A seemingly basic PEMDAS problem...

Question

There's one of those meme-type images posted on Facebook with the equation 6/2(1+2), challenging you to solve it. So, parenthesis first, 1+2=3. Then, multiplication and division proceed left to right, 6/2=3, then 3*3=9. Or so I think...

Most responders have posted the answer as being 1, due to seemingly misevaluating the 2*3 first. I went to the mathway.com equation solver to check, but it rearranges the equation as...

  6
______
2(1+2)

...and gives me the answer as 1. What gives?

score 6 · Answer 1 · answered Apr 18 '14 at 14:48

Just because "most" responders answer "$1$" doesn't mean you're wrong. They are implicitly bracketing the whole of $[2(1 + 2)]$ when arriving at $1$.

Your answer is consistent with PEDMAS + left-to-right evaluation, so I'd suggest you should be proud of "sticking to the rules."

The question itself (since it's floating around FACEBOOK) is designed (in troll-like fashion) to create a stir and get folks arguing over the correct result and/or get them second-guessing what their answers. Anyone serious about testing users arithmetic skills would have/should have erased the inevitable ambiguity by using brackets, to rule out such disagreeing responses.

Hakim · Answer 2 · 2014-04-18T14:54:32.717

1

There's a difference between $$\dfrac{6}{2}(1+2)=9$$ and $$\dfrac{6}{2(1+2)}=1.$$ The better is to put parenthesis around like this: $(6)/(2(1+2))$. And remember, you will never encounter such type of problems if you write everything using concise $\TeX$. ;-)

edited Apr 18 '14 at 14:54

answered Apr 18 '14 at 14:42

Hakim

10,213

Err, shouldn't the second equation evaluate to 1? – Bigbio2002 Apr 18 '14 at 14:44
@Bigbio2002 Thanks, fixed. :p I should stop playing Fifa and writing answers on SE at the same time. – Hakim Apr 18 '14 at 14:45

score 0 · Answer 3 · answered Apr 18 '14 at 14:42

I Think the most sensible think to do here is ask the person who wrote this ambiguous question.

However if that is not an option I would do first the division and then the multiplication, since some teachers tell you operations with the same hierarchy should be done in the order they are listed.

score 0 · Answer 4 · answered Apr 18 '14 at 15:51

0

It is clearly the answer is 9. It is an illegal math move to obtain 1. Once and for all, the answer is 9.

answered Apr 18 '14 at 15:51

Anastasiya-Romanova 秀

19,345

Why is it illegal math move to obtain 1? (No, am not asking this. This could be the reason of the downvote. I am doin undergrad and I never read PEDMAS, BEDMAS or BODMAS or whatever it is. But I know most of the computers give division higher priority than multiplication. they don't use brackets. They use Polish notation to save memory. They convert user entered string into polish notation by using the priority algorithms) – user103816 Jun 04 '14 at 12:13
@user31782 Using PEMDAS, we do the parentheses first, so $6/2(3)$, the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it such as: $6/2(3)=(6)/(2)(3)$. Because MD (multiplication and division) are interchangeable, we work from left to right, so $(6)/(2)=3$ and $(3)(3)=9$.
Just because something is implied rather than written does not give it any special rank in the order of operations.
– Anastasiya-Romanova 秀 Jun 05 '14 at 08:34

A seemingly basic PEMDAS problem...

4 Answers4