... yes but they both have girl brains
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Half of you will get this wrong: 48÷2(9+3) = 288 or 2?
- Thread starter AKIRA
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... yes but they both have girl brains
These equations were from http://www.chemie.fu-berlin.de/chemistry/general/si_en.html The 288 guys should tell them them have all their units wrong.
Electric potential
volt: V = W/A = m2 kg/s3 A
Capacitance
farad: F = C/V = s4 A2/m2 kg
Electric resistance
ohm: Omega = V/A = m2 kg/s3 A2
Conductance
siemens: S = A/V = s3 A2/m2 kg
Magnetic flux
weber: Wb = V s = m2 kg/s2 A
Magnetic flux density, magnetic induction
tesla: T = Wb/m2 = kg/s2 A
Inductance
henry: H = Wb/A = m2 kg/s2 A2
Dynamic viscosity
pascal second: Pa s = kg/m s
Heat capacity, entropy
joule per kelvin: J/K = m2 kg/s2 K
Specific heat capacity, specific entropy
joule per kilogram kelvin: J/kg K = m2/s2 K
Thermal conductivity
watt per metre kelvin: W/m K = m kg/s3 K
Energy density
joule per cubic metre: J/m3 = kg/m s2
Electric field strength
volt per metre: V/m = m kg/s3 A
These guys also are guilty of the same:
http://www.goldstandard-mcat.com/physics-equation-lists/
These guys also do the same for Universal gravitational constant
http://www.collegeboard.com/prod_downloads/ap/students/physics/physics_equation_tables.pdf
Physics Guys Just Must Not Understand Math
Electric potential
volt: V = W/A = m2 kg/s3 A
Capacitance
farad: F = C/V = s4 A2/m2 kg
Electric resistance
ohm: Omega = V/A = m2 kg/s3 A2
Conductance
siemens: S = A/V = s3 A2/m2 kg
Magnetic flux
weber: Wb = V s = m2 kg/s2 A
Magnetic flux density, magnetic induction
tesla: T = Wb/m2 = kg/s2 A
Inductance
henry: H = Wb/A = m2 kg/s2 A2
Dynamic viscosity
pascal second: Pa s = kg/m s
Heat capacity, entropy
joule per kelvin: J/K = m2 kg/s2 K
Specific heat capacity, specific entropy
joule per kilogram kelvin: J/kg K = m2/s2 K
Thermal conductivity
watt per metre kelvin: W/m K = m kg/s3 K
Energy density
joule per cubic metre: J/m3 = kg/m s2
Electric field strength
volt per metre: V/m = m kg/s3 A
These guys also are guilty of the same:
http://www.goldstandard-mcat.com/physics-equation-lists/
These guys also do the same for Universal gravitational constant
http://www.collegeboard.com/prod_downloads/ap/students/physics/physics_equation_tables.pdf
Physics Guys Just Must Not Understand Math
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Now that's really pushing it...
I could understand if you said a/2 b = ab/2 since it is less clear if the b is written in the denominator or beside the a/2. a/2b just really looks like it is intended to be under the line.
Math isn't ambiguous. When written out by hand like it has been for centuries, it is much more obvious if its under the line or beside a fraction. With ASCII computer notation, sometimes the meaning isn't as obvious.
Why is that "pushing it?" It makes it sound like your ego is very attached to being right. Further, your need to rely on irrelevant sexist remarks about women not being able to do math to bolster your position is further evidence that your argument is spurious.
On the other hand, I don't need to call you names or resort to insults. My ego is completely unattached to whether or not you can recognize a correct mathematical argument or not. Mathematics is totally impartial.
It doesn't matter what it "looks like." Operations proceed from left to right with multiplication and division having the same level of precedence. This means that a is divided by the 2 first and the result of that operation is multiplied by b, hence a/2b=(a/2)xb.
Built, I actually find this rather fascinating as it come up in discussions with my colleagues all the time. The question is, how do we, as educators, get our students to let go of their incorrect preconceived notions about mathematics (or physics or any hard science). There are many studies out there that documenting how difficult it is to do. Many students (not all), when presented with concrete arguments or evidence contrary to their beliefs, momentarily give up those beliefs, but revert back to them soon after.
This thread seems like evidence that they never really give up those beliefs at all. I'm sure that if the people here were paying for a class of mine would give up the goat and say yes Dr. T, you're right, but not because they believe me or have seen the error in their logic, but because I'm the one who assigns them a grade. I have students in my Calculus class that still don't understand how I can turn 1/2/2 into 1/4. I've been doing it long enough now that it shouldn't surprise me any more, but you know, it kind of does.
