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I'm going to talk about math for a sec. Sorry.

Has anyone else here stumbled upon one of those Facebook posts with a seemingly simple math equation in it - maybe because a parent left a single number answer in what turned out to be a massive 1.5k comment list full of people arguing about what the answer is?

The latest (and very typical) example I saw was the seemingly simple: 6÷2(1+2), which had splintered into two camps declaring either 1 or 9 to be the right answer and are, at this moment, drawing up battle plans.

It got me thinking... Is there a chance people are being taught different, potentially conflicting things about the correct order of operations?

To me, the answer is 9. Here's how I get there:

In school I was taught the word to remember for order of operations was called 'BEDMAS', standing for Brackets Exponents Division Multiplication Addition Subtraction, and because it was Catholic school, the word was good.

As time went on they would clarify there were caveats: you resolved everything in brackets first (applying BEDMAS to the equation therein if necessary), followed by exponents (anything to the power of 2, 3, etc), then division and multiplication had to be done at the same time - by which they actually meant had to be done from left to right, and then the same had to be done for addition and subtraction.

So following that method, I get: 6÷2(1+2) = 6÷2(3) = 3(3) = 9

Now, my knee-jerk reaction is that those getting back 1 is that they're applying a hard order to the multiplication and division, or a soft order but resolving it right to left instead of left to right: 6÷2(1+2) = 6÷2(3) = 6÷6 = 1 which makes sense to me as a bad result coming from a simple misunderstanding, right?

But then, I saw someone lay out their reasoning by expanding the equation into a chalkboard style over-under equation:

6
------------
2(1+2)

And I have no idea what rationale they use to break the equation down this way as opposed to say:

6
--- x (1+2)
2

Which is a concern to me because that person could just as easily be writing requirements for a discount calculator for some their company's web store - what risks are incurred when the one writing the requirements and the one reading them have fundamentally different understandings of how math works??

Anyway, my question: how were you taught order of operations? How would you apply them to this equation: 48÷2(9+3)

9 is correct as is BEDMAS theory.
Those facebook posts infuriate me

I was taught PEDMAS, although I went to a French school, it's pretty much the same thing.

Since there are still parentheses left mean you would calculate the "2(3)" before the "6/2"? I do realize it's essentially just a multiplication, but my brain tells me to resolve anything involving parentheses until they are all gone.

Edit: I'm by no means a mathematician, so it's likely I've been doing this wrong my whole life

What matters is the final number coming out of the parentheses (in this case, 3), once that's determined its essentially just another number in the larger equation.

So you can express 6÷2(3) as 6 ÷ 2 x 3 at that point and it means the same thing.

 Captain Joystick wrote:
What matters is the final number coming out of the parentheses (in this case, 3), once that's determined its essentially just another number in the larger equation.

So you can express 6÷2(3) as 6 ÷ 2 x 3 at that point and it means the same thing.

Yea when you write it out like that, it leaves no ambiguity. Answer is definitely 9.

PEMDAS says its the following,

6÷2(1+2)=X

So you do 1+2 first because of P.

6÷2(3)=X

No Exponants.

Multiplication comes before division. 2x3 is 6.

6÷6=1

Regardless of if you use PEDMAS/BEDMAS or PEMDAS, Divisions and Multiplications have the same priority, so you do whichever comes first.

 Grey Templar wrote:
PEMDAS says its the following,

6÷2(1+2)=X

So you do 1+2 first because of P.

6÷2(3)=X

No Exponants.

Multiplication comes before division. 2x3 is 6.

6÷6=1

Wrong. Multiplication and division are the same thing, they happen concurrently.

6 / 2 * (1 + 2) = 6 / 2 * 3

From this point you go left to right, effectively turning this into: (6 / 2) * 3 = 3 * 3 = 9.

Just type 6/2(1+2) into google to check.

This can also be demonstrated thusly: 6 * (1/2) * (1+2) = 6 * (1/2) * 3. Even if we follow your assertion that multiplication must take precedence over division we end up with: 6 * 3 * (1/2) = 18 * (1/2) = 18 / 2 = 9.

Software engineer answer: why are you leaving ambiguity, use explicit parentheses instead of making assumptions because otherwise who knows how the compiler will interpret it.

Those don't bother me that much. The ones on facebook that bother me are the ones where they have items that add up to numbers...then they expect you to figure out the last one that is technically impossible.

They'll, for instance, use a pair of boots to mean 10 but the one you're supposed to solve only uses a single boot. We have no way of knowing what a single boot signifies as it was never used before.

 Peregrine wrote:
Software engineer answer: why are you leaving ambiguity, use explicit parentheses instead of making assumptions because otherwise who knows how the compiler will interpret it.

