6÷2(1+2)=???

This problem goes viral on the internet every now and then, so I was very glad to have an opportunity to explain it on the air. I didn't have very long to talk so that's why I gloss over a few details, but the overall point is still true: the (intentional) ambiguity of the mathematical statement is the real issue here. This is not really about order of operations; it's about the importance of clear communication, which is true of mathematics as much as in any other discipline.

[phosphylliteV]

Thank you Eddie, now whenever I see a math problem I can't solve I'll just write "Yes". Harvard, here I come!

[cheeseaddict]

The obvious answer is "5 ± 4"

[ryanstudham]

I strive to have this level of eloquence and patience.

[AbsoluteDementia]

6÷2(1+2)
Solve brackets
6÷2(3)
6÷2×3
Do division and multiplication from left to right
3×3
9

[sweepingtime]

This question might be ambiguous but it teaches us a very important lesson: order of operations is NOT ambiguous and the vast majority of applied math problems don't face this issue, yet in our haste to write equations we may end up confusing ourselves by writing them in an ambiguous way, and that's when mistakes happen.

[XgilPlay]

"I saw a man with a telescope" is the greatest example he could give

[subhapackian]

Anchor: 6÷2(1+2) = ????
Eddie Woo: It's similar to a sentence like 'I saw a man with a telescope'
Audience: We came for 1 answer and now we have two questions....🤯
Lol

[thobiem]

Apparently the real answer to this equation, is the friendships we made along the way.

[jzel]

If you set up the equation with a fraction bar instead of a division symbol, it gets rid of the ambiguity. That's why we don't use division symbols in calculations. It's always a fraction bar.

[Mngalahad]

news: so is it 1 or 9?
eddie: math is a social construct; it can be anything we want.

[raicyceprine]

That correlation to sentence "I see a man with a telescope" is such a good comparison.

It makes you view mathematics as a language just like any other language out there: english, chinese, french, computer language, and math language

[keurikeuri]

For students remember to pass an exam in school, regardless of what is right or wrong in your belief, you still have to know your teacher or whoever makes the exam's understanding in order to pass. You can follow your own belief when you became the teacher or be the boss just make sure it is based on actual facts. Unless you want a stressful time defending your answer for days.

[katerinapierce]

I'm kinda confused. Equation inside the brackets go first. 1+2 = 3. You have left 6:2x3. : and x are both equally in the order, but : stands before x, so : goes first. 6:2 = 3. You have left 3 x 3 which is 9. If the answer was 1 then it would be written like 6:(2(1+2)). At least this is what I learned at school. Order: Brackets, divide/multiply, plus/minus.

[johnwalker]

I feel like the purpose of problems like these is to demonstrate to students why conventions exist, whether they be expressional conventions like in mathematics, or grammatical conventions in written composition. Having a set of rules for how to express something helps to do away with potential ambiguities like this and reduce the chances for miscommunication or misinterpretation.

[WritingGeekNL]

This is simply why most mathematicians use fractions...

[unstabledefusion]

If you type 6/2(1+2) into WolframAlpha, it interprets it as (6/2)(1+2) and spits out 9, which makes sense. If the answer is supposed to be 1, it would be written as 6/(2(1+2)).

EDIT: To clarify my point, I'm thinking like a calculator. For example, if you type 6/2*3 into a calculator, it will say 9 and not 1 because there are no parentheses around the 2 and 3. It's the same as (6/2)*3.

Both yield the same answer. Even if you're not thinking like a calculator, you just use PEMDAS and therefore go left to right with the division and multiplication. First calculate 6/2, then multiply that result by 3 and you get 9.

Just type these things into a calculator to see for yourselves. It's really not ambiguous.

[yesno]

For those of you wondering how we get 1, it's due to something called "multiplication by juxtaposition", which means that we assume 2 or more terms put together indicates that we need to multiply them together first before we process other operations.
To give an example, if we say 6 ÷ 2x, we assume that u multiply 2 and x first, before dividing 6 with it. In other words, you're NOT suppose to have 6 ÷ 2, then × x.
This is the case with the question presented, where we assume (1+2) is the x, which means we need to multiple 2 with (1+2) first before we take 6 and divide by it. The only reason it's in a parentheses is because, you can't put 2 and 1+2 together directly without it looking like 21+2 instead of 2×(1+2).
Hope this clears things out, where I'm from, we never really learned pemdas or bodmas...

[denniskoppo]

I'm a substitute teacher and problems like this are frequently given on tests to evaluate understanding of the "order of operations". One of the weird things is that some calculators come up with different answers to those problems than others.

[ugochukwuudeh]

1 and 9 exist in a super position and cannot be determined until the equation is measured

[Dalinar_Kholin]

As someone who knows 6th grade math, I see this as an absolute win.






Edit 1: Damn ya'll need to stop arguing down there. It ain't that deep XD

Edit 2: Ya'll I told you to stop and you just heated it up like an oven