Math Prof answers 6÷2(1+2) = ? once and for all ***Viral Math Problem***

lol, am I really doing this? Ok, fine. There is a ***viral math problem*** about, uh, order of operations. You know, #BEDMAS or #PEMDAS. The most common form is 6/2(1+2) but it also shows up as 60/5(7-5) and other equivalent forms. What is the correct answer explained by a math prof? Sorry, I don't care. But I'm happy to share a few thoughts on why I think this issue repeatedly going viral says some things about societal views of mathematics.

MY VECTOR CALCULUS PLAYLIST:

OTHER COURSE PLAYLISTS:

OTHER PLAYLISTS:
► Learning Math Series
►Cool Math Series:

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

SOCIALS:

[DrTrefor]

Ok, you ACTUALLY want my answer? I can't just clickbait you all and not tell you which I ACTUALLY prefer? OK fine, but I can see from the comments I'm going to upset a lot of you:D If I wrote this type of thing on the board, my natural inclination is to write division as a big diagonal dash instead that lumps the 2(1+2) on the bottom. That is, when I take this algebraic string of symbols and write it out - without using any brackets - the way I would write typical calculus expressions in my classes, then I would habitually write it in a way that use spatial relationships that interpret it as being 1. If I wanted it to be 9 I'd be explicit and put brackets around the (6/2), when writing on the board. Using spatial relationships (i.e. not a strict left-to-right application of BEDMAS) is extremely common in math, it's just that normally you don't have as your starting part a character string like this because, as I say in the video, the most important part is to be explicit about what you mean when there is a possibility of ambiguity!

[AnthonyOliverio]

If coding has taught me anything, just put parentheses around everything.

[GanonTEK]

I'd easily give this video a 6÷2(1+2) out of 10

[CeceNorman]

I'm 28 years old and just now learning I was taught PEMDAS wrong. For me it wasn't the parentheses that were the issue. Every math teacher I've had said you have to do the multiplication before division. I was never taught that they were on the same level, and we could just do left to right. If I did, they said the answer was wrong.

[AtomicExtremophile]

In my early years I was taught that the number preceding the bracket was part of the bracket - so 2(1+2) = (2*1) + (2 * 2) = 2 + 4 = 6. This was because I was taught algebraically that a(b+ c) has to have the brackets removed, so this becomes ab + ac.

[DarinBrownSJDCMath]

As another math ph.d. myself, my answer is simply, "I would NEVER write such an expression. And I don't think most mathematicians would write such an expression, either."

[jayjpepedreamer]

As a civil engineer, my instinct is to change that devision sign into a diagonal slash and get the answer 1 too. 😅

[Sindraug]

My understanding is that "multiplication by juxtaposition" is a separate step in the Order of Operations that comes before the "multiplication and division" step, and PEMDAS leaves it out for some reason; and that mathematicians, engineers, anyone who does math for a living, does the juxtaposition first and would solve the problem in question as 1. We really just need to clear this up by changing PEMDAS to PEJMDAS.

[JosephWood-izmi]

Beware Excel users!
In Excel:
=6/2*(1+2) shows 9
=6/(2*(1+2)) shows 1
I'm a retired Design Engineer and used Excel for repetitive calculations sometimes. The extensive use of brackets is good insurance. If you use Excel do some random test calculations by hand.
I was educated in the UK mid-20th century. We were taught BlEss My Dear Aunt Sally, not BEDMAS. Or PEMDAS. All the same thing really.
In my opinion brackets/parentheses generally solve most problems.
I went through almost 50 years of work using mathematics in engineering and can't remember ever having to debate simple arithmetic rules until Youtube came along making me doubt my reason for living.
BTW. My answer is 1.

[kobusswart]

As a computer engineer, my instinct is to think of the 2(1+2) as similar to (1x+2x) which is "simplified" to x(1+2) and more clearly written as 6/(2(1+2)) = 1 - Rather use many brackets to provide clarity than leave the next engineer pondering what you meant

[yourmomsfilms]

So basically, both answers are correct. It's the question that's wrong. Just a sloppy set up

[nsn]

The correct answer is that YOU NEVER FRAME AN AMBIGUOUS EQUATION LIKE THAT. YOU HAVE PARENTHESES. USE THEM!!

THE EQUATION DOES NOT NEED TO BE AMBIGUOUS AND SHOULD NOT BE WRITTEN THIS WAY.

[manzerm]

I think the confusing part is the use of the parenthesis without the explicit * sign, so the problem is not 6÷2*(1+2) which would unambiguously be 9, given BODMAS and L to R execution. To examine further, , let us put (1+2) as x, so the expression is 6÷2x which is not the same as 6÷2*x. Although we normally think of 2x as 2*x but in the context of 6÷2x, 2x would mean 6 and the answer would be 1. I do think the expression is ambiguous and the author must rewrite it as (6÷2)(1+2) if he wants 9 to be the answer.

[carlhartzell]

Very happy to see this nonsense described as a language problem and not a math problem. And I know my hard-science colleagues would throw a fit at the comparison to soft science; but when something is ambiguous in the English language the sentence is written in a different way. Thanks for the explanation that the mathematical expression should simply be written in a different way as well.

[KevinKuo]

I agree. This controversy shows that society thinks of mathematics as a machine, full of operations and devoid of creativity. When in fact it is one of the most creative and beautiful fields, and requires extreme levels of ingenuity, creativity, and abstract thinking.

[Ligierthegreensun]

Trying to explain this to anyone who just does math by rote is an exercise in losing brain cells. They furiously exclaim that their way is the only way to interpret the expression.

[BernardGreenberg]

This is exactly right.

Don't forget another use of parentheses: f(5) = 25. Is f equal to 5, or any number of an infinite set of functions whose value is 25 at 5? These are notation jokes. Bravo for giving the "right answer"!

[remainedanonymous]

Sir.... You have solved a war in my house. Not in the way you think! You explained an issue with how my parents communicated with me in general! I did math differently with my step dad and how you explained the 2 differences explained to my logic prone step dad how I function and learned as a creative individual.
Thank you.

[maxxiong]

Argument 2 wins for me, because of this: how you rewrite 1/f(1+2) as a fraction should not depend on whether f is a function or a number.

[davidhuber]

A zillion years ago when I actually did math, I had an RPN (reverse polish notation) calculator. I think using both helped solidify the relationships in my head. At the time I really thought RPN was superior, but had limitations. You had to think to decide which order to type things in. This thinking gelled the thought process of how the numbers related to each other.
I think many math students could benefit from learning RPN as a side project.
I would often do a problem with both, and if my answers disagreed, it let me know that I had some more thinking to do.
I really like how you described this as an English communication problem. Bravo.