# «x times less» – bad way to express a ratio?



## mean machine

I’ve come across an opinion of the native speakers of English that if one says, for example, that «Ann has 3 times less apples than John», this doesn’t equals to «John has 3 times as many apples as Ann does».

They claim that in the strict logical sense, the meaning of the former sentence is that of subtraction (actually, the subtraction of 3*number of apples Ann has from John's), not division. And the correct way of conveying the intended meaning of division would be «Ann has one-third as many apples as John».

Assuming that this chain of reasoning is correct, how does one state that X is, say, 1/25 of Y? (without inverting the sentence to «Y is 25 times as much as X).

I would very much appreciate some clarification on the matter!
(And my apologies if this question had already been discussed here).

UPD: Here is a link to one such debate: http://www.quora.com/English-langua...do-I-have-three-times-more-apples-than-you-do


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## fdb

There are two questions here: grammatical and mathematical.

Grammatically correct would be: “three times fewer….”, not “less”.

Mathematically correct would be: “A third as many…”. This would be unambiguous.


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## bennymix

Hi mean,
"3 times less" [or fewer]  is readily understood as meaning 1/3 of;  as you state.


I don't agree with the opinion you cite.   There is nothing to do with subtraction:  That would be said as, "Ann has three less [fewer] apples than John."


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## JulianStuart

This issue is similar to the one in the following thread "operates at four time less pressure than the old one".  In that case, pressure is uncountable so we cannot use fewer; however, the mathematical confusion can be avoided by using 1/25 as many and avoiding the "more/less than" phrase.


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## VicNicSor

mean machine said:


> «*Ann has 3 times less apples than John*» .....  «John has 3 times as many apples as Ann does».
> 
> They claim that in the strict logical sense, *the meaning of the former sentence is that of subtraction*, not division.


I don't understand how it could be substraction if it's talking about "*times*"
I'd expect:
«Ann has two apples fewer than John has»
Am I wrong?

  cross-posted with bennymix


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## Myridon

Many people do object to it.  "3 times" any number greater than 1 results in a larger number not a smaller number.   I often see this sort of language result in errors and miscommunications and if you involve percentages it gets worse.  
This language is used and generally understood so you should understand what it means when people say that, but I, personally, would suggest that you avoid using it yourself.


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## mean machine

Ok, but I suppose using something like ''1/25 as many as....'' in a non-scientific text would sound pretty odd, wouldn't it? That is the bit that confuses me the most, not the "fewer/less" thing. I'm sorry if I failed to put it clearly in the initial question, but this is the actual problem – how do I express the meaning of "1/25 as many as..." without sounding strange and at the same time be logically correct? (and without inverting the whole sentence).


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## srk

I find nothing strange in saying something is 1/25th (one twenty-fifth) as large as something else.  Maybe the ending "th" is what you're looking for.


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## mean machine

VikNikSor said:


> I don't understand how it could be substraction if it's talking about "*times*"
> I'd expect:
> «Ann has two apples fewer than John has»
> Am I wrong?
> 
> cross-posted with bennymix




Actually, it's seems to be a little bit more complicated than just division/subtraction. Following your comment, I've added a link to my question where the matter is explained in greater detail (see under "UPD").


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## mean machine

srk said:


> I find nothing strange in saying something is 1/25th (one twenty-fifth) as large as something else.  Maybe the ending "th" is what you're looking for.



Well, I really thought that something like "one twenty-fifth as large/big/many etc." would sound quite weird in, say, a news article. If it isn't, well, the case is closed)


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## JulianStuart

X is 4% of Y would be another way 

As long as you avoid a comparative (larger than, less than, smaller than, etc) you can use times or fractions.  If you think your audience might be "arithemtically challenged" (i.e. simply would not understand a fraction like 1/25th) you will need to turn the sentence around and use 25 times bigger than.


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## mean machine

JulianStuart said:


> X is 4% of Y would be another way
> 
> As long as you avoid a comparative (larger than, less than, smaller than, etc) you can use times or fractions.  If you think your audience might be "arithemtically challenged" (i.e. simply would not understand a fraction like 1/25th) you will need to turn the sentence around and use 25 times bigger than.



Nifty idea with percentages, but yes - too cool for most target audiences)


Going by comments, it’s more natural for Anglophones to express ratios by the concept of the «larger» than of the «smaller». This is not the case in any of the other languages I've been studying.


If this larger-instead-of-smaller suspicion of mine is true, then, it’s a very interesting point to arrive at, as long as one is a strong advocate of the Sapir–Whorf hypothesis.


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## Wordsmyth

fdb said:


> _[...] _Grammatically correct would be: “three times fewer….”, not “less”.
> 
> Mathematically correct would be: “A third as many…”. This would be unambiguous.


 In fact the second one would be both mathematically *and* grammatically correct — which, for me, makes it infinitely preferable.


bennymix said:


> _ [...] _"3 times less" [or fewer] is readily understood as meaning 1/3 of _[...] _


 Well, maybe readily understood by some, benny — but not by everyone, as is shown by some of the posts in the thread that JS linked to in #4. (I particularly liked cuchuflete's suggestion of a letter to the editor, asking "Just what the hell do you people mean by "four times less"?). Come to think of it, it seems odd to me that anyone would want to use the complicated and dubious "three times less", when "a third" is so much simpler (and, to me, instinctive).


mean machine said:


> Ok, but I suppose using something like ''1/25 as many as....'' in a non-scientific text would sound pretty odd, wouldn't it?_
> [...] _how do I express the meaning of "1/25 as many as..." without sounding strange and at the same time be logically correct? (and without inverting the whole sentence).


 I don't think it sounds strange. We see, in non-scientific texts, "a thirtieth", "a thousandth", ... Perhaps it's less common with 'unround' numbers, but that's probably because we talk about them less than we do about round numbers, not because there's anything intrinsically odd about "a twenty-fifth".

