mathematically"?
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)