I blame acronyms. How many instances are there in this thread of people reciting some acronym for the order of operations and then go right on to apply it incorrectly? I swear, acronyms are the bane of my existence. Kids memorize acronyms and years later they remember the acronym but not what it means. It's like the acronym strips all the meaning and understanding of why from the problem.
For me, this whole thread just reinforces the importance of K-6 education. It seems like if the wires get crossed at that age, they just go blithely through life with all of these misunderstandings, thinking the people with Master's and PhD's are the ones that have it wrong.
This thread seems like evidence that they never really give up those beliefs at all. I'm sure that if the people here were paying for a class of mine would give up the goat and say yes Dr. T, you're right, but not because they believe me or have seen the error in their logic, but because I'm the one who assigns them a grade. I have students in my Calculus class that still don't understand how I can turn 1/2/2 into 1/4. I've been doing it long enough now that it shouldn't surprise me any more, but you know, it kind of does.
I blame acronyms. How many instances are there in this thread of people reciting some acronym for the order of operations and then go right on to apply it incorrectly? I swear, acronyms are the bane of my existence. Kids memorize acronyms and years later they remember the acronym but not what it means. It's like the acronym strips all the meaning and understanding of why from the problem.
For me, this whole thread just reinforces the importance of K-6 education. It seems like if the wires get crossed at that age, they just go blithely through life with all of these misunderstandings, thinking the people with Master's and PhD's are the ones that have it wrong.
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This looks like a good place to post this:
What's your ego and where is it located?
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Oh - I see what you did here - you began the list of SI Derived units partway down, so you wouldn't have to include the instruction that Freie Universität Berlin posted at the top to indicate they were breaking from convention, presumably for the sake of typographic brevity.
I'll fix that for you here:
_______________________________________________
SI Derived Units
(Please note: all units to the right of the slash are actually in the denominator!)
Frequency
hertz: Hz = 1/s
Force
newton: N = m kg/s2
Pressure, stress
pascal: Pa = N/m2 = kg/m s2
Energy, work, quantity of heat
joule: J = N m = m2 kg/s2
Power, radiant flux
watt: W = J/s = m2 kg/s3
Quantity of electricity, electric charge
coulomb: C = s A
Electric potential
volt: V = W/A = m2 kg/s3 A
Capacitance
farad: F = C/V = s4 A2/m2 kg
(and so on)
I'll fix that for you here:
_______________________________________________
SI Derived Units
(Please note: all units to the right of the slash are actually in the denominator!)
Frequency
hertz: Hz = 1/s
Force
newton: N = m kg/s2
Pressure, stress
pascal: Pa = N/m2 = kg/m s2
Energy, work, quantity of heat
joule: J = N m = m2 kg/s2
Power, radiant flux
watt: W = J/s = m2 kg/s3
Quantity of electricity, electric charge
coulomb: C = s A
Electric potential
volt: V = W/A = m2 kg/s3 A
Capacitance
farad: F = C/V = s4 A2/m2 kg
(and so on)
"The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "??" sign) indicates that the juxtaposed values must be multiplied together before processing other operations"
http://www.purplemath.com/modules/orderops2.htm
Even though math is an exact science, there are habits or uses in every science, where people tend to do the same thing when presented to the same problem, just to avoid interpretation.
Just my two centd
http://www.purplemath.com/modules/orderops2.htm
Even though math is an exact science, there are habits or uses in every science, where people tend to do the same thing when presented to the same problem, just to avoid interpretation.
Just my two centd
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I cant believe this is still going. Built and her friend are 100% correct. I dont even know why "multiplication by juxtaposition" is being brought up. You work from left to right when the signs have the same rank. It is something that either I forgot, or simply had a major brain fart on. Hell, maybe I was having a bad day and never learned it. I will say it is very rare that this issue (working left to right) comes up. It is a secondary rule, but a rule nonetheless.
Work out some other problems in the same style on your own and you will see why.
Work out some other problems in the same style on your own and you will see why.
That question is completely superfluous the the discussion at hand.
Deflection.
A commonly used female tactic to avoid acknowledgement of an
inferior argument.
If this is superfluous to the discussion, then why did you make a post
about it?
Deflection.
A commonly used female tactic to avoid acknowledgement of an
inferior argument.
If this is superfluous to the discussion, then why did you make a post
about it?
It's not deflection. When you posted your question you conveniently left off the part that asked why the OP why he thought I was "pushing it." The OP made it personal when he posted that. My response about his "ego" was merely a side note on the way people make it personal when they can't admit that they are wrong. And yes, indeed, my comment was superfluous to the discussion. As are all the sexist remarks.