Also, we often use forms other than "as ... as". We hear "1/25th the size of", "1/25th the depth of', etc. With numbers, it can be "1/25th the number of", provided that fits with the rest of the sentence. 





mean machine said:


> Nifty idea with percentages, but yes - too cool for most target audiences) _[...] _


 Really?! In this day and age, when people have percentages rammed down their throats at every turn (even down to the curious "0% interest"), I'd have thought "4%" would be unremarkably ordinary.   


mean machine said:


> _[...] _Going by comments, it’s more natural for Anglophones to express ratios by the concept of the «larger» than of the «smaller». This is not the case in any of the other languages I've been studying. _[...] _


 Which comments were those, mean machine? And what do you mean by "larger-rather-than-smaller"? 
And if you're advocating Sapir-Whorf, what's the anglophone perception in question? ... and what's the linguistic structure that's influencing it?

Sorry, but your last post has me bewildered. Can you cast some light?

Ws


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## RM1(SS)

To me, "three times less than X" means -2X.


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## Wordsmyth

Me too. 

(As I said, benny: 'not by everyone' )

Ws


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## JulianStuart

RM1(SS) said:


> To me, "three times less than X" means -2X.



I still have trouble with comparatives 

So, if X=1, then "three times less than X" means 1 - (2 x 1) = -1?


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## JamesM

No, not subtracting 2X but  (2*X) as a negative number.  It would be -2, not -1.

I have no idea how you could have 3 _times_ less/fewer than someone else.  That's similar to saying we've reduced expenditures by 300%.  How is this logically possible?  Once you've reduced expenditures by 100% you have no more expenditures.


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## Wordsmyth

JulianStuart said:


> _[...]_ So, if X=1, then "*three* times less than X" means 1 - (*2* x 1) = -1? _[...]_


 "*three* times less than X" means 1 - (*3* x 1) = *-2* 

... assuming that "three times" means "three times X" (and I can't see what else it could mean).

_[Edit]_ To any ardent supporters of the idea that "three times X" means "one-third of X" (and I don't see any in this thread so far), I would say "Do you say _two times less_, or _twice less_, instead of _half._? If not, why not?"

Ws


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## JulianStuart

Gotcha (finally!)   The result of "three times less than X" is "-2X".  (in arithmetic terms:  X -3X = -2X ) The use of "times" means something has to be _multiplied_ by three, so this is what I'd probably have ended up with, too.


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## Wordsmyth

That's it, JS.

Ws


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## bennymix

To Word and others,



> Originally Posted by *JulianStuart*
> 
> _[...]_ So, if X=1, then "*three* times less than X" means 1 - (*2* x 1) = -1? _[...]_
> "*three* times less than X" means 1 - (*3* x 1) = *-2*
> 
> [Wordsmyth:] ... assuming that "three times" means "three times X" (and I can't see what else it could mean).
> 
> _[Edit]_ To any ardent supporters of the idea that "three times X"  means "one-third of X" (and I don't see any in this thread so far), I  would say "Do you say _two times less_, or _twice less_, instead of _half._? If not, why not?"



===

Hi Word,
"3 times less" means 1/3,  as I said in post #3.

To answer your question. Yes, one says 2 times less, and that means one half of.

The link to the pressure cooker story and its content make it clear that the new version has '4 times less' pressure than 15 psi.    And though that puzzled some posters, it likewise, clearly, means 1/4.   I note that Panjandrum seems to have given the same analysis, and no other poster proposed an answer to the question of the OP.

http://forum.wordreference.com/showthread.php?t=1488998
article:   http://www.dailymail.co.uk/femail/f...en-housewifes-staple-cooker-makes-return.html

Wordsmyth and Julian, your purported demonstrations are purely fanciful.    Checking the term in the wild and properly applying the 'times' (multiplication) principle show the correct interpretation of these expressions.


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## JulianStuart

bennymix said:


> To Word and others,
> 
> 
> 
> ===
> 
> Hi Word,
> "3 times less" means 1/3 as I said in post #3
> 
> To answer your question. Yes, one says 2 times less, and that means one half of.
> 
> The link to the pressure cooker story and its content make it clear that the new version has '4 times less' pressure than 15 psi.    And though that puzzled some posters, it likewise, clearly, means 1/4.
> http://forum.wordreference.com/showthread.php?t=1488998
> article:   http://www.dailymail.co.uk/femail/f...en-housewifes-staple-cooker-makes-return.html
> 
> Wordsmyth and Julian, your purported demonstrations are purely fanciful.    Checking the term in the wild and properly applying the 'times' (multiplication) principle show the correct interpretation of these expressions.



Please help me
When I learnt my multiplication tables, I got a pretty good understanding of the meaning of "times".  Three times four equals twelve.  Or in general "A times B = A*B". (Arithmetically the operator " * " ) 
When someone says "A is C less than B", I know that B - C = A is true.  (Arithmetically the operator " - ".)
So when "A is three times less than B", what gets multiplied by what (the "times" word) and what gets subtracted from what (the "less than" phrase)?

(I don't deny that when some people say "A is three times less than B" they do mean "A is 1/3 the size of B" but I am trying to understand the grammar here


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## RM1(SS)

bennymix said:


> Checking the term in the wild and properly applying the 'times' (multiplication) principle show the correct interpretation of these expressions.


I see no errors in the multiplication in posts 8 and 9.


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## srk

_A is three times greater than B_ is as confusing as _A is three times less than B_, and they are both confusing.  _A is three times as large as _B is as straightforward as _A is one third as large as B,_ and they are both plain.  What is as large as B is B, and what is three times as large as B is 3B.  What is three times greater than B or three times less than B is a mystery solved only by bennymix and perhaps a few others.  Nothing says that the author of the Mail Online article knew what she meant.

Under atmospheric pressure, water boils at 212F, and there is no way to increase the temperature in an open vessel, because the water boils away rather than become hotter - all the added heat from the burner is expended in changing the state of the water from liquid to gas.  Pressure cookers work by allowing the water inside the device to become hotter than 212F.  (Hotter water cooks stuff faster.) They do this by trapping steam, increasing the pressure in the cooker.  The higher the pressure, the higher the boiling point.

A pressure cooker that operates at lower pressures above one atmosphere would cook faster than at atmospheric pressure, but not as fast as older cookers.  *A quarter the usual pressure* in a pressure cooker would  be *below atmospheric pressure*.  If "4 times less" means "one quarter the original", it doesn't make cooking sense.  I don't think it makes any sense.


