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If someone says "Fifteen divided by half", I would interpret that literally to mean 15/0.5, or 30. However, I usually see it interpreted as 15/2, or 7.5.

Which interpretation is correct?

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If someone says "Fifteen divided by half", it's probably either a slip of the tongue, or an understandable error by a non-native speaker. Most likely the intended expression would have been "Fifteen divided in half". –  FumbleFingers Aug 24 '11 at 21:43

3 Answers 3

up vote 4 down vote accepted

It's simply grammatically incorrect, so it has no literal meaning. (And before anyone shows up to argue against prescriptivism, the very concept of a "literal meaning" contrary to what is meant/understood is prescriptivist at a basic level)

You could say "divided by one half", or "divided by 0.5" for one meaning; or "divided in half" for the other.

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Random832 is right here. I would go further and insist that it's simply a typo/misspeech for "divided in half". For those who insist that it means "15 / 0.5", I would argue it means 15 divided by half of 15. The correct answer is 2. Any number divided by half is going to come out that way (except for zero, infinity, imaginary numbers, etc.) –  JeffSahol Aug 24 '11 at 19:47
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Whether it is grammatically incorrect depends on the speaker, though I’ll grant that by a half and by one-half are probably significantly more common than by half. The idea that a prescriptively incorrect expression is ipso facto meaningless is not only absurd on its face but obviously false. –  Brian M. Scott Aug 24 '11 at 19:51
    
@JeffSahol: When 7.5 is intended, it probably is an error for divided in half, but the rest of your comment is, not to put too fine a point on it, nonsense. (And the mathematics is partly wrong as well: dividing an imaginary number other than zero by half of that number does indeed yield 2.) –  Brian M. Scott Aug 24 '11 at 19:54
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@Random832: Yes, one can. Divided by half has a very clear literal meaning, which may or may not be the one intended by the speaker: it is synonymous with divided by one-half, which is misused and misunderstood in exactly the same way. –  Brian M. Scott Aug 24 '11 at 21:22
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@Brian I beg to differ. one half or a half is a numerical quantity, but half is not, and cannot be used that way. –  Karl Knechtel Aug 25 '11 at 3:17

You're right. Fifteen divided by half is 30, and that's that. Any other interpretation is incorrect. However, fifteen by half could be interpreted as fifteen [multiplied] by half, which would then give 15/2 or 7.5.

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For completeness you might add that when 7.5 is intended, 15 divided by half may be an error for 15 divided in half (JeffSahol’s suggestion) or a conflation of half of 15 with 15 divided by 2. Of course this accounts only for errors in production; errors in interpretation are harder to understand. –  Brian M. Scott Aug 24 '11 at 19:59
    
"Half" is not a number, and that's that. –  Random832 Aug 24 '11 at 20:31
    
@Random832: Your assertion is contradicted by actual usage. People really do say and write things like three-quarters is more than half. You may, if you wish, deprecate the usage, just as I find your how it is generally understood to mean ungrammatical, but your assertion here is counterfactual rubbish. –  Brian M. Scott Aug 24 '11 at 21:18
    
"People really do say and write things like three-quarters is more than half." [citation needed] –  Karl Knechtel Aug 25 '11 at 3:18
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More than half what? Half a cheeseburger? Half past ten? –  Random832 Aug 25 '11 at 6:25

As others have said, it's probably a grammatically incorrect attempt to say something was halved. It seems to be a somewhat common mistake if my peers in math classes are any indication. It seems to me to be a mix-up of "divided in half" and "reduced by half".

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