48÷2 (9+3) argument

[SmartKit]

Fail, answer=2

I'm glad you aren't doing my taxes!

 

[SmartKit]

When I calculate that, I get the answer is beer.

Strangely enough I got that on my first attempt to!

 

[Necuno]

Fail, answer=2

Sy moer, jys mal.

 

[Swa]

No. The question should be put in such a way that multiplication and division could be done in any order. (And no, division does NOT precede multiplication as is commonly believed, division is only the multiplication of the inverse, so it is the same operator, and has the same precedence.)

This question is ambiguous and has no clear answer.

This is lunacy. Multiplication and division is done in the order they occur. There's only one answer and a lot of ambiguous people.

I'm pretty sure I know my maths. Obtaining two results by choosing whether to divide or multiply first, means that there is a problem with the expression.

No you don't. You can only switch them around when the terms remain the same so
48 x (9+3) ÷ 2 is the same as 48 ÷ 2 x (9+3)
What you are doing is saying
2 x (9+3) ÷ 48 should be the same as 48 ÷ 2 x (9+3)
You are switching them around.

.

I wish people would quite replying in quotes. Left to right is not just a convention. It's a rule to use the convention of the language which is left to right. What if it was 1 - 2? By your logic there is no way to write it unambiguously because brackets can't change the order of the operation. The rule is to go by convention of the language used. It's the same as the word 'not.' In Arabic it would be 'ton.' But we don't presume it's Arabic.

You are right it's done on purpose. It's done to cause a heated debate between those that know their math rules and those that don't.

It's a hoax!

Well apparently it has to be. Proven by the people who argue math rules are ambiguous.

And in other news, school handbooks still not delivered. Cosatu calls for students failing maths tests to pass.

 

[Bar0n]

Hmmm.. I don't see how you would get from 8 * x / 2 * x to 4 * x * x working from any direction. That is a completely erroneous step that is not at all suggested by the syntax or the order of precedence.

Okay let's try it again:

8x / 2x
= 8 * x / 2 * x
= 8x / 2 * x
= 4x * x
= 4x^2

You are right it's done on purpose. It's done to cause a heated debate between those that know their math rules and those that don't.

Well as has been shown, math rules are not followed consistently, e.g. my example given above, the fact that multiplication by juxtaposition is very often given precedence over normal multiplication (even by Wolfram Alpha) as Wikipedia explains, etc.

Fields are usually understood to be commutative, but some authors do not assume this.

Are you sure? Fields are derived from commutative rings, so they should inherently be commutative? Or is the author trying to make a point by proving commutativity?

 

[GreGorGy]

Okay let's try it again:

8x / 2x
= 8 * x / 2 * x
= 8x / 2 * x
= 4x * x
= 4x^2

WTF?
if x=9:
8x/2x = 72/18 = 4
4x^2 = 4*9^2 = 4*81 = 4

Oh, sorry, didn't see that.

 

[Bar0n]

WTF?
if x=9:
8x/2x = 72/18 = 4
4x^2 = 4*9^2 = 4*81 = 4

Oh, sorry, didn't see that.

It's to prove that strictly working from left to right ignoring multiplication by juxtaposition will result in incorrect (or at least unconventional) answers.

The thing to take away here is not about "right" or "wrong". It's about realising the importance of communicating properly. No-one writes problems in this fashion. I cannot recall the last time I even saw someone use that division symbol instead of the conventional "/".

 

[Mike Hoxbig]

Well apparently it has to be. Proven by the people who argue math rules are ambiguous.

And in other news, school handbooks still not delivered. Cosatu calls for students failing maths tests to pass.

Uhm, yeah. As I said before, I never knew that we had so many maths experts on this forum. It's like all those Average Joes who offer legal, medical and psychological advice.

In the past 12-13 pages of this thread I know of at least two mathematicians (let's see if you can spot who), and both agree that no mathematician would write an expression like this because it does introduce ambiguity. They also agree that the order of operations is a guideline, and not mathematical law. Fancy that.

 

[Quantum Theory]

Is this still going?! The answer is 2.

*walks away*

 

[The_Ogre]

Is this still going?! The answer is 2.

*walks away*

^5

 

[lived666]

Is this still going?! The answer is 2.

*walks away*

indeed it is, though I can see why the 288 comes into play, its because the 12 is still left in brackets, but to remove the brackets you have to multiply the 12x2 first, that's just how the cookie crumbles, you left with 2 and not 288

 

[labratza]

288? Following PEMDAS, I get 2:

48÷2*(9+3) = 48÷2*(12) = 48÷24 = 2

The reason why some people are getting 288 is that they're forgetting that there's an invisible multiply sign in the expression.

Honestly though, if I ever saw this I would apply a facepalm. It's not good notation and like you're seeing, it's ambiguous without proper use of parentheses and will confuse people. It's better notation to say
482(9+3)

 

[pjjdp]

Isn't the maths rule that you have to "get rid" of the brackets first then calc the rest?

Is so, then it's def 2.

 

[MrGray]

288? Following PEMDAS, I get 2:

48÷2*(9+3) = 48÷2*(12) = 48÷24 = 2

The reason why some people are getting 288 is that they're forgetting that there's an invisible multiply sign in the expression.

Honestly though, if I ever saw this I would apply a facepalm. It's not good notation and like you're seeing, it's ambiguous without proper use of parentheses and will confuse people. It's better notation to say
482(9+3)

FAIL.

Following PEMDAS:

48÷2*(9+3) = 48÷2*(12) = 24*(12) = 288

(You've also got to work left to right - you worked right to left.)

 

[Chevron]

FAIL.

Following PEMDAS:

48÷2*(9+3) = 48÷2*(12) = 24*(12) = 288

(You've also got to work left to right - you worked right to left.)

You changed the equation by adding the *.

48÷2(9+3) = 48÷2(12) = 48÷24 = 2

 

[lived666]

FAIL.

Following PEMDAS:

48÷2*(9+3) = 48÷2*(12) = 24*(12) = 288

(You've also got to work left to right - you worked right to left.)

you have to get rid of the bracket first, its as simple as that
so its not 24x(12) because before you do the division you first have to get rid of the bracket, so its:
48/24 = 2
If you dont get rid of the bracket, then sure, you get to 288, but then its wrong.


**bored with this now, going to watch traffic.

 

[MrGray]

you have to get rid of the bracket first, its as simple as that
so its not 24x(12) because before you do the division you first have to get rid of the bracket, so its:
48/24 = 2
If you dont get rid of the bracket, then sure, you get to 288, but then its wrong.


**bored with this now, going to watch traffic.

LOL. I don't think you understand PEMDAS very well.

 

[MrGray]

You changed the equation by adding the *.

No, labratza added the *. I just fixed it.

 

[Mike Hoxbig]

LOL. I don't think you understand PEMDAS very well.

I think you take it too seriously.

 

[zippy]

http://knowyourmeme.com/memes/48293

However, solving the problem like this would be considered erroneous because multiplication and division hold equal precedence.[19]


It is helpful to remember that division and multiplication are inverse operations, and thus represent the same operation written in a different way. Division is the same as multiplication of the reciprocal, and multiplication is the same as division of the reciprocal. This is similar to how addition is the same as subtraction of the negative, and how raising to the nth power is the same as taking the 1/nth root.

and

If there are two or more operations with equal precedence (such as 10÷2÷5 or 7÷2*9), those operations should be done from left to right.