[Math4u] Re: 26 - 14 : 2 x 3 + 4² = ?

There is a big difference between the division symbol and the colon.

Let's take the quadradic equation as an example:

-b+ (the square root of b^2 -4ac):2a

we all know that even though this formula is one big fraction, all operations above and below the fraction are done before dividing.

What would happen written like this?

-b+ (the square root of b^2 -4ac)/2a

If I read / as a division symbol, I would complete all equations under the square root and then divide it by 2a before I complete the addition/subtraction with the lonely b

regards

PC

--- In Math4u@yahoogroups.com, "Rob van Wijk" <robvanwijk@...> wrote:
>
>
> Here's the recap and all solutions for these non-problems:
>
> Order of operations:
> - Plus and minus are at the same priority level (defining minus to be
> higher priority than plus is a cute hack, but since an expression such
> as "1 - 2 - 3 = ??" will still require the additional "in case of same
> precedence, eval from left to right"-rule, it's pretty pointless).
> - Same for multiply and divide.
> - In case of even the slightest possibility of doubt: just add braces,
> then you are *sure* everyone understands!!
>
> Division symbol:
> - In elementary school we were first tought to use the "colon with a dash"
> symbol. Then "just plain colon" was introduced as a "shorthand" for that.
> Later on, in highschool we switched to using a slash. Sorry, can't link
> to a website (or would you like a link to the website of my elementary
> school? :p ).
> - This mailing list is kinda bound to computers. Yes, there *is* a symbol
> for division. However (sparing you the technical details) there are quite
> severe problems with actually using it (as has been demonstrated). In the
> interest of using a solution that is easy and works universally, in comp.
> sci. we just use a slash for division. May I recommend everyone here also
> follows that convention?
>
> And, to give the long-awaited answer to the original formula:
> (note the use of "^2" instead of "²"; another case of "easy solution that
> just works")
> 26 - 14 : 2 x 3 + 4^2
> == { exponentation }
> 26 - 14 : 2 x 3 + 16
> == { multiply and divide, left to right, first operator encountered }
> 26 - 7 x 3 + 16
> == { multiply and divide, left to right, second operator encountered }
> 26 - 21 + 16
> == { add and substract, left to right, first operator encountered }
> 5 + 16
> == { add and substract, left to right, second operator encountered }
> 21
>
> Google calculator agrees with me:
> http://www.google.nl/search?q=26+-+14+%2F+2+x+3+%2B+4%5E2
> 26 - ((14 / 2) x 3) + (4^2) = 21
> (My my, what a nice coincidence, I had to change both the ":" and "²" to
> "/" and "^2" respectively to make it work. Maybe this is the universally
> accepted solution to a non-problem...?)
>
> Grtz,
> Rob
> // If this mail sounds like I'm annoyed with this thread it's because I am
>
>
> -------- Original-Nachricht --------
> > Datum: Sun, 25 Nov 2007 17:01:24 -0000
> > Von: "princecharming134" sossi82@...
> > An: Math4u@yahoogroups.com
> > Betreff: [Math4u] Re: 26 - 14 : 2 x 3 + 4² = ?
>
> > [Brian's comment to Princecharming134: This is useful information on how
> > to make the "÷" sign. However the "/" sign has a very precise meaning
> > and implies nothing. OK, you treated ":" as "( )/( )" but is this right
> > or are you just making up stuff? Can you quote a reputable website?]
> >
> > There is a division symbol available on your PC.
> >
> > It looks like this ÷
> >
> > You can copy and paste it from this post if you wish or you may click
> > on "insert" then "symbols" then look for the division sign on
> > Microsoft word.
> >
> > For those who are not aware as to how to make the division symbol,
> > they have been using /. the problem is that this can imply
> > either a fraction or a division sign.
> >
> > My previous post I treated the : as a fraction.
> >
> > 26 minus 14 over 2 times 3 plus 4 squared.
> >
> > In which case, you must complete all operations above and below the
> > fraction before you can divide.
> > regards,
> > Princecharming134
> >
> >
>
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