fractions - "Ten times fewer the number" versus "one-tenth the number"


Lately I've been hearing and reading statistics that are communicated in wording that, frankly, confuses me. Forgive me for not citing specific instances, but I can give a hypothetical statistic that exemplifies the kind I'm referring to:



Comparing the number of tax returns the IRS audited in 2002 and 2010, the number of unlucky folks who had their returns audited in 2002 was ten times fewer than the number in 2012.



There is something about that wording that bothers me, and I'm not sure why.


After a fruitless search on the internet using numerous combinations/permutations of words and phrases such as "X times fewer," "X times less," "mathematical expressions of 'times fewer' as opposed to 'a fraction fewer,' or 'a fraction less,'" and more, I came up empty. Perhaps this question is more appropriate on a math website, but in the off-chance members of EL&U might give their imprimatur to this question, here goes:


Here's a second hypothetical example. Is it grammatical—not to mention mathematical—to say the following?:



There are ten times fewer pollinating honeybees worldwide today than there were in 1912. [Though this is a made-up statistic, there has been a dramatic reduction in the number honey bees in America of late!]



Should not the expression be:



There are one-tenth fewer honeybees worldwide today than there were in 1912.



On the surface, the "ten times fewer" locution seems to me to be a contradiction in terms. How can something less be 10 times fewer?


I can understand readily how, for example, 2012's bee population of, say, 90 million can be one-tenth (point one) less than 1912's population of 100 million, but ten times fewer?


I'm confused. Which expression is "more" correct?



Answer



"There are ten times fewer pollinating honeybees worldwide today..." IMO is definitely incorrect and meaningless. It implies there is a property called "fewness", that can be possessed in different amounts. In the same way, "ten times slower", "ten times cheaper", "ten times colder", "ten times closer".


"There are one-tenth fewer honeybees worldwide than there were in 1912" This is correct, but for a different statistic: one-tenth of the bees have disappeared, leaving nine-tenths behind.


"There are one-tenth as many pollinating honeybees..." is a correct way to express the statistic...


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