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## bennymix

One can describe increase(decrease) in a multiplicative way or an  additive way.   The former is indicated by 'times', also the word  'factor'.   (Percentages are a different notation, but are  multiplicative.)  Natural growth processes are generally
multiplicative.   Suppose the bacteria colony today is 'half again as large' in number, as it was yesterday. (Multiply by 1.5). 
Today  there are 1.5 million and yesterday, 1 million.  One will expect that  the new number, reproducing for a day, will generate a larger number  than .5 million;  the 'base', so to say, is greater. (As with a compound  interest investment.)  The new number should be 1.5 million multiplied by 1.5, or 2.25 million.


Lets assume yesterday's size of the  bamboo sprout was 3.33 cm.  Today's size is 10 cm.  Tomorrow's  (expected) size, 30 cm.  (Measurements taken at the same time, each  day.)

The daily growth is by a factor of 3, moving from earlier  to later.  On a graph, there is an upward sloping (to the right) line,  whose slope is 3.    If we move in the other direction, the daily  decrease is by a factor of 3.   That would be division by 3 or  multiplication by 1/3.  Moving leftward, the line slopes down; measuring  in reverse, the slope is -3.

These are equivalent:  A. *Today's size is 3 times yesterday's. *  B.  *Yesterday's size times 3 is today's size.*

Equivalent to A, is       A*:  *Today's size is 3 times more than yesterday's. 
*
Now, what is the meaning of '3 times less'?  What would this sentence mean?  
C:*  Yesterday's size is 3 times less than today's.*

We  must get to 'less' and it must be by multiplication (because of the  word 'times').   Proposal: Inverse multiply, that is, divide by 3  (multiply by 1/3)

We propose, then.   A* *Today's size is 3 times more than yesterday's  *as equivalent to 
C.  *Yesterday's size is 3 times less than today's.*

The  number tells you the multiplier ('times' tells you to multiply) and  'more' or 'less' tells you whether to multiply to make bigger, or  inverse-multiply (divide) to get smaller.

The number 1 will  generate no increase or decrease.  'X's value is now 1 times more than  X's value yesterday', means the two values are the same.   'X's value  yesterday is 1 times less than today's value'  means no change.

The above proposal is consistent with common usage, and above text may help explain it, except to the wholly unregenerate.  

http://www.nytimes.com/2007/10/28/opinion/28iht-edfreeman.1.8081659.html?_r=0


> But  'times less' has tradition, if not logic, on its side; it was idiomatic  English for at least two centuries before anyone claimed it was  confusing, according to Merriam-Webster's Dictionary of English Usage.
> 
> Jonathan  Swift, for instance, used it in 1711, writing "I am resolved to drink  ten times less than before." It wasn't till the 20th century that  language commentators - not mathematicians - came up with the notion  that "three times closer" and "100 times slower" were illogical and  confusing.


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## bennymix

Reply to srk

srk


> _A is three times greater than B_ is as confusing as _A is three times less than B_, and they are both confusing.  _A is three times as large as _B is as straightforward as _A is one third as large as B,_  and they are both plain.  What is as large as B is B, and what is three  times as large as B is 3B.  What is three times greater than B or three  times less than B is a mystery solved only by bennymix and perhaps a  few others.  Nothing says that the author of the Mail Online article  knew what she meant.
> 
> Under atmospheric pressure, water boils at 212F, and there is no way to  increase the temperature in an open vessel, because the water boils away  rather than become hotter - all the added heat from the burner is  expended in changing the state of the water from liquid to gas.   Pressure cookers work by allowing the water inside the device to become  hotter than 212F.  (Hotter water cooks stuff faster.) They do this by  trapping steam, increasing the pressure in the cooker.  The higher the  pressure, the higher the boiling point.
> 
> A pressure cooker that operates at lower pressures above one atmosphere  would cook faster than at atmospheric pressure, but not as fast as older  cookers.  *A quarter the usual pressure* in a pressure cooker would  be *below atmospheric pressure*.  If "4 times less" means "one quarter the original", it doesn't make cooking sense.  I don't think it makes any sense.



I'm sorry you are confused by the pressure cooker article (as were some other posters in that old thread).

It said,

http://www.dailymail.co.uk/femail/f...en-housewifes-staple-cooker-makes-return.html    WiKook model.



> Like the classic version it [WiKook] uses pressure to heat food 25 per cent quicker than a saucepan, ensuring nutrients are better preserved.
> 
> But unlike the old stainless steel cooker, the aluminium WiKook model from Tefal can be opened at any time during cooking so you can stir, season or add a forgotten ingredient.
> 
> This is because it operates at four times less pressure than the old pressure cookers.



Normal atmospheric pressure is 14.7 pounds per square in, absolute.  The usual pressure cooker works at about 15 pounds per square inch, 'gauge.' that is on top of the normal. (In other words, 29.7 psi absolute.)

The WiKook apparently generates a quarter of that ("four times less), or 15/4 psi guage, or 3.75 pounds per sq inch on top of the normal  (that is, 18.45 psi absolute), which speeds up cooking.

I'm not sure how you came up with 





> A pressure cooker that operates at lower pressures above one atmosphere  would cook faster than at atmospheric pressure, but not as fast as older  cookers



I suspect you took the gauge pressure of 15, for the cooker as absolute, and divided by 4, and construed that as likewise absolute pressure, i.e. 3.75 pound absolute, which is less than the normal 14.7 for the atmosphere.

Alternatively, you may have converted the 15 psi gauge to  absolute, making it 14.7 + 15, or 29.7.   Then you divided that by 4, getting an absolute number, 7.43. which is less than the normal atmosphere, in absolute.

In any case, the answer is rather simpler than going through all the hoops you did.


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## Wordsmyth

bennymix said:


> _[...]_ To answer your question. Yes, one says 2 times less, and that means one half of. _[...] _


 I've obviously never met the "one" who says that. Or perhaps I just have: Hi, benny. Seriously. I don't think I've ever heard a native English speaker say it (and I don't consider I've led a linguistically sheltered life!).


bennymix said:


> _ [...] _These are equivalent:  A. *Today's size is 3 times yesterday's. *  B.  *Yesterday's size times 3 is today's size.
> *
> Equivalent to A, is A*: *Today's size is 3 times more than yesterday's. *_[...]_


Let's call yesterday's size H1 and today's size H2 (and I'll use _x_ to indicate 'times', for readers who aren't so familiar with *)
- Sentence A says: H2 = 3 x H1
- Sentence B says: H1 x 3 = H2 (which is indeed mathematically equivalent to A)

Now let's look at sentence A*:
- Yesterday's size is H1. 'One time more' is H1 + H1 = 2H1 .—. 'Two times more' is H1 + 2H1= 3H1.—. 'Three times more' is H1 + 3H1= 4H1
..So sentence A* says: H2 = H1 + 3H1 ... which equals 4H1.
..So sentence A* is not equivalent to sentence A.

