Babbler's Den: [Math4u] Re: Mathematical notation

error

you wrote :

"This logic of why multiplication and addition take precedence over .........."

Division, sir

Bodor

--- In Math4u@yahoogroups.com, Vinaire <vinaire@...> wrote:
>
> Thanks. Actually, that was a summary at the end of a 12 page paper of what was explained simply and with examples earlier.
>
> Vinaire
>
>
> ----- Original Message ----
> From: Brian E. Jensen brianejensen@...
> To: Math4u@yahoogroups.com
> Sent: Thursday, December 6, 2007 12:20:15 PM
> Subject: Re: [Math4u] Mathematical notation
>
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> Regarding operations that are opposite each other, it is fun for a student to
> discover but boring to listen to someone tell it. You could tell a first grader
> to add five to a number and then ask what to do to get the original number. But
> if you tried to tell a first grader this stuff, there would be no benefit. When
> you try to make first grade stuff sound like Ph.D. level, you kill brain
> cells.
>
> I'm too lazy to look up "mathematical expression." I guess if you write a
> string of different operations, then you have "mixed operations."
>
> Multiplication of whole numbers is repeated addition. After that, it gets
> more complicated.
>
>
> This logic of why multiplication and addition take precedence over addition
> and subtraction doesn't make sense to me. We could just as easily agree that
> addition and subtraction take precedence over multiplication and addition and
> then use brackets as needed. But the way things work, such as a farmer having
> various plots of land and trying to find the total acreage or a customer buying
> numerous quantities of various items and trying to find the total price makes it
> so that less brackets are used if we agree that multiplication and division take
> precedence over addition and subtraction. We only make this agreement to cut
> down on brackets. There doesn't need to be any agreement at all but it would
> take a lot more brackets to write an equation.
>
> You sure are determined to make division take precedence over multiplication
> and subtraction take precedence over addition. I think you have a very complex
> way of thinking that I would avoid teaching anyone else. We can get along just
> fine saying that division and multiplication have exactly equal precedence We
> can say that addition and subtraction have exactly equal precedence. We agree
> that they are performed left to right. We could have just as easily agreed that
> operations are performed right to left and probably on 50% of other planets they
> do this.
>
> You are an intelligent guy and you make us think
> though.
>
> regards,
>
>
> Brian
>
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>
> ----- Original Message -----
>
> From:
> Vinaire
>
> To: Math4u@yahoogroups. com
>
> Sent: Thursday, December 06, 2007 9:09
> AM
>
> Subject: Re: [Math4u] Mathematical
> notation
>
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> I have
> just written this summary for my "Milestone" on MIXED OPERATIONS. I shall be
> interested in receiving your comments.
>
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> The operations of addition and subtraction are opposite of each other,
> but they are of the same order. When one adds and then subtracts the
> same quantity, the two effects cancel each other out.
>
>
>
> Similarly, the operations of multiplication and division are opposite
> of each other, but they are of the same order. When one multiplies and then
> divides by the same quantity, the two effects cancel each other
> out.
>
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> When all these operations are present together in a
> mathematical expression we have mixed
> operations.
>
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> A multiplication is "repeated addition." Similarly a division is
> "repeated subtraction." Therefore, the operations of multiplication and
> division are of a higher order and, in mixed operations, they take precedence
> over the operations of addition and subtraction.
>
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>
> Those portions of a mathematical expression that contain a series of
> multiplication and division are called terms. The terms are
> separated from each other by plus (addition) or minus (subtraction) .
> NOTE: Any operations within parentheses are considered a term. A term
> could also be a single number.
>
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> In reducing mixed operations, one reduces the terms first, and then the
> mathematical expression.
>
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> Normally, one reduces an individual term from left to right. Otherwise,
> within the term, division takes precedence over multiplication. Then, one
> reduces the mathematical expression from left to right. Otherwise, subtraction
> takes precedence over addition.
>
>
>
> Understanding the logic involved in reducing mixed operations is very
> important. Only when this logic is understood, do the "formulas" about
> precedence of operations make sense.
>
>
> Vinaire
>
>
>
>
>
> -----
> Original Message ----
> From: Buck Dick
> kcubar34@yahoo. com>
> To: Math For You
> math4u@yahoogroups. com>
> Sent: Sunday, December 2, 2007 9:07:14
> AM
> Subject: [Math4u] Mathematical notation
>
>
>
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>
> Brian wrote:
>
>
>
> "...but I would like everyone to speak the same
> language."
>
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> Thank you (again) Brian (and Vinaire).
>
>
>
> One of the universal appeals of mathematics is that the
> notation used by those who know the subject is standard. It makes no
> difference what (meta)language is being used for the text, the symbolic
> language is the same all over this world. It makes no difference if you
> read left to right or right to left or top to bottom, the mathematical
> symbolism is standard.
>
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> There are thousands of mathematical dictionaries and
> encyclopedias published in most of the written languages used in this
> world. One of them should be part of every person's library, especially
> if they are students of the subject.
>
>
>
> The internet has some good sites for mathematics, the
> ultimate being Wolfram's sites, but there is a lot of incorrect information
> out there, since anyone can post anything they wish to post, right or
> wrong.
>
>
>
> So look it up, use it correctly and then we will all be
> able to communicate with the same understandings, don't just try to pass a
> test or pass that course because it is needed for your degree. Learn
> something about the subject.
>
>
>
> By the way, my four mathematical dictionaries all
> define the colon symbol as used in mathematics to be the symbol for a "ratio,"
> and a ratio as the comparison or division of two quantities that are
> expressed in the same units. If the units are different, the
> comparison is called a "rate."
>
>
>
> Also, the horizontal line which separates the
> "numerator" (Latin for "number") and "denominator" (Latin for "name") of a
> fraction has a name. It is a "vinculum." (Look it up; the name has
> also been used for other things since the original Latin, but in mathematics
> it is still the horizontal line separating the parts of a fraction.)
> Now, of course, the backslash is generally used since it is easier to put
> things all on one line, but then parentheses need to be used to indicate the
> grouping, etc., etc., etc.
>
>
>
> My point is simple: Learn the symbolic language
> used in mathematics if you want to try to communicate your ideas.
>
>
>
> Buck Dick
>
>
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>
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Saturday, December 08, 2007

[Math4u] Re: Mathematical notation

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