How do you interpret ambiguous math questions?

[Knight of Cydonia]

Are you by-the-book and calculate each of these problems exactly how the rules are supposed to be followed (i.e. with BEDMAS/PEDMAS)? Then you'll probably pick B every time. Or do you think that there is room for interpretation? For instance, does the appearance of spaces change your interpretation of the question?

 

Was just wondering this after seeing one of those stupid Facebook math problems. They are almost always poorly-written/ambiguous, intentionally so. I'm of the opinion that there is actually more than one acceptable convention of interpreting these kinds of math problems, and thus many of them have "more" than one answer.

[Guest]

I have Dyscalculia so how I interpret them is literally just as a blur of numbers that I can't make any sense of lol.

[SkyWorld]

I don't usually see things in black or white, but math is the exception. It's either right or wrong, no matter what, because it's universal. It just is.

[Knight of Cydonia]

38 minutes ago, SkyWorld said:

I don't usually see things in black or white, but math is the exception. It's either right or wrong, no matter what, because it's universal. It just is.

But the "order of operations" that you would use to evaluate these are not universal truths like 2+2=4. Evaluating these kinds of expressions depends on convention, and there isn't actually one universally accepted convention.

 

Some people are taught that the "/" in axb/cxd means to divide everything on the left by everything on the right. Others are taught that multiplication should be carried out first, followed by division. Others are taught that for cases of multiplication and division, you should work left to right...

[Baam]

Anyone who presents a problem like this needs to go back and rewrite it. If they are ambiguously written then they have ambiguous answers, as you said. Real maths never has these kinds of issues, 'Facebook maths' is a whole different story.

 

Having said that, if you write something like 2a, the 2 and the a usually go together. In fact, you could write it in simpler terms by defining c = 2a to avoid these ambiguities. Also, when you have a quotient, you would never write a product of that quotient on the right hand side without the use of parentheses. So the first answer would definitely be 1/(2a), because if you wanted to multiply the a by a half, you would write a*1/2 = a/2. Writing functions and equations sensibly is just about common sense, really.

[iff]

In the first two questions, I went for the first choice. In the last three questions, I went for the second choice.

 

In question 1 and 2, I saw the letter as being attached to the preceding number.

 

In question 4, there is a space between them but for me, as division and multiplication way equally, I read this across the same as question 3.

 

In question 5, I did the two indices first, then as it was multiplication and division, I completed it as if I was reading a sentence.  Got 20 billion as an answer.

 

The mnemonic device we used in school was bomdas. 

[timewarp]

When would that happen? Well, if I'm asked to review a paper. My interpretation? Major revisions.

[Member4445]

I send them to @Santa's little timewarp

[Homer]

[x] Yuck, maths.

[michaeld]

It depends on context. If you're typing these into a computer programming language (or a computer algebra system) then it's always b. In print, it's more ambiguous. Mathematicians will often write 6 / 2x3 to mean 6 / (2x3). This occurs especially if the denominator is 2pi.

[RK800]

Ambiguous?

*shakes head Autistically*

 

PEMDAS is the only thing I have to hold on to. Math is exact, otherwise I can't make sense of it.

[Grumpy Alien]

I went with the first answer EXCEPT the last one, which I would think is the second answer. I used PEMDAS.

[Grumpy Alien]

5 hours ago, festiff said:

The mnemonic device we used in school was bomdas. 

What does the o stand for?

[praetorius]

Mostly, I've just got to infer from context. Some things are fairly conventional in print typography, without adhering to an entirely consistent set of rules --- for example, I wouldn't be surprised to see something like "f / 2 pi" in a paper to indicate "f/(2 pi)". Once expressions get much more complicated than that, people tend to provide appropriate parentheses and brackets. Granted, I don't spend much time reading "stupid facebook math problems"; in scientific papers, the author is usually making a good faith effort to help you understand what they're saying, rather than trip you up over poorly-specified technicalities.

 

Question 5 with the "scientific notation" style exponents would always, in anything I encounter, imply the "choice a" grouping, with the internal multiplication and exponentiation being part of a convention for expressing "a single number" rather than "a bunch of math operations I need to calculate out," in much the same sense that I would never mistake 1234 for 12 * 34, no matter how badly kerned the digits were.