Your reason for disagreeing with that, benny, was:


bennymix said:


> _ [...] _The number 1 will generate no increase or decrease. 'X's value is now 1 times more than X's value yesterday', means the two values are the same. 'X's value yesterday is 1 times less than today's value' means no change. _[...] _


 
Apart from the grammatical problem with "1 times" (1 is singular), do you honestly believe that if you said "X's value is now 1 time more than X's value yesterday", anyone would take that to mean the two values are the same? For that to be so, your listener would have to think that "1 time more than" means "the same as"! 

If you've seen a movie three times, and I've seen it "one time more than you", then I've seen it four times. But by your argument I've seen it only three times!

The fundamental difference between your principle and that of the 'unregenerate' (i.e. most of us) is that you don't seem to differentiate between "3 times" and "3 times more". So if you ever stamp your foot and complain that I have *more* candy than you, I can reply that there's no problem, 'cos you actually have the same.

Ws


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## srk

bennymix:

You know more about pressure cookers than I do.  I thought they operated at a few psi above atmospheric pressure, not at twice atmospheric pressure.  I've carried my wrong idea around over the years from who-knows-where, thought it was right, and didn't think it was worth checking. Even then, I was thinking absolute rather than gauge pressure.  That's all really bad.  I apologize.


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## wandle

JulianStuart said:


> Gotcha (finally!)   The result of "three times less than X" is "-2X".  (in arithmetic terms:  X -3X = -2X ) .


That can hardly be the meaning of the original, though:


> Ann has 3 times less apples than John.


Suppose John has nine apples. If the operation is *x - 3x = -2x*, then Ann has 9 - 27 = -18 apples.
How is she going to get -18 apples into her shopping-bag?
Perhaps she would be able to carry home -18, but if John bought, say, a couple of hundred, Ann might have difficulty keeping her feet on the ground.


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## Wordsmyth

Amusing thought, wandle. But since the statement does mean that (even if the speaker didn't intend it to), your examples go to show that the original sentence is pretty nonsensical. 

If I hear "Ann has 3 times less (fewer) apples than John", my first thought is 'That can't be true, so the speaker must mean something else'. Of the other things that the speaker might mean, "a third" is the most likely (if not the only) possibility. However, if the first misstatement was down to muddled thinking, I wouldn't be sure that my assumption was the right one, so (if I cared) I'd end up having to ask what the speaker really meant.

The problem is greater with "three times more", because it makes sense in the first place. If John has nine apples, then Ann has 36 apples (not 3 times John's, which would be 27, but 3 times more than John: 9 + 3x9). Unfortunately, some people use it to mean that Ann has 27 (instead of saying, correctly, "Ann has 3 times as many apples as John"). So the sentence "Ann has 3 times more apples than John", whilst not senseless, is actually useless: if I heard it, I wouldn't have the slightest idea whether the speaker meant 36 or 27.

Ws


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## JamesM

bennymix said:


> To Word and others,
> 
> 
> 
> ===
> 
> Hi Word,
> "3 times less" means 1/3,  as I said in post #3.
> 
> To answer your question. Yes, one says 2 times less, and that means one half of.



I have heard a few people say this and, honestly, I wouldn't trust them to calculate their share of the tab at a restaurant.    I've read through the thread and still don't see where 2 times _what_ is explained.  What are you multiplying by two in order to get the result?

If I have 100 dollars and you have 2 times less and you say this means 50 dollars, then 1 time must be 25 somehow.  100 - (2*25) is the only way I see to figure out what is being multiplied by 2 in order to get the answer you propose.

I consider it sloppy speaking that I assume is a result of sloppy thinking.  That is my prejudiced opinion, I know, but it is my honest reaction.


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## Wordsmyth

As I understand it, James, benny was proposing (and I paraphrase) that "times" on its own means 'multiplied by', and that "times more" means the same, but that "times less" indicates 'divide the original number by the number immediately preceding this phrase'. Not a definition I've ever seen in any dictionary, nor in any maths textbook.

Ws


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## JamesM

I certainly wouldn't recommend using "times less" to mean "divided by previous number" to a non-native speaker.  I don't think that's a general consensus at all among English speakers. 

5 times less than 100 = 20 
100 divided by 5 = 20 
1/5th of 100 = 20 
20% of 100 = 20 

(The logic doesn't make sense to me.  So "one times less" is same as the thing itself?  One times less than 100 is 100. ???  That's too convoluted for me.)


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## bennymix

Hi Wordsmyth.

Your speculations are rather out of touch--in my  unbiased opinion.  Essentially you say that Ann, in your example, with  36 apples, has 





> "3 times more than John: 9 + 3x9). "


   36, you say, is 3 times more than 9.

This is a well debated topic on the 'net, e.g.,

http://languagelog.ldc.upenn.edu/nll/?p=4263

and  the 'reasoning' by 'your' side has always seemed a bit wacky to me.    It reminds me of those who say,  "I don't know nothing" actually means,  "I know something" because "two negatives make a positive."   But, to my mind, the realities of language use always trump such attempts at reason.

Your  example is self made, and not surprisingly, self serving--contrived by  you to corroborate this wacky ratiocination.   {Not that you, my friend,  as less than entirely sane, rational and empirical, here, but maybe  you've been bitten by some strange internet bug!    }



> The problem is greater with "three times more",  because it makes sense in the first place. If John has nine apples, then  Ann has 36 apples (not 3 times John's, which would be 27, but 3 times more than John: 9 + 3x9). Unfortunately, some people use it to mean that Ann has 27 (instead of saying, correctly, "Ann has 3 times as many apples as John"). So the sentence "Ann  has 3 times more apples than John", whilst not senseless, is actually  useless: if I heard it, I wouldn't have the slightest idea whether the  speaker meant 36 or 27.