Oh, my! I've just realized that this is the first time since I joined the forum that I disagree with Built! Tell me, Built, will I be punished this? I was thinking black tight leather clothes and a whip ;-p
I'll forgive you since you are new but this website is all about irrelevant sexist remarks... It's what makes it fun.
so if it looks like this:
a
____
2b
does it matter now? My point is how it is written. With a/2b it looks like it is under the line just as much as my above example.
Actually I didn't start it half way down to not post that part... I was in a hurry (going to work) and didn't actually read that part.
Yes they did mention "(Please note: all units to the right of the slash are actually in the denominator!)" because they are explaining the convention they are using... which seems a pretty common one because I see it on lots of other sites that don't explain.
They never said they are breaking from convention. They said "(Please note: all units to the right of the slash are actually in the denominator!)"... this is because when written on a single line like that, it is kind of ambiguous and could be taken either way.
This doesn't help your argument. They aren't saying they are breaking from convention. They are simply explaining because the notation isn't as cut and dry as you say (or they wouldn't have to explain it)
And it does nothing to explain the other two links that use the same convention and don't feel a need to explain (because it is obvious)
Evaluating Algebraic Expressions Order of Operations/P.E.M.D.A.S.
This page takes you through this equation
(4-2)^3 + (3+2)^2 / 5(8-7)
Here are the steps
2^3 + (3+2)^2 / 5(8-7)
2^3 + 5^2 / 5(8-7)
2^3 + 5^2 / 5(1)
8 + 5^2 / 5(1)
8 + 25 / 5(1)
.... and for the most interesting step... drum roll....
8 + 25 / 5
Yes, that's right, they did the right multiplication first
This page takes you through this equation
(4-2)^3 + (3+2)^2 / 5(8-7)
Here are the steps
2^3 + (3+2)^2 / 5(8-7)
2^3 + 5^2 / 5(8-7)
2^3 + 5^2 / 5(1)
8 + 5^2 / 5(1)
8 + 25 / 5(1)
.... and for the most interesting step... drum roll....
8 + 25 / 5
Yes, that's right, they did the right multiplication first
It seems that text books and math authorities don't all agree on this either and that different conventions are in use.
This is the best answer I have been able to find:
"Mathematics is supposed to provide you with single, definitive answers. However, in this case, it does not. I really scoured the internet and countless textbooks for the proper answer and have made inquiries with few people I know whom I venerate as some of the greatest minds that I have had the luxury of meeting and the answer isn't as definitive as you would hope. Sadly, the real answer is that both sides are correct to a point. (…and it pains me to even remotely admit that anything outside of 288 could be the answer).
Position 1: The Order of Operations: This stance states that since the standard order of operations puts multiplication and division on the same rank, the equation can be read as (48÷2)*(9+3). This reigns with truth as 48÷2(9+3) is the same as 48÷2*(9+3). Using the standardized left-to-right notation, the answer can be nothing outside of 288. This left-to-right concept is indicative of “PEMDAS” that we all learned in grade school.
Position 2: The Distributive Property: This stance states that multiplication through juxtaposition, being a commonplace concept, naturally makes a parenthetical implication around grouped numbers. Thus, the equation appears as 48÷[2(9+3)]. This technique is correct as well. However, this makes the answer 2.
If you are bored enough to read [reference 1], you’ll see that the writer has noted multiplication by juxtaposition as being used in algebraic nomenclature dating 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. As Doctor Peterson mentions in [reference 2] “When algebraic notation was first being developed, it was common for each writer to begin by explaining his own notation.” That seems to still be true as students are still being taught the distributive property and multiplication by juxtaposition as well as the standardized left-to-right order of operations. The correct answer breaks down to who is asking the question.
As much as you’d like it to be a single definitive answer, alas, it is not. In my opinion, that needs to change. Someone should standardize it. But the real answer here, to end all further questions on this topic, is the ambiguity of the formula makes it faulty to begin with. 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.
To summarize, as much as one would like to claim one answer or the other, the sad reality is; being as there is no current standardization in this case, the answer is relative to the inquirer. In the future, if an “ab/cd” –type equation is proposed, you’re better off inquiring as to the proposer’s notation preference.
Source(s):
[Reference 1]: Earliest Uses of Symbols of Operation
[Reference 2]: http://mathforum.org/library/drmath/view/57021.html "
This is the best answer I have been able to find:
"Mathematics is supposed to provide you with single, definitive answers. However, in this case, it does not. I really scoured the internet and countless textbooks for the proper answer and have made inquiries with few people I know whom I venerate as some of the greatest minds that I have had the luxury of meeting and the answer isn't as definitive as you would hope. Sadly, the real answer is that both sides are correct to a point. (…and it pains me to even remotely admit that anything outside of 288 could be the answer).
