How mathematical expressions are written and evaluated is determined by agreed upon conventions. I believe that what Vinaire is saying is not the agreed upon convention for the United States and England. The following websites describe the convention for the order of calculations.
| http://www.math.com/school/subject2/lessons/S2U1L2GL.html |
| http://www.mathgoodies.com/lessons/vol7/order_operations.html |
| http://mathforum.org/dr.math/faq/faq.order.operations.html |
The first message I read from Vinaire on this topic turned on a light bulb for me. What Vinaire calls "(2)" is not just a way the calculations can be done, but the method recommended by agreed upon convention.
I misunderstood Vinaire's point (3) the first few times I read it. When he says "When we choose a random order," he means "When we choose to perform calculations on a sequence of additions and subtractions in a random order instead of the recommended left to right,."
If you want to replace the accepted convention of performing calculations from left to right by Vinaire's novel method, you will usually get the same answer. As Vinaire's method avoids, if you have a plus term that follows a negative term, you cannot add the plus term to the negative term or you will be subtracting the plus term from the final result instead of adding it to the final result. Similarly, if you have two minus terms next to each other, you cannot perform the second subtraction first or you will wind up adding it to the final result instead of subtracting it from the final result.
I think it is fine if Vinaire can calculate it in a different method. But I consider this a heresy and a threat to western civilization.
Regards,
Brian
__._,_.___----- Original Message -----From: VinaireSent: Tuesday, November 27, 2007 9:20 AMSubject: Re: [Math4u] Re: 26 - 14 : 2 x 3 + 4² = ?
Precedence and priorities are two different things.(1) Addition and Subtraction have the same priority as they are the same order of operations.(2) Mixed operations can always be solved from left to right among the same order of operations.(3) However, when we choose a random order, subtraction has precedence over addition, and not the other way around. This fact simplifies calculations as well where it can be applied.(4) Similar consideration applies to multiplication and division.Vinaire----- Original Message ----
From: Rob van Wijk <robvanwijk@gmx.net>
To: Math4u@yahoogroups.com
Sent: Tuesday, November 27, 2007 6:26:56 AM
Subject: Re: [Math4u] Re: 26 - 14 : 2 x 3 + 4² = ?
Vinaire <vinaire@yahoo. com> wrote:
> (..)
> 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
>
Uhm yeah, and 54 + 46 - 37 is easier with addition first. Nice examples,
but they've been specifically constructed to work out nicely (97-87 = 10,
a round number, 46/23 = 2, also a round number). I agree "substraction
first" will keep numbers smaller and might therefore be somewhat easier
in practice (unless working with negative numbers...), but the question
was about the precedence of operators, not tricks to make mental math a
little easier. (Note that I called the trick "pointless" (which might've
been an overly harsh conclusion), I *didn't* call it "wrong".)
Grtz,
Rob
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