=====

The best way  to bring actual reason to the matter--and I say this dispassionately--  is to start with the higher numbers, and take examples "from the  wild" **.   They are quite clear for the higher numbers, and very favorable  (to my interpretation) for the lower.  Two and three (times more) are  debated,  but my proposal is very simple   "X times more than" something  is means the same as "X times" [Corrected 4 pm EST, Feb 13](as many as that something or the measure of that something),   assuming we're talking of some things that are, respectively, countable  or quantifiable) . 

Here are some examples--I've chosen sources with numerical data so that matters are clear.

http://www.rockyviewweekly.com/arti...-two-times-more-snow-than-normal-for-december

[Alberta Can, newspaper]

*County sees two times more snow than normal for December*

By: Sara Wilson

  |  Posted: Monday, Dec 30, 2013 11:43 am


> If you were thinking there’s more snow this month as there was last year, you are right – two and a half times more.
> 
> According  to Environment Canada from the beginning of November until Dec. 18 a  total of 70 centimetres (cm) has accumulated in Airdrie and surrounding  county communities.
> 
> That’s two-and-half times the normal accumulated amounts of 28 cm.
> 
> “There’s been lots of snow,” said Bill McMurty, meteorologist with Environment Canada.



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books.google.ca/books?isbn=0674033442
Vladislav Zubok - 2009 - ‎History

In  1971–72 there were 105,000 Jewish students in Soviet universities, two  times more than the number of university students in Israel. Among sixty  thousand .

===
http://discovermagazine.com/2014/jan-feb/43-ten-times-the-lyme#.Uv0Sq_szDgs

*Lyme Disease Ten Times More Prevalent Than Previously Thought*

The  CDC now estimates that 300,000 Americans are infected with Lyme — and  other tick-borne illnesses are a growing threat as well.

By Jeff Wheelwright, Breanna Draxler




> When  the Centers for Disease Control and Prevention (CDC) estimated last  summer that the number of people diagnosed with Lyme disease each year  was 300,000 — 10 times as high as the official counts — the agency must  have expected headlines, and it got them. The alarmingly high figure  justified assertions by patient advocacy groups that the 30,000 cases  reported annually were just the tip of the iceberg.



===


===

Hens: Why Women Are Different - Page 61 - Google Books Result
books.google.ca/books?isbn=0741429543
Carl Fors - 2006 - ‎Social Science


> Red meat has six times as much zinc as a chicken breast and ten time[s] more than fish. Men need 45% more zinc than woman.




http://www.news-medical.net/news/20...children-with-brain-injury-or-concussion.aspx

Depression remains two times more likely in children with brain ..
.
www.news-medical.net/.../Depression-remains-two-times-more-likely-in-...‎



> Oct  25, 2013 - Adults with head injuries are known to be at high risk for  depression, and yet little research had been done on the topic related  to children.  [...]
> 
> Using data from the 2007 National Survey of  Children's Health, researchers identified more than 2,000 children with  brain injuries, reflecting the national child brain injury rate of 1.9  percent in 2007; and 3,112 children with diagnosed depression, mirroring  the 3.7 percent national child depression rate that year. Compared to  other children, 15 percent of those with brain injuries or concussions  were diagnosed as depressed-a 4.9 fold increase in the odds of diagnosed  depression.


==

This same approach may be  applied to "X times less than" and there are lots of examples (re Swift,  in my post #5) showing that in common usage, the expression means "1/X  times" whatever measured entity--typically a rate-- is being spoken of.

===
**ADDED:   James, below makes a good point about the 'wilds' of the internet.    I should have said to look for "actual usage"--not constructed--preferably from published sources, e.g., books from well-known publishers, scholarly journals,  respected magazines and better newspapers.


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## JamesM

I agree that "X times more" is in common usage, but I would argue that "X times less" is far less common.   We can find examples "in the wild" of all sorts of errors.  In fact, many of the threads on this forum testify to that.    I don't think examples in the wild is a measure of accuracy or even commonality.

Here is an interesting paper on typical errors made when describing mathematical comparisons:

http://web.augsburg.edu/~schield/MiloPapers/984OfSigCompare3.pdf

Among the most common errors:



> .Using ‘times less’ as an inverted form of ‘times as much’.  Since six is three times as much as two, it is tempting to say that two is three  times less than
> six.  But if two were three times less than six, then six should be three times more than two. Recall that six is three times as much as two – two times more than two.  ‘Times
> less than’ is an inverted form of ‘times more than’ – not ‘times as much’.



His correction for "times less than" is an interesting one:



> When using ‘times more/less than’:  Five is 0.25 times more than four.  Four is 0.20 times less than five.



I can see the math in this:   5 - (5 * 0.2) = 4


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## JamesM

On the "more than" side, the paper has this to say:

http://web.augsburg.edu/~schield/Mil...igCompare3.pdf



> If B is three times as much as A, then B is two times more than A – not three times more than A. The essential feature is the difference is between ‘as much as’ and ‘more than.’  ‘As much as’ indicates a ratio;  ‘more than’  indicates a difference. ‘More than’ means ‘added onto the base’



So, Wordsmyth's self-made example follows this "wacky" reasoning.    I would apply the same reasoning.  If you have $100 and I have twice _as much as_ you, I have $200.  If I have two times _more than_ you I have $300.

If I have half as much as you have and you have $100 I have $50.
If I have half again more than you have I have $150.


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## Wordsmyth

bennymix said:


> Hi Wordsmyth.
> 
> Your speculations are rather out of touch--in my  unbiased opinion.  _[...] _


 Given the number of opinions in this thread in favour of your arguments, benny, vs those that are not (and I won't be saying how many more are in the second group than in the first ), I leave it to any unbiased reader to decide who's out of touch.


bennymix said:


> _[...] _This is a well debated topic on the 'net, e.g., http://languagelog.ldc.upenn.edu/nll/?p=4263
> 
> and the 'reasoning' by 'your' side has always seemed a bit wacky to me.  _[...] _


 Well there's some pretty wacky thinking by the guy on that site who (I suppose) is on your side. He declares that a speed of 1000 ft/min is "hundred*s* of times faster" than 10 ft/min. Now I'll agree that 1000 ft/min is hundreds of ft/min (990 ft/min to be exact) more than 10 ft/min. But by your own definition (and his, and in fact anybody's), "times" requires multiplication; and 1000 = 100 x 10. *Since when is 100 = "hundreds"? *(If I've told you once, I've told you a million times, don't exaggerate!)