Position 1: The Order of Operations: This stance states that since the standard order of operations puts multiplication and division on the same rank, the equation can be read as (48÷2)*(9+3). This reigns with truth as 48÷2(9+3) is the same as 48÷2*(9+3). Using the standardized left-to-right notation, the answer can be nothing outside of 288. This left-to-right concept is indicative of “PEMDAS” that we all learned in grade school.
Position 2: The Distributive Property: This stance states that multiplication through juxtaposition, being a commonplace concept, naturally makes a parenthetical implication around grouped numbers. Thus, the equation appears as 48÷[2(9+3)]. This technique is correct as well. However, this makes the answer 2.
If you are bored enough to read [reference 1], you’ll see that the writer has noted multiplication by juxtaposition as being used in algebraic nomenclature dating 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. As Doctor Peterson mentions in [reference 2] “When algebraic notation was first being developed, it was common for each writer to begin by explaining his own notation.” That seems to still be true as students are still being taught the distributive property and multiplication by juxtaposition as well as the standardized left-to-right order of operations. The correct answer breaks down to who is asking the question.
As much as you’d like it to be a single definitive answer, alas, it is not. In my opinion, that needs to change. Someone should standardize it. But the real answer here, to end all further questions on this topic, is the ambiguity of the formula makes it faulty to begin with. 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.
To summarize, as much as one would like to claim one answer or the other, the sad reality is; being as there is no current standardization in this case, the answer is relative to the inquirer. In the future, if an “ab/cd” –type equation is proposed, you’re better off inquiring as to the proposer’s notation preference.
Source(s):
[Reference 1]: Earliest Uses of Symbols of Operation
[Reference 2]: http://mathforum.org/library/drmath/view/57021.html "
rockybaudoin05
Registered
2 all day every day son
Sexist remarks are never superfluous to the discussion on this site... either are random "You're Gay" pictures
This was a German site, and considering so much of the notation mathematicians use comes through Leibniz (THANK GOD - if you've seen Newton's notation, you'd be as grateful as I am!), I'm sure they were establishing that these units of measure are to be read as if the slash indicates a fraction rather than a simple division, as would otherwise be the convention.
Germans are famous for engineering and for calculus (ask a German who invented calculus and the answer is "Leibniz"; ask a Scot and it's "Newton"), and as a culture, are rule-abiding. The explanation offered on a German educational site is in keeping with this; they were breaking from convention because they were listing units of measure, not calculation formulae; the notation (on that, and on the other pages you linked) is shorthand, and within this context, and with the explanation in place, it is clear.
Personally, I blame calculators for a lot of this mess. Not for the usual reasons - I don't think they are evil or that they make people lazy; in the real world if you don't use computers for your calculations, nobody would trust your results. No, my reason for blaming them comes from what is written on the buttons, and by how their algorithms are sometimes designed.
We've already seen instances of where calculation algorithms don't jive, but consider trigonometry for a moment. Inverse functions undo each other, right? These are not always simply reciprocal function, and yet, this is exactly the way most calculators indicate them. For example, the inverse of tan(x) is arctan(x), yet calculators indicate this as tan^-1(x). I've taught trig to grade 12 students who did not even know the word "arctan" - they just call it the inverse tan; I've had a number of these students not realize that inverse tan and 1/(tan(x)) are not the same thing. Given the now-standard notation for which we can thank calculator buttons, this is unsurprising.
Other than some of the calculators I have tried, I have never before seen the juxtaposition rule being interpreted in this way - and I have studied both number theory, and math history.
When manipulating symbols, it is standard notation to leave off the multiplication operator - thus "a" times "b" becomes simply "ab". We cannot do this with numbers unless they're beside a bracket: 2 x 5 written this way would become 25, which is clearly wrong, although 2(5+6) is plainly equal to 2??(5+6); thus the operator is omitted.
This statement: b(c+d) would virtually NEVER be written as b??(c+d), because there is no question that they are equivalent in every way, whether or not as part of a larger calculation.
That being said, "eschew obfuscation" is a motto of mine, and to be perfectly fair, were I to write a question such as a÷b(c+d) , I would likely arrange it as either a(c+d)÷b, or, if I meant for the entire right hand side to act as a divisor, as a÷(b(c+d)) so as not to trick the reader.
When I design instructional math questions (I still tutor the occasional student), I try hard to keep this in mind. I want them to demonstrate fluency in mathematics, not the ability to second-guess the notation I've offered.
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