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Re: [Phys-L] just for fun

Several people have helpfully pointed out that I misread the problem, as can readily be seen by my second line. Mea culpa!

Yes, upon careful consideration, I agree that 25/28 is NOT 1 - 2/28. Ha ha! I guess this is why my wife insists on balancing our checkbook.

But ... Question for Brian Whatcott: Is your comment intended to indicate some further problem with what I wrote? The comment "it does not follow" seems to point to this part of it:

Since it's obvious that
1 = 1
and 2/28 < 2/17,
--------------------
It follows that
1 - 2/28 > 1 - 2/17

But that part I still stand by. It's the next line that fails because of incorrect subtraction:

and therefore
25/28 > 15/17

To correct it, I would have to say (changing the given problem):

"and therefore 26/28 > 15/17."

In other words, I would say that the "it follows" part is correct, but the "and therefore" part is not.

Now, although this was not the problem as stated, it still highlights a useful technique that is somewhat similar to modulo arithmetic, and exactly the same as switching one's attention from the sale price of an item to the discount applied to the price. For example, paying 75% of the sticker price means one got a discount of 25% off the sticker price, and vice versa. I generally mentally translate fractions that are above 50% to "discounts" in this way. For example, back in my elementary school days I learned decimal equivalents for small denominator fractions (d<=10). But it was easier for me to remember

1/6 = 0.1666...

than

5/6 = 0.8333...

But there's no need to remember both of these, since

5/6 = 1 - 1/6 = 0.9999... - 0.1666... = 0.8333...

Similarly, I stopped trying to remember 4/7 or 5/7 or 6/7 or 5/8 or 7/8, since I knew 3/7, 2/7, 1/7, 3/8 and 1/8.

It was this that the problem reminded me of, and clearly I homed right in on that idea to the exclusion of all else, even omitting basic proofreading for subtraction errors! I apologize again for the stupid mistake, but hope that this more complete explanation will interest some on the list, although this wasn't the problem as posed.

Season's greetings to all fellow phys-l-ers,

Ken Caviness

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of brian whatcott
Sent: Thursday, 19 December, 2013 3:56 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] just for fun

Ahem....
On 12/19/2013 9:27 AM, Ken Caviness wrote:
That's effectively the way I automatically saw the problem, too:

25/28 <=?=> 15/17

1 - 2/28 <=?=> 1 - 2/17

Since it's obvious that

1 = 1
and 2/28 < 2/17,

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

It follows that

1 - 2/28 > 1 - 2/17

and therefore

25/28 > 15/17
It does not follow!



One generalization is that (n-c)/n > (m-c)/m iff c/n < c/m iff n > m.

KC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Surendranath
Sent: Thursday, 19 December, 2013 9:56 AM
To: Phys-L@phys-l.org
Subject: Re: [Phys-L] just for fun

how about 25/28 = (28-3)/28 = 1-3/28

and 15/17 = (17-2)/17 = 1-2/17

and compare 3/18 and 2/17


Best Wishes,

Surendranath

www.surendranath.org
www.youtube.com/user/Surendranath1954
https://play.google.com/store/search?q=pub:Surendranath.B.


On Thu, Dec 19, 2013 at 7:34 PM, John Denker <jsd@av8n.com> wrote:

The question was:

Which is bigger: 25/28 or 15/17? [1]


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