But I would agree that "hundreds of times more than" expresses the same idea as "hundreds of times as many as", because 'hundreds" is very approximate. So if I have 800 apples and you have only one, it's true to say that I have hundreds of times as many (800 = 'hundreds') or that I have hundreds of times more (799 = 'hundreds'). That's not the same case as "X more than", where X is an exact number. 


bennymix said:


> _[...] _It reminds me of those who say, "I don't know nothing" actually means, "I know something" because "two negatives make a positive."_[...] _


 But it can mean just that — if, for example, you say to me "You know nothing", and I reply "But I don't know nothing, I know quite a lot". It's not because a group of people use language 'approximately' (he said with restrained politeness), that the rest of us should be scorned for using it accurately. The same applies to the 'approximate' use of "X times more/less/fewer than".


bennymix said:


> _[...] _But, to my mind, the realities of language use always trump such attempts at reason.


 But the 'realities of language' include both reasoned and unreasoned usage. I don't see how something can trump an intrinsic part of itself.


bennymix said:


> _[...] _Your example is self made, and not surprisingly, self serving--contrived by you to corroborate this wacky ratiocination. _[...]_


 Look back! My example was neither self-made nor contrived. It was the sentence that the OP asked about in post #1! Should we now stop answering OPs' questions in case someone who disagrees might think our comments to be self-serving?

Your repeated but very subjective use of "wacky" reminds me of the guy in the straightjacket being hauled off by the men in white coats, as he cried out "I'm the sane one. Everyone else is crazy."

Finally, as James has pointed out, quoting numerous sources (even those as impressive as the Rocky View Weekly) doesn't prove the acceptability of a language form by everyone, or even by most people. It just shows that it's used by some people. What makes this discussion different from most is that we're talking about a language form that is used to communicate a mathematical fact — and mathematics is (mostly) an exact science based on reason. I'd say that supports the case for reason trumping muddled usage. 

Ws


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## bennymix

There are some muddles in your post, but let's try to clarify the most obvious one.

You say   





> //My example was neither self-made nor contrived. It was the sentence that the OP asked about in post #1! //



Let's look at the OP, then at your text in post 30, *esp. its last para-- the one I quoted as an example and commented on.


OP



> I’ve come across an opinion of the native speakers of English that if one says, for example, that «Ann has 3 times less apples than John», this doesn’t equals to «John has 3 times as many apples as Ann does».
> 
> They claim that in the strict logical sense, the meaning of the former sentence is that of subtraction (actually, the subtraction of 3*number of apples Ann has from John's), not division. And the correct way of conveying the intended meaning of division would be «Ann has one-third as many apples as John».
> 
> Assuming that this chain of reasoning is correct, how does one state that X is, say, 1/25 of Y? (without inverting the sentence to «Y is 25 times as much as X).



Wordsmyth said, post 30.



> Amusing thought, wandle. But since the statement does mean that (even if the speaker didn't intend it to), your examples go to show that the original sentence is pretty nonsensical.
> 
> If I hear "Ann has 3 times less (fewer) apples than John", my first thought is 'That can't be true, so the speaker must mean something else'. Of the other things that the speaker might mean, "a third" is the most likely (if not the only) possibility. However, if the first misstatement was down to muddled thinking, I wouldn't be sure that my assumption was the right one, so (if I cared) I'd end up having to ask what the speaker really meant.
> 
> The problem is greater with "three times more", because it makes sense in the first place. If John has nine apples, then Ann has 36 apples (not 3 times John's, which would be 27, but 3 times more than John: 9 + 3x9). Unfortunately, some people use it to mean that Ann has 27 (instead of saying, correctly, "Ann has 3 times as many apples as John"). So the sentence "Ann has 3 times more apples than John", whilst not senseless, is actually useless: if I heard it, I wouldn't have the slightest idea whether the speaker meant 36 or 27.


===


I commented on the highlighted para  as follows (my post #34)  



> Your example is self made, and not surprisingly, self serving--contrived by you to corroborate this wacky ratiocination.



wordsmyth, replies, post 37



> Look back! My example was neither self-made nor contrived. It was the sentence that the OP asked about in post #1! Should we now stop answering OPs' questions in case someone who disagrees might think our comments to be self-serving?


===

I was clear about the example, and indeed it's made by you.   It not from the OP.    In fact "times more" is not even mentioned in the OP.

===
===
As to the examples I furnished, you say, post #37,



> Finally, as James has pointed out, quoting numerous sources (even those as impressive as the Rocky View Weekly) doesn't prove the acceptability of a language form by everyone, or even by most people. It just shows that it's used by some people. What makes this discussion different from most is that we're talking about a language form that is used to communicate a mathematical fact — and mathematics is (mostly) an exact science based on reason. I'd say that supports the case for reason trumping muddled usage.




If I've show my interpretation is shared and used by some, I'm content.  Debates on the 'net can't canvass masses
of evidence. _The fact remain that, esp. for the larger numbers (e.g. 10 times more than), you've not shown that anyone, in real life, in a respectable publication speaks the way you believe to be dictated by reason._

I can't really make out your argument about mathematics.   You want to argue that findings from 'an exact science'
trump 'muddled usage.'  You haven't shown anything about 'muddled usage' and "X times more than..." as "X times..."
is a common equating; calling it muddled is simply arguing in a circle.    

Your view of 'trumping' seems to be like that of a boy physicist whose mother says,  "Come here this instant."  
The boy replies, "In the science of physics an instant has no duration;  no one can move to another location in an instant.  Further 'this instant,' even if I could come in it,  has already passed.  You make no scientific sense.  Your command is a muddle."

One wants language usage to have a certain consistency and coherence in its best use.  This is not the rigorous consistency of mathematics.  Nor does ordinary usage present scientific truths. "He's over the moon" is not a scienfic statement.  Thus language as ordinarily used is not subject to correction by scientific findings.  

