Re: [Math4u] Re: 26 - 14 : 2 x 3 + 4² = ?

OK, I learn something by making examples:

Example, calculating left to right the correct way:

2 + 17 - 7 - 5 + 3 = 10

We can do it in any order:

2 + 3 + 17 - 5 - 7 = 10

We can add the negative terms and subtract them all together:

2 + 3 + 17 - (5 + 7) = 10

We can perform an addition or subtraction if it comes after an addition:

(2 + 17) - 7 - 5 + 3 = 10

2 + (17 - 7) - 5 +3 = 10

We get the wrong answer if we perform an addition or subtraction that comes after a subtraction:

2 + 17 - (7 - 5) + 3 = 20 off by 5*2

2 + 17 - 7 - (5 + 3) = 4 0ff by 3*2

The same is true of multiplication and division because it is the same as adding and subtracting logs.

Example, calculating left to right the correct way:

2 * 17 / 7 / 5 * 3 = 2.9143

We can do it in any order:

2 * 3 * 17 / 5 / 7 = 2.9143

2 * 3 * 17 / (5 * 7) = 2.9143

We can do a multiplication or division first if it doesn't follow a division:

(2 * 17 ) / 7 / 5 * 3 = 2.9143

2 * (17 / 7 ) / 5 * 3 = 2.9143

We get the wrong answer if we do a multiplication or division first that follows a division:

2 * 17 / 7 / (5 * 3) = 0.3238   which is off by a factor of 3^2

2 * 17 / (7 / 5) * 3 = 72.857  which is off by a factor of 5^2

So there's the requested examples. I was thinking of letting it drop, but I learned something making these examples. As it becomes clearer in my mind, it seems like nothing to argue about.

Sorry,

Brian

 

----- Original Message -----

From: Asif Lodhi

To: Math4u@yahoogroups.com

Sent: Tuesday, November 27, 2007 5:24 PM

Subject: Re: [Math4u] Re: 26 - 14 : 2 x 3 + 4² = ?

Hi Brian,

On 11/28/07, Brian E. Jensen <brianejensen@prodigy.net> wrote:
> 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.

It would help the list users if you could elaborate the above text
with some examples.

> consider this a heresy and a threat to western civilization.

I don't think so. Research into anything is always good. I don't think
any research is a heresy or a threat to any civilization. We just get
to learn more that way. After all, we are all here to find out more
about maths! :) It doesn't matter who's coming from where.

--
Best regards,

Asif

__._,_.___

Your email settings: Individual Email|Traditional
Change settings via the Web (Yahoo! ID required)
Change settings via email: Switch delivery to Daily Digest | Switch to Fully Featured
Visit Your Group | Yahoo! Groups Terms of Use | Unsubscribe

__,_._,___