Can you do this simple maths problem?

[Defiant47]

Guys.. listen.. If somebody writes 2/5*5, I am not going to assume this means 2/(5*5). That doesn't make sense.

Unless you put the whole term in brackets, it does not belong in the denominator.. unless you do it like this

2
---
5*5

But if someone writes 2/5a where a=5, then it is 2/(5*5).

 

[innonimatu]

Guys.. listen.. If somebody writes 2/5*5, I am not going to assume this means 2/(5*5). That doesn't make sense.

Unless you put the whole term in brackets, it does not belong in the denominator.. unless you do it like this

2
---
5*5

What id someone presents you with x/yz, what do you assume?

Someone mentioned Worfram Alpha, try "x/yz = 1" there. It's interpreted as x/(yz), not (x/y)*z. And it does interpret y and z as separate variables. Is there a convention for numbers and another for variables? It just shows that there are no reliable conventions.

 

[Hehehe]

There is nothing unclear about this. The answer is 288 (see: order of operations). The reason why 1/5a is usually 1/25 if a=5 is because 5a is often though of as a single term. If it is 1/5*a the the answer would be 1 (again, assuming a=5). Also in the case of variables, x/yz is often intepreted as

x
--
yz

because there is no multiplication between y and z. There is no multiplication to be done there, that is why it's x/(yz). If you write it as x/y*z, then it is (x/y)*z. I see nothing unclear here.

EDIT: In case I didn't make myself clear 5a is considered a single term, thus no multiplication, while 2(9+3) is not. Though there is no multiplication mark between 2 and the brackets, multiplication must be performed nevertheless to calculate this, thus order of operation applies.

 

[Camikaze]

48÷2(9+3) = ?

I find this to be a much easier question than 48/2(9+3) = ?, because 48/2(9+3) indicates to me that 2(9+3) is all beneath 48 in a fraction. So I'd definitely say 288 for the OP question, but I'd probably answer 2 for 48/2(9+3) = ?.

 

[ParadigmShifter]

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

48/2(9+3)
48/2(12)
48/24
2

Am I missing something?

Yes.

Parenthesis
Exponents
Multiplication,Division
Addition,Subtraction

Stuff on the same line has the same precedence and are evaluated left to right (by convention).

 

[stuge]

My initial reaction was "it's 2, what's the deal here?" I can see how it would be 288. Just goes to show how important clear formalism is in maths.

Oh, BTW.

The case of the plane and conveyor belt:

A plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the wheel rotation speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?

The plane will take off just fine.

 

[Truronian]

Maths teacher here.

The answer is 288. Even if you have no knowledge of the precedence system explained by Paradigm (and just use the operations in BIDMAS order) you should arrive at this answer.

On a somewhat related note, I don't like BIDMAS. BIDMAS requires the 'same precedence' stuff because it is in a bad order. If we instead went for BIDMSA then you could do away with the 'same precedence' without issue.

 

[Defiant47]

Why do people keep calling it bidmas??? What are "ixponents"??

 

[Truronian]

Why do people keep calling it bidmas??? What are "ixponents"??

The I stands for indices.

 

[Yizume]

The case of the plane and conveyor belt:

A plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the wheel rotation speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?

I believe that the lift the plane requires comes from air passing over the wings and in this scenario that plane would not be moving relative to the air around it and so would be unable to take off.

 

[Truronian]

I've not seen the plane on a conveyor belt problem posed that way before. I'm pretty sure the conveyor belt breaks. Nothing it does is going to stop the plane moving forwards so there is going to be a positive feedback loop between the conveyor speed and the wheel's rotational speed.

 

[warpus]

Putting in the multiplication star means it's not an implicit operation, no one is disagreeing about that.

If somebody writes 2/5x, you get:
2
---
5x

Yes, it's a conventional thing, yes, it's probably something that people in different countries have a little different culturally. But I'd like to ask people to at least actually try and find a single published example of this anywhere that supports the 2/5x = (2/5) * x, even for kids. On the other hand that are thousands of texts, journals, etc... across pretty much all technical fields where formulas are written all the time as wx/yz = (wx) / (yz) and the like, and nobody would ever, ever write wx/yz = wxz/y.

I agree. 2/5x is a bit more ambiguous looking.

But hey, in the end nobody competent will write an equation this way, so it doesn't really matter.

Good points my young padawans! You have changed my mind about something.. on the internet! I expect the tubes to shut down any moment now

As for bidmas, I've always known it as bedmas. I used to remember it by picturing mass in bed.

 

[Roller123]

Guys.. listen.. If somebody writes 2/5*5, I am not going to assume this means 2/(5*5). That doesn't make sense.

Thats a failed exam if you solve a math problem with "it doesnt make sense". Math doesnt care if a human doesnt believe it, as do many other things which are rather unknown for a human.

Same with the plane on a conveyor belt, it doesnt take off. Common sense doesnt work, only Physics.

Stuff on the same line has the same precedence and are evaluated left to right (by convention).

The funny thing, half a page ago, i just listed a bunch of programming daily-use operators which are evaluated strictly from right to left. No wonder buggy software is still so common

Truronian
Thats the original question, but yeah, if the conveyor belt breaks, which is rather an unorthodox solution, the plane will not go anywhere just as well sadly. with no ground under it.