Suppose one is asked the meaning of "He's in seventh heaven."  One should seek, I would say, to understand the sentence in terms of the language usage and language world (religious and philosophical worldview) of the time when the expression originated.    If one asks what that means, one doesn't  expect someone to say,  "Science has found no evidence of a 'heaven,' not to say a 'seventh level.'  Further 'he' with a physical body, cannot be in heaven,  which has no physical location.  So the statement is nonsense as it stands.  The person should abandon muddled usage and simply say, 'He's very happy.' "


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## Loob

I got a bit lost with your last post, benny.

But here are my reactions:

*Three times as much as x**
Three times more than x*: _sort of  (though I'm not 100% sure what it means)_*
Three times less than x*: _definite  - it makes my brain hurt._


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## bennymix

Hi Loob,
If you follow my suggestion and take a big number you'll get lots of hits.  For  "ten times less than", it's over a million--and I've scanned the first 20 Google pages, where there are, perhaps a 100 good examples.

Though I'm sure Word and James will pooh pooh such examples and suggest that we defer to their mathematical speculations, the language usage is clear as to its meaning (many articles give the numbers).

http://www.ipsnews.net/2013/07/europes-youth-count-ten-times-less-than-its-banks/

*Europe’s Youth Count Ten Times Less than Its Banks*

By Roberto Savio Reprint |       | Print | Send by email



> In this column, Roberto Savio, founder and president emeritus of the Inter Press Service (IPS) news agency and publisher of Other News, argues that European leaders’ recent decision to allocate 60 billion dollars to banks, but only six billion dollars to fight youth unemployment, paints a clear picture of the region’s priorities: financial institutions above the well-being of the people.


===
*
Free Will: A Guide for the Perplexed *- Page 24 - Google Books Result
books.google.ca/books?isbn=1441102094
T. J. Mawson - 2011 - ‎Philosophy



> If I borrow ten pounds off one man and a hundred pounds off the other, then my debt to the first is a debt for an amount ten times less than is my debt to the [second].



===
I've taken the more difficult case ('less').   For 'ten times more than,' there's a small sample in my last post.   The usage and its meaning are crystal clear.


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## wandle

Here are two examples of 'five times more than'.

Local Government Association  Care loans scheme could cost councils up to five times more than estimated

_Figures published by the Local Government Association (LGA), which represents councils in England and Wales, show the cost of the scheme could reach more than £1.1 billion by 2025 – in comparison to an estimate based on Government assumptions of £230 million._

Facebook Has Five Times More TV Chatter Than Twitter

_After all, Facebook has a billion users to Twitter’s 200 million, so that 5x ratio makes plenty of intuitive sense._

In each case, 'five times more than' represents 'multiply by five'. This is so natural, I find it difficult to imagine that anyone would in practice understand the expression any differently. The phrase 'five times more than' contains only one term that expresses a mathematical operation, namely 'times (more than)'. This simply means 'multiply'. If addition were meant to be performed as well as multiplication, this would need to be expressed by a term such as 'plus' or 'add', and there would also need to be something to show what should be added to what.

Are there any examples from reputable sources in real life (as distinct from examples made up for the sake of argument) where 'five times more than' means 'multiply by five and add the number you first thought of'?


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## RM1(SS)

It contains two terms - _times_ and _more than_.  The first indicates that something is to be multiplied, the second that something is to be added.


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## wandle

That, with respect, is assertion. The examples in post 41 go to show that 'five times more than' means simply 'multiply by five'.

Do you know of any real-life examples (in the sense mentioned above) where 'five times more than' means 'multiply by five and add to the first number'?


----------



## JamesM

It's a good point, wandle, and yes, I know you're not the first to make it in this thread.

I've looked for real-life examples and haven't found any yet.    So, "5 times as much" and "5 times more than" are equivalent in practice, even though there are plenty of educational sources that say otherwise?  I may have been converted by this thread.  

It still doesn't make logical sense to me, but much of language doesn't make logical sense.  I still would avoid using them if I wanted to make sure that the number I was picturing was the number the listener was hearing.  It seems so odd that "as much as" and "more than" can be equivalents, in any context, but I haven't seen real-life examples to support my prejudice... yet.  

I'm still not sold on the "five times less than". If "5 times more than" is "multiply by five", how can "5 times less than" be other than "multiply by five and subtract"?  I don't see how it can be "divide by 5".  I may just have to sit with it for a while.


----------



## Wordsmyth

bennymix said:


> _ [...] _I was clear about the example, and indeed it's made by you.   It not from the OP.    In fact "times more" is not even mentioned in the OP.


 The example (a typical sentence representing the subject under discussion) was the OP's. The analysis of it was mine. By the time I made that analysis, others had already extended the discussion to the "times more" concept (including you in your bamboo sprout example in #25, but I won't make any accusations about it being contrived or self-serving.).

As for your examples (and analysis) of other expressions, "Come here this instant", "He's over the moon", "He's in seventh heaven", they have nothing to do with the present subject. The first (relative to the 'scientific' definition) is hyperbole. The last two are metaphors. None of them communicates an arithmetic expression that leads to a numerical answer. There is nothing metaphorical, nor hyperbolical, about "times less/more than".

--------------------------------

What's clear is that there are people who understand "times more than" to have an 'approximate' definition, and others who understand it literally. Of the former, some use "times less than" as a sort of inverse form, while others find it meaningless. For those who understand "times more than" literally, "times less than" is nonsense (except where negative values are relevant). Oh, and then there are those who recognise "times more than" (sort of), but aren't 100% sure what it means (and I'm sure Loob's not alone!)  

Proof of all that exists in this thread, but also in numerous other discussion forums, as well as in educative sources. No amount of time-consuming searching for individual instances is going to change that.

So the only practical conclusion is that "X times more/less than" should be avoided in favour of less confusing forms: "X times as much/many as", "X times as _[any appropriate adjective]_ as", "X times the number of", "X times the size of", etc.

A cautionary tale to illustrate the wisdom of that. A large company I once worked for strongly prohibits the use of "X times more/less than", because they once used it in an ad, with the 'arithmetically incorrect' interpretation. They were threatened with legal action for false advertising, but settled out of court via a mediation body. The mediator accepted that there was no deliberate intent to deceive (so there'd be no risk of punitive damages), but concluded that the ad was at best ambiguous, and, strictly speaking, incorrect.

