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It's obvious you didn't click the link - because it's a google search that shows that the only hits for "earth 6000 year old" on .edu sites are discussing YEC as a system that some crazies believe, not claims that it's legit.
I don't know, unless they are no longer teaching the order of operation any more. 288 is correct. It's alarming that this thread is so long.
You are very right. Some people seem to believe that multiplication has a higher order of precedence than division, without realizing that they are simply the inverse to each other and both carry the same weight.
Therefore the equation is solved left to right, and there has been enough proof submitted that even the most challenged person with a modicum of intelligence should be able to understand the conclusion.
The ONLY thing I can come up with that makes sense is either they refuse to learn, they are incapable of learning, or they are simply trolling.
It's obvious you didn't click the link - because it's a google search that shows that the only hits for "earth 6000 year old" on .edu sites are discussing YEC as a system that some crazies believe, not claims that it's legit.
I am relieved. However, the point was to your throwing up websites and claims of math teachers saying something is so, as somehow proof that you are correct. I was showing that websites and even "teachers" making proposterous claims, such as a young earth, does not make it so. I think you missed that point, but I am sure you would agree.
There is a difference between people saying the earth is 6000 years old, and proof that the earth is 6000 years old. We know from carbon dating the earth is in fact much older.
There is however proof and explanations behind the proof concerning the solution of this equation. I guess it's easier to kvetch that no one else knows what they are talking about than it is to learn why the answer you provided is inaccurate.
Quit trolling.
Carbon dating is only good for ~50,000 so we really don't use that for dating the earth. Besides you really missed the point as well.
I am relieved. However, the point was to your throwing up websites and claims of math teachers saying something is so, as somehow proof that you are correct. I was showing that websites and even "teachers" making proposterous claims, such as a young earth, does not make it so. I think you missed that point, but I am sure you would agree.
The hilarious part about your charade is that the last three websites I posted were purely regarding the Order of Operations. And you're claiming that not only are they incorrect, but proposterous(sic)? If the Order of Operations (as described in my links) are preposterous and/or wrong, then please provide any links you can regarding the "correct" Order of Operations.
But until then, here's a couple of other great examples to why the Order of Operations is important.
The hilarious part about your charade is that the last three websites I posted were purely regarding the Order of Operations. And you're claiming that not only are they incorrect, but proposterous(sic)? If the Order of Operations (as described in my links) are preposterous and/or wrong, then please provide any links you can regarding the "correct" Order of Operations.
But until then, here's a couple of other great examples to why the Order of Operations is important.
The one I find the funniest is the "debate" over 10+10*0. That one cracks me up.
This thread alone shows the ambiguity of the notation. However from the AMS Mathematical Reviews Database - Guide for Reviewers
that "multiplication indicated by juxtaposition is carried out before
division." Thus, in general, for any variables a, b and c, we would
have a/bc = a/(bc) (assuming, of course, that b and c are nonzero). As stated way up on the thread it is just bad notation and introduces the ambiguity. Different answers are given dependent on either following the distributive method or the The Order of Operations method. Pick your poison.
Look at how this has been addressed in the past.
In 1892 in Mental Arithmetic, M. A. Bailey advises avoiding expressions containing both ÷ and ×.
In 1898 in Text-Book of Algebra by G. E. Fisher and I. J. Schwatt, a÷b×b is interpreted as (a÷b)×b.
In 1907 in High School Algebra, Elementary Course by Slaught and Lennes, it is recommended that multiplications in any order be performed first, then divisions as they occur from left to right.
In 1910 in First Course of Algebra by Hawkes, Luby, and Touton, the authors write that ÷ and × should be taken in the order in which they occur.
In 1912, First Year Algebra by Webster Wells and Walter W. Hart has: "Indicated operations are to be performed in the following order: first, all multiplications and divisions in their order from left to right; then all additions and subtractions from left to right."
In 1913, Second Course in Algebra by Webster Wells and Walter W. Hart has: "Order of operations. In a sequence of the fundamental operations on numbers, it is agreed that operations under radical signs or within symbols of grouping shall be performed before all others; that, otherwise, all multiplications and divisions shall be performed first, proceeding from left to right, and afterwards all additions and subtractions, proceeding again from left to right."
In 1917, "The Report of the Committee on the Teaching of Arithmetic in Public Schools," Mathematical Gazette 8, p. 238, recommended the use of brackets to avoid ambiguity in such cases.
In A History of Mathematical Notations (1928-1929) Florian Cajori writes (vol. 1, page 274), "If an arithmetical or algebraical term contains ÷ and ×, there is at present no agreement as to which sign shall be used first."
Modern textbooks seem to agree that all multiplications and divisions should be performed in order from left to right. However, in Florida Algebra I published by Prentice Hall (2011), a problem asks the student to evaluate 3st 2 ÷ st + 6 for given values of the variables, and the answer provided comes from dividing by st. A representative for the publisher has acknowledged that the expression is ambiguous and promises to use (st) in the next revision.
Multiplication by juxtaposition as being used in algebraic nomenclature dates as far back as the fifteenth century. That being said, the standard left-to-right order of operations predates even that. The real problem is that both techniques are taught in our school systems, depending on the chosen literature. Both forms can be found dating far enough back that there’s a solid argument for either chosen notation. Sadly, there is no current ‘authority’ to standardize which is appropriate.
All fun aside, the real answer here is the ambiguity of the formula makes it faulty to begin with. This was addressed quite a bit earlier in this thread. No self respecting mathematician would have used this notation. Formula ambiguity can destroy the outcome. This should have been written as 48 / (2 * (9+3)) or (48 / 2)*(9+3), thus guaranteeing the desired result. You can even order T-shirts with this equations. That tells you something. Who doesn't have fun bucking convention.
