Where priorities are the same, executing minus before plus, and division before multiplication, allows ease in calculation because one is now dealing with smaller numbers. It does not cause any error. This was how it was done in India with mental math before calculators came about.
For example, 84 + 97 - 87 is much easier to execute with subtraction first, compared to left to right rule.
Similarly, 42 x 46 / 23 is much easier to execute with division first.
Vinaire
From: Rob van Wijk <robvanwijk@gmx.net>
To: Math4u@yahoogroups.com
Sent: Monday, November 26, 2007 12:12:25 PM
Subject: Re: [Math4u] Re: 26 - 14 : 2 x 3 + 4² = ?
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@yahoo. com>
> 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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