Math problem wreaking havoc

[Urstadt]

My friends, and their friends, have been in a 10-day long debate over a math problem. I am hoping people on here can help us settle it.
 

6²   ÷  2(3)   +   4

 
About 60% of the commenters say the answer is 10:
 
 

6²   ÷  2(3)   +   4
36   ÷   6   +   4
6   +   4
10

 
 
but the other 40% are adamant that the answer is 58.
 

6²   ÷  2(3)   +   4
36   ÷   2(3)   +   4
18(3)   +   4
54    +   4
58

 
What do all y'all say?

Edited August 2, 2015 by Urstadt

[Guest]

Bahaha. Did you mean to write the title as you did? I'm sure you'll get more views that way. . .

[Urstadt]

Bahaha. Did you mean to write the title as you did? I'm sure you'll get more views that way. . .

 

Oooops..... Freudian typo.

Edited August 2, 2015 by Urstadt

[David13]

Yeah sure.

I never would have tuned in to Math Problem.

dc

[Vort]

My friends, and their friends, have been in a 10-day long debate over a math problem. I am hoping people on here can help us settle it.

 

 

About 60% of the commenters say the answer is 10:

 

 

 

 

but the other 40% are adamant that the answer is 58.

 

 

What do all y'all say?

 

This is purely an order-of-precedence problem, and as such, is of only trivial interest. But I think it's interesting (which shows, I suppose, that I'm trivially minded).

 

If you accept parentheses as the first-order precedent, then 2(3) must be calculated before anything else:

 

6²   ÷  2(3)   +   4

6²   ÷  6   +   4

 

36   ÷  6   +   4

6   +   4

10

 

But if you view the parentheses as just another way to express multiplication, then left-to-right order determines order of precedence in multiplication and division:

 

6²   ÷  2(3)   +   4 (can be rewritten as)

6²   ÷  2  x  3   +   4

36   ÷  2  x  3   +   4

18  x  3   +   4

54   +   4

58

 

I personally go for the first idea, that parentheses lead the order of precedence. Don't know if there's a canonical answer.

[Urstadt]

Thank you to the moderator who corrected the title. :)

 

Vort, the math teachers on that post are adamant, almost violent, that the answer is the second one. Thank you for your thoughts.

Edited August 2, 2015 by Urstadt

[Guest]

Thank you to the moderator who corrected the title. :)

 

Aw, who ruined the fun?

[Vort]

Thank you to the moderator who corrected the title. :)

 

Vort, the math teachers on that post are adamant, almost violent, that the answer is the second one. Thank you for your thoughts.

 

Honestly, I don't put much faith in math teachers. They are hidebound and tend to be very narrow. This looks like a hidebound, narrow sort of issue, but I don't think it's cut-and-dried.

 

The problem comes up because of computer programming, where parentheses always take precedence. The problem is that, in computer programming, parentheses represent groupings or functions, not operations. Thus, if you use parentheses to imply multiplication, the parentheses might reasonably be thought to fall back into the regular order of precedence.

 

So the math teachers are probably right on this one, but I don't give their word per se much authority. I would go further and say any math teacher that gave such a problem and then marked the first answer wrong is a crummy math teacher.

Edited August 2, 2015 by Vort

[MrShorty]

In the democratic, let's vote on it, spirit, I will add my vote. I agree with Vort in every point. It is a simple "order of operations" questions. On first glance, I, too, went with the parentheses first, so performed the 2(3) operation before the exponentiation. On second glance, I could see the ambiguity where one could wonder if the notation being used wants to have the 2(3)=6 performed first, or if it should be treated as simple multiplication 2(3)=2*3.

 

I will also agree with Vort that the either answer is "correct" given the ambiguity in the notation. A teacher that really wants the second answer, needs to be sure to communicate to their students exactly how they want 2(3), notated like that, treated. If this was not clearly communicated to the students, then they should give full marks for either answer, and use the quiz/test/homework as an opportunity to explain how they prefer to read the notation. I might also suggest that a less ambiguous notation be used, if the teacher wants to give preference to either answer.

 

6^2÷(2*3)+4=10 if the first answer is preferred.

6^2÷2*3+4=58 if the 2nd answer is preferred.

[Josiah]

Thought this looked familiar somehow. Your situation is not new! Both answers are right; the problem is the problem. 

 

See this incredibly reliable source:

http://knowyourmeme.com/memes/48293

 

(Side note: Even though technically both are correct, if we're voting...throw me solidly in the 58 camp.)

Edited August 2, 2015 by Josiah

[Laniston]

It's the second answer. The parenthesis only matter if there is something going on inside them. If you change (3) to (3×1×1×1×1×1×1×1×1) it might be more fun but the answer is the same.

the first answer would have to be 6^2 ÷ (2×3) + 4

Edited August 2, 2015 by Laniston

[Maureen]

There are math rules for the order of calculating.

 

Check out the link.

 

http://www.mathgoodies.com/lessons/vol7/order_operations.html

 

M. 

[Anddenex]

This is why I have a hard time with math.  I was taught you do the multiplication of the parenthesis first and then go left to right to finish the answer performing multiplication and division first.  So in this case the answer as I was taught would be #1.

 

What Maureen provided is the rule is left to right, excluding the parentheses (unless they are encapsulated within parentheses (2 x 3) vs. 2(3) ) so #2 would be the correct answer.  

 

As for me, if we want something common then don't put 2(3) because as for me this groups the two and three to be accomplished first, where as 2 x 3 separates them in a longer equation.  I don't see much difference between 2(3) and (2x3), both are grouped.  That is just me though.