Well, my calculus teacher and my mathematical concepts teacher would both disagree.
Interesting enough, even the google calculator comes up with 288.
You see multiplication and division, being the inverse of each other have equal priority.
Since both are equal in priority, the proper execution of the problem takes place from left to right, with the sole exception of the addition which are in the paren, and is accomplished before the multiplication is accomplished.
Maybe if you took less time attempting to insult your betters, and stuck to utilizing proper technique, you wouldn't end up becoming the object of the idiom, "It's better to remain silent and thought a fool, then to speak up and remove all doubt".
This thread alone shows the ambiguity of the notation. However from the AMS Mathematical Reviews Database - Guide for Reviewers
that "multiplication indicated by juxtaposition is carried out before
division." Thus, in general, for any variables a, b and c, we would
have a/bc = a/(bc) (assuming, of course, that b and c are nonzero). As stated way up on the thread it is just bad notation and introduces the ambiguity. Different answers are given dependent on either following the distributive method or the The Order of Operations method. Pick your poison.
Look at how this has been addressed in the past.
In 1892 in Mental Arithmetic, M. A. Bailey advises avoiding expressions containing both ÷ and ×.
In 1898 in Text-Book of Algebra by G. E. Fisher and I. J. Schwatt, a÷b×b is interpreted as (a÷b)×b.
In 1907 in High School Algebra, Elementary Course by Slaught and Lennes, it is recommended that multiplications in any order be performed first, then divisions as they occur from left to right.
In 1910 in First Course of Algebra by Hawkes, Luby, and Touton, the authors write that ÷ and × should be taken in the order in which they occur.
In 1912, First Year Algebra by Webster Wells and Walter W. Hart has: "Indicated operations are to be performed in the following order: first, all multiplications and divisions in their order from left to right; then all additions and subtractions from left to right."
In 1913, Second Course in Algebra by Webster Wells and Walter W. Hart has: "Order of operations. In a sequence of the fundamental operations on numbers, it is agreed that operations under radical signs or within symbols of grouping shall be performed before all others; that, otherwise, all multiplications and divisions shall be performed first, proceeding from left to right, and afterwards all additions and subtractions, proceeding again from left to right."
In 1917, "The Report of the Committee on the Teaching of Arithmetic in Public Schools," Mathematical Gazette 8, p. 238, recommended the use of brackets to avoid ambiguity in such cases.
In A History of Mathematical Notations (1928-1929) Florian Cajori writes (vol. 1, page 274), "If an arithmetical or algebraical term contains ÷ and ×, there is at present no agreement as to which sign shall be used first."
Modern textbooks seem to agree that all multiplications and divisions should be performed in order from left to right. However, in Florida Algebra I published by Prentice Hall (2011), a problem asks the student to evaluate 3st 2 ÷ st + 6 for given values of the variables, and the answer provided comes from dividing by st. A representative for the publisher has acknowledged that the expression is ambiguous and promises to use (st) in the next revision.
Multiplication by juxtaposition as being used in algebraic nomenclature dates as far back as the fifteenth century. That being said, the standard left-to-right order of operations predates even that. The real problem is that both techniques are taught in our school systems, depending on the chosen literature. Both forms can be found dating far enough back that there’s a solid argument for either chosen notation. Sadly, there is no current ‘authority’ to standardize which is appropriate.
All fun aside, the real answer here is the ambiguity of the formula makes it faulty to begin with. This was addressed quite a bit earlier in this thread. No self respecting mathematician would have used this notation. Formula ambiguity can destroy the outcome. This should have been written as 48 / (2 * (9+3)) or (48 / 2)*(9+3), thus guaranteeing the desired result. You can even order T-shirts with this equations. That tells you something. Who doesn't have fun bucking convention.
Well isn't that interesting. Going from a stark "itis2" to "It's ambiguous" in one post flat. How peculiar.
Also, links are easier to read than a badly done copy and paste from here and here.
The former being an opinion pieces with a single reference point for juxtaposition > regular multiplication and the response being "never heard of that before". Yet with that, something interesting caught my eye. There are numerous claims of "multiplication indicated by juxtaposition is carried out before division" referencing a single publishing of the AMS - with no rhyme or reasoning as to why they place a form of multiplication higher than others... other than "it looks prettier when printed".
Either way, this is the full statement regarding juxtaposition:
Quote:
Formulas. You can help us to reduce production and printing costs by avoiding excessive or unnecessary quotation of complicated formulas. We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division. For example, your TeX-coded display
So we're back to exactly where we started: Juxtaposition/implied multiplication/"distributive property of multiplication" and where it sits in regards to the Order of Operations. The way I see it "all multiplication is multiplication with equal weight" because additional "except in cases where x,y, and z, then you do this" clauses for math seems like a silly idea. This is Math, not poetry. Strict Order of Operations with no wiggle room makes the most sense to me.
I had to think on this one, but my first thought was "Easy its 2". Then looking at the comments, 288 is correct. The contents of the parentheses come first, then multiplication/division left to right. Full disclosure: Graduate and Employed as a Chemical Engineer.
48/2(9+3)
becomes
48/2(12)
When you see just 2(12) you know it is twenty-four.
This is because if we simplified it to x and y...
In x(y), x denotes the quantity of y.
2(12) is saying there are two twelves, which we sum and recognize as 24.
Back to 48/2(12)
Lets write this equation verbally.
Forty-eight divided by two twelves.
Forty-eight divided by twenty-four.
Two.
If the equation were written 48/2*12
It can be verbally expressed as follows:
Forty-eight divided by two multiplied by twelve.
Forty-eight divided by two is twenty-four.
Twenty-four multiplied by twelve.
Two-hundred eighty-eight.
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