 

[Truronian]

Truronian
Thats the original question, but yeah, if the conveyor belt breaks, which is rather an unorthodox solution, the plane will not go anywhere just as well sadly. with no ground under it.

The form I've heard has the conveyor belt go at the same speed as the plane. A subtle difference, but one necessary for the puzzle to make sense.

The plane would take off; the conveyor would break, not disappear.

Physics-wise the only thing that matters to a plane at ground level is the reaction force, which acts perpendicularly to any conveyor belt's effect. The conveyor belt is a massive red herring, you can have it doing anything you like and it still won't stop the plane taking off.

 

[Roller123]

Truronian
True but thats not the original question, which is the interesting one, the one you mention is indeed quite trivial. (still it hasnt stopped people from discussing it right, hehe). Try to solve that one.

 

[Earthling]

The answer is 288. Even if you have no knowledge of the precedence system explained by Paradigm (and just use the operations in BIDMAS order) you should arrive at this answer.

The answer is 2, and even with no experience you should arrive at that answer by correct order of operations. You may be qualified to say that 288 is what an 8 year old in Britain might say and I'd gladly defer to that. Though I don't know if you're saying you actually have experience teaching 8 year olds, 9 year olds (or whatever). That doesn't really stand as an answer in any other way though.

On a somewhat related note, I don't like BIDMAS.

I agree with this though. Firstly, because it's nonsense using the wrong words for "B" and "I" as everyone else would point out. Secondly because all such acronyms leave out too many useful operations to be helpful to anyone outside of gradeschool, lots of functions, factorials, you name it. The question asked isn't "what would an 8 year old say" - and people have given quite enough evidence that even that should vary. Though it would be fun to assert that, say, (sin x) / (x) = nsi because that's how an 8 year old would see it, that's not really true.

True but thats not the original question, which is the interesting one, the one you mention is indeed quite trivial. (still it hasnt stopped people from discussing it right, hehe). Try to solve that one.

Regarding the plane/conveyor question - in the original Russian I believe the problem posited something like "image a hypothetical conveyor belt which applied a force to cancel an airplane's horizontal momentum), to which the plane wouldn't r, take off (a helicopter or VTOL aircraft or something in contrast, could). Otherwise it's an Internet troll question though, the answers are obvious whichever way you ask the question, and the only debate is pretending that the question is asked differently than it is.

 

[Bill3000]

The I stands for indices.

I'm sorry, but that's objectively inferior to PEMDAS.

 

[Truronian]

The answer is 2, and even with no experience you should arrive at that answer by correct order of operations. You may be qualified to say that 288 is what an 8 year old in Britain might say and I'd gladly defer to that. Though I don't know if you're saying you actually have experience teaching 8 year olds, 9 year olds (or whatever). That doesn't really stand as an answer in any other way though.

Correct order of operations gives division and multiplication equal precedence, and operations with equal precedence are performed from left to right. Therefore we have...

48 ÷ 2 x (3+9)
48 ÷ 2 x 12
24 x 12
288

That is the answer you'd be expected to get in a GCSE or foreign equivalent, which also happens to the only level of mathematics where such banalities are even contemplated.

I agree with this though. Firstly, because it's nonsense using the wrong words for "B" and "I" as everyone else would point out. Secondly because all such acronyms leave out too many useful operations to be helpful to anyone outside of gradeschool, lots of functions, factorials, you name it. The question asked isn't "what would an 8 year old say" - and people have given quite enough evidence that even that should vary. Though it would be fun to assert that, say, (sin x) / (x) = nsi because that's how an 8 year old would see it, that's not really true.

Order of operations as a topic has a changed reason for even existing in the secondary school syllabus as of late. It used to be that it had to be taught to stop people making daft errors with their 90's calculators. The advent of increasing snazzy Casio calculators have made this element of the topic somewhat redundant; now it really serves as more of an introduction to brackets and why we need them.

Regardless, BIDMAS is not an acronym designed to help anyone that has even half a clue what a sine function is, it's their to help the less able mathematicians establish the correct order in which to do a calculation. That's why I tend to teach B for brackets; kids know what brackets are. They don't know what parentheses are. 'Indices' on the other hand in certainly inferior to 'powers'. They are typically the missing untouched letter though; the focus in secondary school is on brackets and the four operations.

[I know one teacher who teaches BODMAS with the O standing for "other stuff" or "other funtions". Not a bad idea IMO.]

Regarding the plane/conveyor question - in the original Russian I believe the problem posited something like "image a hypothetical conveyor belt which applied a force to cancel an airplane's horizontal momentum), to which the plane wouldn't r, take off (a helicopter or VTOL aircraft or something in contrast, could). Otherwise it's an Internet troll question though, the answers are obvious whichever way you ask the question, and the only debate is pretending that the question is asked differently than it is.

How exactly could a conveyor belt produce a force to cancel an airplane's horizontal momentum?

I'm sorry, but that's objectively inferior to PEMDAS.

See above. Parentheses and Exponents are certainly much cooler words, but they are not words that are understood by your typical D grade GCSE student.

 

[ParadigmShifter]

We don't need brackets. We have RPN, Forth and LISP

EDIT: Ok, you need parentheses for LISP (which stands for Lots of Irrelevant Spurious Parentheses).

 

[Quackers]

Ahhhhh so operation predecdence begins from left to right -- didn't know that gonna retake my MATHS GCSE def