[Anddenex]

I just had my son perform this math problem and he said "10" right off the bat.  Then I showed him the other way and he said "Oh, I can see why they did it that way."  He grouped 2(3).  

[cdowis]

In the democratic, let's vote on it, spirit, I will add my vote.

 

As someone said, "Be sure to vote, and vote often."

[MrShorty]

As for me, if we want something common then don't put 2(3) because as for me this groups the two and three to be accomplished first, where as 2 x 3 separates them in a longer equation. I don't see much difference between 2(3) and (2x3), both are grouped. That is just me though.

Going through the references in Josiah's post (#10) was interesting. In some circles, they call this form of the notation "implied multiplication", and some circles like to say that implied multiplication should be done first (see Wikipedia's reference to the journal "Physical Review" that explicitly states that implied multiplication has higher precedence under order of operations https://en.wikipedia.org/wiki/Order_of_operations ).

 

It seems that, with these kind of problems, the main concern is how to treat this "implied multiplication" type notation. It seems that many (maybe a majority) want this to be treated the same as explicit multiplication, but this convention is not universally accepted. This is where I think it is important that the instructor needs to be clear how they want to treat this before declaring one variation right or wrong.

[Jamie123]

I agree the question is badly expressed, but strict application of the rules of arithmetic make the answer 58.

 

When I was at school we were always taught the acrostic BEDMAS:

 

Brackets: There is only a 3 inside the bracket so nothing changes

Exponentials: 6^2=36

Division:36/2=18

Multiplication: 18(3)=54

Addition: 54+4=58

Subtraction: There is none so the answer is 58

 

If you wanted the answer to be 10, the correct way of writing it would be 6^2/(2x3)+4: The brackets around 2x3 forces that calculation to be performed first so 36/6=6 and 6+4=10. 

 

This is "grammar" of arithmetic, but very often the rules are broken - even by people who write physics textbooks! How often (I'm talking to physicists and engineers now) have you seen Coulomb's law written Q1 Q2/4pi e0 r^2?

 

P.S. - I wrote this a little prematurely before I read MrShorty's response above. Now I have, I wonder if the expression of Coulomb's law is an example of implied multiplication having a higher priority than division - rather than plain sloppiness (as I had hitherto always assumed). Food for thought - if this is true perhaps we should stop teaching children about BEDMAS.

Edited August 2, 2015 by Jamie123

[Urstadt]

A comrade on a popular Linux forum was able to explain to me, canonically and intellectually, how this problem truly works out. He said: "It's a question of operator precedence so it really boils down to the order of the multiplication and division. The 'raise to the power of 2' is done first and the 'plus 4' is done last. So there's no question about those. That means the question really is what '36 / 2 * 3' evaluates to. And since multiplication and division are the same priority, languages are going to go left to right. Meaning the division is first."

He added, "It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse). Which would turn the math in question to, '36 * (1/2) * 3 -OR- 36 * 0.5 * 3.' This can now easily be worked out to 58." ----> 36 * 0.5 * 3 + 4 = 58 (Moving left to right)

[Guest]

Ugh.  Math in the Philippines (including computer programming) teaches PEMDAS.  Multiply first then Divide.  So, the answer is 10 in the Philippines.

 

Note on the Parenthesis... the expression INSIDE the parenthesis takes precedence.  Anything outside of the Parenthesis - including the 2 in the OP's function - goes to the EMDAS part of PEMDAS.

 

So, 60% of the answer matches mathematics taught in Asia.

 

So, here goes - the order of precedence is like the Metric system.  America just has to have their own thing. 

Edited August 3, 2015 by anatess

[Jamie123]

Ugh.  Math in the Philippines (including computer programming) teaches PEMDAS.  Multiply first then Divide.  So, the answer is 10 in the Philippines.

 

Note on the Parenthesis... the expression INSIDE the parenthesis takes precedence.  Anything outside of the Parenthesis - including the 2 in the OP's function - goes to the EMDAS part of PEMDAS.

 

So, 60% of the answer matches mathematics taught in Asia.

 

So, here goes - the order of precedence is like the Metric system.  America just has to have their own thing. 

At least you don't do the adding/subtracting first!

 

A few years ago, there was a TV quiz in the UK called "Are You Smarter than a 10 Year Old" in which adults were pitted against 10-year-old kids answering questions set by teachers of 10-year-olds. The quiz master was Noel Edmonds.

 

On one show, a question was "What is 5 + 3 x 0?" The adult answered something like 15, and was pooh-poohed by Noel Edmonds with a patronizing "anything multiplied by zero is zero!" The 10-year-old did get 0 and was awarded the point.

 

Now the adult got it wrong anyway, but that didn't stop hordes of mathematicians barraging the TV company with complaints. The teacher who set the question issued a clarification that "children of 10 are taught to do their sums left to right, so 5x3=15, and 15x0=0."

 

So perhaps the show should have been renamed "Do You Do Math the Same Way as a 10 Year Old"!

 

P.S. I was schooled here in the UK and I was taught BEDMAS, so its not just the US that likes to be different. We are not fully metricated here either. We are more metricated than the US; for example we buy our timber in centimetres and our fuel in litres, but still use miles and m.p.h. on the roads and buy our milk and beer by the pint. (Though a UK pint is not quite the same as a US pint.) When a friend from the US came to visit me a few years ago she was both surprised and delighted to learn that we use miles here; everyone had told her that "Europe uses kilometres". (This of course depends on whether you consider Great Britain to be part of Europe: politically it is, but culturally we have much more in common with America.)

Edited August 4, 2015 by Jamie123