[michaeld]

While math may be exact (and tbh even this is debatable - in the sense there are different philosophies of math, and the absoluteness of math is debated by those who work in foundations), mathematical conventions are not necessarily absolute. BODMAS / PEDMAS / etc is something taught at school but is not the final word on the subject. It does (with very few exceptions) work for computer systems though.

 

If a paper contains a formula like T = S / 2pi, then very few would doubt that it means T = S / (2pi). An editor may request that it's re-written with parentheses or perhaps T = \frac{S}{2\pi} (i.e. as a fraction) but this would be far from universal.

[elmrain]

When I see formulae containing letters and/or having more than one operation on either side of a divisor, I would generally interpret it as a fraction, rather than a 'division' (i.e. ½ rather than 1 ÷ 2), in which case, I would solve the 'smaller' equations before dealing with the 'overall' equation. For relatively simple equations (as in Q.3), I would follow BIDMAS and divide first, but, the presence of the spaces in Q.4, would lead me to solve it as (6÷2)x3.

[XYZ96]

under all of them (except the third and fourth) I‘d make a note saying that the problem is missing parentheses, making it confusing...

the first one would depend how mad I am at the missing parentheses, if I didn’t care, then I calculate 1/(2a) if I was mad, then (1/2)a, same thing for the second one, if I didn’t care: (10a)/(5a), if I was mad, then ((10a)/5)a 

the third I would calculate as (6/2)*3 and the fourth as 6/(2*3)

the last one I‘d interpret as 6 * 10^(5/3) * 10^4, and if upset at the missing parentheses, then ((6*(10^5))/3)*(10^4)...

[iff]

7 hours ago, Graceful said:

What does the o stand for?

order

[Yatogami]

I have always used PEMDAS with Left to right priority. 

[Groovy Teacakes]

Question 5 my initial thought is: (6x10^(5/3))x10^4 although, upon reflection, (6x10^5)/(3x10^4) makes more sense in the context of normal mathematical conventions.

[Zsareph]

This is why we use brackets.

[Sleepy Skeleton]

Things would be simpler if people would just use the division simple instead of a slash, I think. I will always read things like 2/3 as two-thirds, not two divided by three. I know they're basically the same but when you have multiple operations in one problem it makes it easier the simplify things.

 

For the last problem, I see it as

(6x10^5)   
_____________

(3x10^4)

 

Like a fraction.

 

Or, you know, maybe y'all should start using parentheses if something needs to be solved a certain way. It's not like they're wrong.

[Guest Jetsun Milarepa]

Being a wordsmith, I tend to avoid calculating anything....

[TheAP]

I see the slash as a fraction/division sign indicating that everything before it goes on top and everything after it goes on the bottom. But yeah, I was confused by that in high school math too.

[Skycaptain]

Q1, 2,5 I read as option a, Q3, 4 I read as option b 

[Tintinfan]

Wouldn't you use BIDMAS 

Brackets 

Indices 

Division

Multiplication

Addition

Subtraction 

[Yatogami]

Parenthisis

Exponents

Multiplication

Division

Addition

Subtraction

 

if not, left to right I believe on certain equations. But unfortunately, math is the devil and I hate it. *angry face*

[Guest Jetsun Milarepa]

...errr, what's maths again? I think I remember it from my schooldays.....

[SpaceDustbin]

Brackets are the easiest way to avoid confusion (or at least... part of it)

 

When I was in school (in NL), we used the "Meneer Van Dale Wacht Op Antwoord" method, which I think is similar to PEMDAS, with roots  squished between divisions and additions. I think nowadays they put exponents and roots on the same level (which makes a big difference compared to the old method), followed by mutiplying/division, and add/subtract, and if you have elements of the same level of importance, it's left to right, I guess?

 

Either way... I ended up answering 1 to q's 1, 2, 4 and 5 (3 had me too confused )

 

 

[scarletlatitude]

There should be a "throws math book out the window" option