SOLUTION: Write an algebraic expression: Kristie has six times less hockey cards than her brother Mark.

Question 1164279: Write an algebraic expression: Kristie has six times less hockey cards than her brother Mark.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.

In English, this wording construction DOES NOT WORK in mathematical problems.

English is a VERY SPECIAL/specific language.

In many other languages this wording construction is very REGULAR/routine and works perfectly, without making misunderstanding.

But in English, it is NOT SO.

I hope that other tutors will confirm it and will explain it to you even better than me.

If not, then I will return to this post/spot later and will add more explanations.

So, keep your eye in this spot and return to it from time to time to see updates and to learn more.

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For reference and as the info for other tutors:

In other languages, the phrase "X is six times less than Y" means X = . Same as in English "X is as much/(as many) as of Y".

Let me tell you an interesting story.

In the Internet, I saw web-site, analyzing statistical data on usage (frequency usage) of the canonical English form
of such statements and ANTI-canonical English "every day" version, which is used normally (as I explained) in many other languages.

Everything was stable at the times of Shakespeare, Dickens, at the era of "steam and coil" and even in the era
of "steal and electricity" till 40-ies of the last century. After that the era came, when ANTI-canonical usage started raising after 40-ies.

They placed a Table and the plots (graphs) in their web-site, showing that canonical and ANTI-canonical usage reached
EQUAL frequency somewhere around 2000-es.

With the prognosis that the ANTI-canonical version will become the only usable and DOMINANT version soon.

It is not surprising due to great inflow of immigrants to western countries, who bring their native understanding
of the words usage.

Many of you know that Great Britain, after many CENTURIES (!) usage feet, inches, pounds etc. REPLACED
them recently (and finally) by metric system's kilograms and meters.

Same will happen INEVITABLY with English regarding using that forms I discussed above.

Here is the link to the above mentioned web-site

https://english.stackexchange.com/questions/221323/has-the-illogical-three-times-bigger-replaced-three-times-as-big-in-common-u

Look in it: it is worth your time and attention.

Also, look into the comments of readers at the bottom of this page.

Take into account that the equilibrium was just reached around the year 2000.

Also, take into account that the young generations (from 0 to 20-30 years old) practically are UNFAMILIAR
with the canonical form usage and use ANTI-canonical version ONLY.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A phrase like "6 times less than" is commonly used in everyday language; but in fact is is ALWAYS used incorrectly.

"Product A is 3 times less expensive than product B."
"My new laptop takes 5 times less time to do a job than my old one."
etc., etc. You hear it all the time.

But it makes no logical sense.

"less than" in a mathematical statement implies subtraction.

So, given a number, for example 10, "6 times less than 10" means 10, minus 6 times 10, which is 10-60 = -50.

In general, "6 times less than" a number n means n-6n = -5n.

Clearly in this problem we are talking about positive numbers, in fact positive integers. 6 times less than a positive integer is a negative integer; and a negative integer is not valid for the number of hockey cards Kristie has.

The only interpretation of the words "Kristie has six times less hockey cards than her brother Mark" that makes ANY sense is that she has one-sixth as many.

But grammatically, that is not what the words say.

The phrase "n times less than' should NEVER be used.

Whenever you hear an advertisement for a product that uses the phrase, you can bet you are not hearing the true data.

And whenever you see a math problem that uses the phrase, you can throw it in the trash bin.

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