Can you do this simple maths problem?

[KMRblue1027]

They apparently think that the multiplier and divisor operands are on different precedence levels, or they don't know about left associativity.

That why I posted the wiki article for backing but this is 6th grade stuff honestly.

 

[Earthling]

KMRblue, it's the correct way. You should read the whole thread and you'd see it

And Formaldehyde, the only reason the thread went this long is because Truronian came here to invent an unrelated argument about the obelus and solidus which isn't borne out by evidence, and post links to stuff that didn't actually discuss said tangent either.

 

[Defiant47]

BEDMAS:

Brackets, Exponents, Multiplication and Division, Addition and Subtraction

This is the order of operations that everyone gets taught in grade school. Everyone knows this. Stop spouting it around.

However, once you move on to high school and university, a new form of operation is introduced: implicit multiplication. This is typically done to make equations look nicer, typically because students are smart enough to deal with it, and it's much more succinct.

The real order of operations is thusly:

Brackets, Exponents, Implicit Multiplication, Multiplication and Division, Addition and Subtraction

What is 2x?? There is no operator between the two operands. Convention states that 2x means 2*x. To an early grade school student, you'd have to explain this, but the bigger kids understand.

What is 2x/3y?? There are operators missing (and potentially brackets as well). Typically if two operands are beside each other, this means multiplication. However, convention states that this implicit multiplication takes precedence over explicit multiplication and division. And so we have

2x/3y =/= (2xy)/3

It is a simple convention used in mathematics to streamline the flow of equations, and it is used globally.

Reciting grade school rules that are not applicable and are incomplete is not going to prove anything.

 

[Formaldehyde]

There is no difference between implicit and explicit multiplication, and they both have exactly the same precedence. The former is just a shorthand which can be converted to the explicit form by placing the multiplication operand in the proper place. Check the references listed above.

 

[Defiant47]

There is no difference between implicit and explicit multiplication, and they both have exactly the same precedence.

This is plain wrong.

The former is just a shorthand which can be converted to the explicit form by placing the multiplication operand in the proper place. Check the references listed above.

In order to transform an equation from implicit to explicit you need more than just a multiplication operand - you need some brackets as well.

2x/3y = (2*x)/(3*y)

 

[Earthling]

Yes, every reference listed above proves I'm correct, Formaldehyde. Please bother to actually read the references and understand what you're reading. You'd see, for instance, that nothing anyone else posted as a reference besides me even discusses or presents examples of implicit multiplication. Truronian, who was claiming his posted links show "side-by-side examples of the difference between the obelus and solidus" don't even do that either, but it's irrelevant.

Also, this is a nice F*** YEAH CANADA here. Sometimes the Canadians are all right. Despite using the "BEDMAS" acronym the British use a Canadian teachers organization still gets the rest of it correct

http://bctf.ca/diversity/ResourceInventory/LessonsTopics/Davies/BEDMAS.pdf


edit - I want to put things clearly in this post, so let's summarize:

Pretty much any math, physics, science, engineering publication and textbook ever - an expression like h / 2π is always, always h / (2*&#960 Have fun writing to like every physics textbook author ever to explain your rage to them or whatever. It's painfully obvious that no one will ever write in any printed work an expression looking like the one in the OP to mean "288". But furthermore, and I think this is important, there are actually thousands and thousands of examples where people DO use the implicit multiplication convention, in published journals and textbooks. Yes, even mathematics textbooks, people have found examples and cited books with things like y''/y'x. It's actually a common convention.