Also this, from a Physicist viewpoint. All of these types of "trick" maths problems are always due to the same lack of instant clarity in the way the problem is written. They are incredibly annoying because they are intentionally written to avoid being clear when all they need is another set of parentheses to make it immediately clear.

I suck at math and I know the answer is 9.

I feel better about myself now

 Peregrine wrote:
Software engineer answer: why are you leaving ambiguity, use explicit parentheses instead of making assumptions because otherwise who knows how the compiler will interpret it.

You are technically correct, (the best kind of correct.) and it works great until the business unit comes along three years later and asks to see the equation because they want to tweak it.

Then you send it and they schedule a meeting. D:

 Captain Joystick wrote:


But then, I saw someone lay out their reasoning by expanding the equation into a chalkboard style over-under equation:

6
------------
2(1+2)

And I have no idea what rationale they use to break the equation down this way as opposed to say:

6
--- x (1+2)
2

Which is a concern to me because that person could just as easily be writing requirements for a discount calculator for some their company's web store - what risks are incurred when the one writing the requirements and the one reading them have fundamentally different understandings of how math works??

The equation 6÷2(1+2) is poor which is why there is the confusion. The equation confuses algebraic mathematical terminology with notational terminology. By doing this it confuses which is the numerator and which is the denominator. In algebraic terms you would read the equation as 6 / X where X = 2(1+2) = 6 and hence the answer is 1. In notational maths you would do the actions in order of the brackets first and then the multiplication/division followed by any further addition/subtraction. So hence it would be 6÷2x(1+2) = 6 ÷ 2 x 3 = 9. So either the equation should be written


6 / 2(1+2) which would mean 6 is the numerator (before the line) and 2(1+2) would be the denominator (after the line). To be completely transparent you should write 6 / (2 (1+2)); or
6 ÷ 2 x (1+2) which would mean 6 and (1 + 2) are the numerators and 2 is a denominator. To be completely transparent it should read (6 ÷ 2) x (1+2)

So the answer is both 1 and 9 because it depends on the interpretation of the viewer as to whether it is notational or algebraic maths you are considering.

Those things annoy me no end. They have vague questions and then talk down to people who get it “wrong” ie chose the other answer. In reality the person who set the question is an idiot who should be smacked hard with a TI-92.

 A Town Called Malus wrote:

 Peregrine wrote:
Software engineer answer: why are you leaving ambiguity, use explicit parentheses instead of making assumptions because otherwise who knows how the compiler will interpret it.

Also this, from a Physicist viewpoint. All of these types of "trick" maths problems are always due to the same lack of instant clarity in the way the problem is written. They are incredibly annoying because they are intentionally written to avoid being clear when all they need is another set of parentheses to make it immediately clear.

This.

I was a math major, and I don't recall any mathematician ever using that division symbol, certainly not in a problem using parentheses.

It's probably because the QWERTY keyboard doesn't have instant ready access to the normal division symbol, and online / is (at least in my experience) always taken as short hand for it. Computer programming too (all the languages I vaguely remember anyway). If you want to calculate a fraction with computer code you have to write it as ()/() or the computer will just do normal order of operation.

I hadn't consider the angle though, so now I feel stupid and bad at math again XD

 LordofHats wrote:
It's probably because the QWERTY keyboard doesn't have instant ready access to the normal division symbol, and online / is (at least in my experience) always taken as short hand for it. Computer programming too (all the languages I vaguely remember anyway). If you want to calculate a fraction with computer code you have to write it as ()/() or the computer will just do normal order of operation.

I hadn't consider the angle though, so now I feel stupid and bad at math again XD

If you're addressing me, I got my degree when math professors wrote it all out by hand. The Textbooks were obviously typed, but no QWERTY on earth has ready access to most of the symbols needed in them.

 BobtheInquisitor wrote:

 LordofHats wrote:
It's probably because the QWERTY keyboard doesn't have instant ready access to the normal division symbol, and online / is (at least in my experience) always taken as short hand for it. Computer programming too (all the languages I vaguely remember anyway). If you want to calculate a fraction with computer code you have to write it as ()/() or the computer will just do normal order of operation.

I hadn't consider the angle though, so now I feel stupid and bad at math again XD

If you're addressing me, I got my degree when math professors wrote it all out by hand. The Textbooks were obviously typed, but no QWERTY on earth has ready access to most of the symbols needed in them.

Yeah. Even now most professors will still be writing stuff out by hand at university when it comes to maths and equations, either on a whiteboard/blackboard or by using a camera pointed at paper which is then projected onto a screen (a visualiser).

To write out equations quickly in word processing software the software needs to be designed for it, such as something like LaTeX. In which case you are writing it like computer code anyway.

Ignore all this. Please delete.

Both answers are wrong. The correct answer to all of these stupid "puzzles" is either a) don't play or b) 42.