Ws


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## Kunio

This is an interesting thread 

"Ann has 3 times fewer apples than John."
It is said this way to emphasize how little Ann has in relation to John.  If you wanted to emphasize John's good fortune, you could say "John has three times more apples than Ann."

It's still multiplication either way.
(Ann's apples) * 3 = (John's apples)


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## JamesM

It's not really multiplication, as I see it.  I ran across an article that helped me to accept it.  It explained it as an informal way to describe a ratio.  

However, I'd be curious to see how you would write "Ann has 3 times fewer apples than John" as math.  It's not really (Ann's apples) * 3.  That's a conversion of the original statement.  It's (John's apples) / 3 = (Ann's apples), as far as I can see, which is the part that bugs those of us who think in formulas when we see word problems.

So how would you write the second sentence as a multiplication problem, assuming you have to make the formula's components match the order of words in the sentence:

"John has three times more apples than Ann" = "(John's apples) = 3 * (Ann's apples)"
"Ann has three times fewer apples than John"  = ???


----------



## Kunio

"Ann has 3 times fewer apples than John" and "John has three times more apples than Ann." are two different ways of speaking the same equation.
There is technically no such thing as division.  You could say "John's apples times .3 repeating equal Ann's apples" and mean the same thing but the person you're talking to will probably make fun of you 

(Ann's apples) * 3 = (John's apples)

A computer, for example, could not possibly see this two ways.  It's (Ann's apples) * 3 = (John's apples) and nothing else makes any sense.


----------



## JamesM

> There is technically no such thing as division.



That's interesting.  On the face of it, that seems like a ludicrous statement.  I'd love to hear the explanation of that but we've wandered too far afield already, I'm afraid.  You're welcome to PM me, though.


----------



## Kunio

It's not that far afield.  I just meant to explain why I think "x has 3 times fewer than y" is a valid statement.

I was just thinking from a logic standpoint, like in a computer, division is a compounded subtraction.  "9 divided by 3" is just "the number of times you have to subtract 3 from 9 to get 0".  Dividing is really just subtraction, just like multiplication is really just addition.  (Ann's apples) + (Ann's apples) + (Ann's Apples) = (John's apples)


----------



## JamesM

That explains the "more than".  How does that apply to the "fewer than"?


----------



## RM1(SS)

wandle said:


> That, with respect, is assertion. The examples in post 41 go to show that 'five times more than' means simply 'multiply by five'.
> 
> Do you know of any real-life examples (in the sense mentioned above) where 'five times more than' means 'multiply by five and add to the first number'?


You are asserting that those examples are correct English.  I disagree.

Your opinion seems to be that if I have three apples and Morag has four times more than I have, then Morag has twelve apples.  Hamish has four times as many apples as I have; how many does he have?


----------



## wandle

Four times three equals twelve in both cases.

Naturally each contributor is asserting a view, but some contributors are providing examples which show objective support for their view: that is, derived from the published statements of others (not thought up by the poster). 

In the following wind energy example, the text shows that the two expressions 'four times more than' and 'four times as much as' are seen as equivalent in meaning.

Wind energy costs four times more in the UK than Brazil

_Families in the UK are paying four times as much to subsidise wind energy as those in Brazil thanks to the size of levies on their bills, a new study has claimed. ....
The findings from the Policy Exchange showed that the cost of wind farm subsidies in the UK is currently £95 per megawatt hour for onshore wind farms. This is nearly four times as much as the £27 per megawatt hour that is added to bills in Brazil, where they are the cheapest in the world._


Germany’s KfW Earns Four Times More Than Deutsche Bank

_Kreditanstalt fuer Wiederaufbau, Germany’s third-biggest bank by assets, said profit rose 15 percent to 2.4 billion euros ($3.1 billion) in 2012 ... 
Deutsche Bank AG (DBK), Germany’s biggest lender based in Frankfurt, had a profit of 611 million euros in 2012._


----------



## RM1(SS)

wandle said:


> the two expressions 'four times more than' and 'four times as much as' are seen as equivalent in meaning.


You think that they are correctly seen as equivalent.  I do not.  I can not see any way in which _more than_ and _as much as_ can possibly mean the same thing.

Let's rob a bank, shall we?  I'll keep 90 percent of the loot and give you 10 percent, and when you complain that I have more than you, I will happily agree that I have as much as you, since you consider the terms to be equivalent....


----------



## JamesM

I can understand you thinking, RM1(SS), but this is more like an idiom.  The position is that "10 times as much as" and "10 times more than" are equivalents in actual practice, whether it's logical or not.  I have yet to find an example where my original concept (which was the same as yours) was actually used in real life.

Can you find one?  Honestly, I've spent a fair amount of time looking for one because I was sure that "five times more than X" gave you 6x while "5 times as much as X" gave you 5x, but I don't see that borne out in any actual text other than sites that simply agree with my interpretation.  There are no real-life examples of it being used this way.

I agree with your logic but when I can't find even a single example I have to doubt that it is ever used that way in practice.


----------



## JulianStuart

A perfecty good, unambiguous resource for simple mutiplication: John has three times as many apples as Jane. 
Simple resource for subtraction: Jane has six fewer apples than John.

Some simply see ambiguity created by using words that are used differently in other situations, and see it as a potentially "mixed case" because it mixes the words from different unambiguous cases: 
Jane has three times fewer apples than John.  

Others simply do not see the potential ambiguity.

This post is not concerned with the "correctness" of either group.

One maxim we use when teaching is to discourage the use of words or sentences which have any possibility of ambiguity for the listener. Thus, to the OP's question I say "Yes, it would be a bad way to express it" simply because this discussion has pretty conclusively proved that its meaning is ambiguous/contentious.


----------



## Loob

JulianStuart said:


> Thus, to the OP's question I say "Yes, it would be a bad way to express it" simply because this discussion has pretty conclusively proved that its meaning is ambiguous/contentious.


Nicely put, Julian - I agree with you.


----------



## Cagey

As the original question has been well answered I am closing the thread.
It is clear that the differences between the two (or more) views on the matter will not be resolved. 
However, the views have been clearly explained, and anyone who reads this thread will decide for themselves what makes the most sense to them. 

Thank you, everyone,  for your participation.   

Cagey, 
English Only moderator.


----------