Programming languages, calculators, and computer tools: You will get different answers here. It was already all over the Internet anyway, people have screenshots or photos of different calculators and programs simultaneously giving different answers, or errors. However, it's also acknowledged by everyone with a rudimentary education that computer tools are only as smart as users and can make mistakes. Hence why Google does 1/3i differently and Wolfram thinks sin 2pi is equal to sin(2) * pi. None of my argument really depends on any of this anyway, but if the sole basis of yours is that Google gave you an answer, you'd have to say that every other thing input into Google that is obviously wrong is right. It's not a tenable position. (Furthermore we have the issue that actual documentation of producers of such things like the company TI that suggest that the implicit multiplication convention is a higher standard, just not implemented in all calculators, so be careful)

Using the division sign, or obelus symbol, aka this symbol here "÷" : This is the one case that somebody could provide reasonable contrary evidence for. Finding a text for 10 year olds in Britain or something that's different. None of you have posted such a text, and now that I have both American publications and then the lovely Canadian link above I'm even happier. And again, nothing Truronian or someone else posted actually was an example of this in Britain. The point wasn't "prove that the obelus sign exists, by posting 6 ÷ 3 = 2." or whatever. Completely irrelevant, Truronian. You'd need to find an example of an expression like 2a ÷ 3b as in the OP.

The better answer is 2

 

[Formaldehyde]

This is plain wrong.



In order to transform an equation from implicit to explicit you need more than just a multiplication operand - you need some brackets as well.

2x/3y = (2*x)/(3*y)

Ah, that form of implicit multiplication. You are correct, but it doesn't come into play here. I was referring to the implicit multiplication in the problem:

48÷2(9+3) = ?

which is equivalent to:

48÷2*(9+3)

which is equivalent to:

(48÷2)*(9+3)

Just try it with Mathematica or any programming language in existence to see for yourself.

 

[Defiant47]

Ah, that form of implicit multiplication. You are correct, but it doesn't come into play here. I was referring to the implicit multiplication in the problem:

48÷2(9+3) = ?

which is the same as:

48÷2*(9+3)

which is the same as:

(48÷2)*(9+3)

I posit that it is the same form of implicit multiplication. And if you click on Earthling's link just up above (it's not that long, 6 pages, all to the point), you'll see that the same rules apply to the brackets.

24 / (2)(3) = 24 / 6 = 4

 

[Defiant47]

Just try it with Mathematica or any programming language in existence to see for yourself.

This kind of math and the way such stuff is written is obviously meant for on-the-board or on-the-paper calculations. Programs aren't the most flexible things, and they aren't always right.

If you wanted to write it into a program, you'd have to actually be careful to write it very explicitly and to cover everything.

On paper you'd write 48/2(9+3). In Mathematica you'd write 48/(2*(9+3)).

 

[Formaldehyde]

I posit that it is the same form of implicit multiplication. And if you click on Earthling's link just up above (it's not that long, 6 pages, all to the point), you'll see that the same rules apply to the brackets.

24 / (2)(3) = 24 / 6 = 4

Actually, it doesn't at all. It agrees with me and the refererence I posted as well as the Wiki entry posted earlier. Under the "rule for BEDMAS" on page 1 it clearly states "do whichever one comes first in the equation". It also clarifies what it calls "Hidden multiplication signs" which I referred to above as implicit multiplication.

This kind of math and the way such stuff is written is obviously meant for on-the-board or on-the-paper calculations. Programs aren't the most flexible things, and they aren't always right.

If you wanted to write it into a program, you'd have to actually be careful to write it very explicitly and to cover everything.

On paper you'd write 48/2(9+3). In Mathematica you'd write 48/(2*(9+3)).

This is flatly wrong. It would be represented as (48/2)(9+3) which is equivalent to (48/2)*(9+3). As I said, try it with Mathematica or any programming language in existence. They will all agree the correct answer is 288. After all, Mathematica is the leading authority in these matters and programming languages which all agree with each other can't all be wrong.

 

[Defiant47]

Actually, it doesn't at all. It agrees with me and the refererence I posted as well as the Wiki entry posted earlier. Under the "rule for BEDMAS" on page 1 it clearly states "do whichever one comes first in the equation".

Page 1 is irrelevant. BEDMAS is irrelevant. Stop referencing it and stop quoting it. Like Earthling has said, it has nothing to do with what's going on here.

It also clarifies what it calls "Hidden multiplication signs" which I referred to above as implicit multiplication.

Page 4, Question 3:

24 / (2) (3) = 24 / 6 = 4

 

[Earthling]

Formaldehyde, MATLAB, Microsoft Excel, C++ say the answer is 2 after correcting for parsing errors. Most programming languages won't interpret what's in the OP and get an error as default. So I could just as easily say Java, Python etc... give 2 as the answer too, since you have to add brackets and use different symbols anyway. Casio and TI calculators of different versions but able to display on their screens what's in the OP will get either answer. As do Wolfram and other Internet calculators if you change trivial things, like putting a space character in or using a variable, which is not justified by any real life convention anywhere.

 

[Defiant47]

This is flatly wrong. It would be represented as (48/2)(9+3) which is equivalent to (48/2)*(9+3). As I said, try it with Mathematica or any programming language in existence. They will all agree the proper answer is 288.

It would be represented as (48/2)*(9+3) in Mathematica. Which is why you need to be careful and explicitly state all your order of operations. Pretty simple for a program to just read implicit multiplication, insert a multiplication sign there, and then evaluate it as explicit - doesn't mean it's right.

I'm pretty sure these program provide some sort of warning about use and making sure to state things explicitly. To me such adjustment is implicit, but maybe it's also stated.

On paper, I'd write 48/2(9+3). In Mathematica, I'd know that I'd need to write 48/(2*(9+3)) to get the correct answer.

 

[Formaldehyde]

Formaldehyde, MATLAB, Microsoft Excel, C++ say the answer is 2 after correcting for parsing errors.

There are no "parsing errors" if you merely put a multiply operator where it properly belongs. And, once again, the only correct answer is 288. Every reference cited so far agrees.

 

[Defiant47]

In case it was missed:

edit - I want to put things clearly in this post, so let's summarize:

Pretty much any math, physics, science, engineering publication and textbook ever - an expression like h / 2π is always, always h / (2*&#960 Have fun writing to like every physics textbook author ever to explain your rage to them or whatever. It's painfully obvious that no one will ever write in any printed work an expression looking like the one in the OP to mean "288". But furthermore, and I think this is important, there are actually thousands and thousands of examples where people DO use the implicit multiplication convention, in published journals and textbooks. Yes, even mathematics textbooks, people have found examples and cited books with things like y''/y'x. It's actually a common convention.

Programming languages, calculators, and computer tools: You will get different answers here. It was already all over the Internet anyway, people have screenshots or photos of different calculators and programs simultaneously giving different answers, or errors. However, it's also acknowledged by everyone with a rudimentary education that computer tools are only as smart as users and can make mistakes. Hence why Google does 1/3i differently and Wolfram thinks sin 2pi is equal to sin(2) * pi. None of my argument really depends on any of this anyway, but if the sole basis of yours is that Google gave you an answer, you'd have to say that every other thing input into Google that is obviously wrong is right. It's not a tenable position. (Furthermore we have the issue that actual documentation of producers of such things like the company TI that suggest that the implicit multiplication convention is a higher standard, just not implemented in all calculators, so be careful)

 

[Defiant47]

There are no "parsing errors" if you merely put a multiply operator where it properly belongs.

Once again:

48/2(9+3) =/= 48/2*(9+3)

If you're inputting a different equation, of course you'll get a different answer.

 

[Earthling]

Every reference cited so far agrees.

The statement you posted here, is not true. Post the screenshot of what you're referring to if you think it is. Especially since it's not only not true by omission, pretending evidence was posted that wasn't, but not true in the sense that you weren't able to read sources that were posted.

 

[Defiant47]

The statement you posted here, is not true. Post the screenshot of what you're referring to if you think it is. Especially since it's not only not true by omission, pretending evidence was posted that wasn't, but not true in the sense that you weren't able to read sources that were posted.

Don't bother, it will just be more BEDMAS. Or PEMDAS. Or PIDMAS.

 

[Formaldehyde]

I think I'm going to take the word of every programming language in existence, every article cited so far, as well as the leading authority in these matters, Wolfram Research.

Once again, and for the very last time, try it for yourself. They all agree.

 

[Earthling]

Bill3000's post is best in the thread, though JollyRoger's post #2 was probably the wisest. Especially so if he hadn't seen this elsewhere on the Internet, rather prescient.