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Yeah, nah, this equation is whack. Any mathemagician worth their salt doesn’t write an equation like this. This isn’t difficult math, it’s ambiguous and dumb.
Write it like:
8/[2(2+2)] or (8/2)(2+2)
problem solved.
This isn’t difficult math, it’s ambiguous and dumb.
All of these ragebait math posts are. It’s so shitty and obvious, but it always seems to work.
Because there are no parentheses around the first and last two, it should be assumed to be the latter, yeah?
I arrived at 1 prior to trying to understand how it could be 16…
As written, 8÷2… Is the same as 8/2… It would require those brackets/parentheses otherwise.
This is ambiguous because in other, simpler contexts, implicit multiplication is implied to take priority over non-implicit division. And that’s just usual convention, not a set rule.
If I write 1/2n, most likely it will be understood as 1/(2×n). While 1/2×n or 1÷2×n would be anyone’s guess. Again, 1/2n is not even a rule, just “convenient” and it “seems” like 2n is a block, but make that expression more complex with more operands and it’ll get confusing fast.
There is no correct interpretation of a random ambiguous expression, it’s pointless trying to find one.
“worth their salt”
I haven’t heard that in a while…
This is exactly why I’m an abuser of parentheses when left to my own devices.
For example when writing code, it doesn’t matter that the compiler acts as a strict system underlying it that may or may not conform to my expectations. I want the human reading the code to understand my intentions so I’m going to group things until it’s logically clear at a glance.
problem solved.
But you never solved the problem?
Who teaches orders of operation other than PEMDAS?
I think the confusion is in the way it’s displayed. The notation in the comic is ambiguous, where the division is shown as a symbol, while the multiplication is implied with the brackets, so some people see the question as
8/(2*(2+2))=1, while others see it as8/2*(2+2).For the later, my understanding is that multiplication and division actually have equal priority and are solved left to right (rather than an explicit order as PEDMAS and BEDMAS seem to suggest). So the second interpretation would give
8/2*(2+2)=8/2*(4)=4*4=16The reason this isn’t a problem more often is because
- math questions should be written unambiguously, using symbols everywhere and fraction bars
- in real life problems, there is a certain order in which you manipulate the numbers, and we can use correct notation (with an excessive number of brackets if needed) to keep it crystal clear
Also the (2+2) bit isn’t relevant to the confusion. We might as well replace it with 4 when discussing the problem. No one should be messing that bit upI’ve heard it both ways that in PEMDAS, it’s really more like P,E,MD,AS. As in, when you reach the multiplication and division steps, it’s assumed you do them together in written order, followed by addition and subtraction after.
And like you said, the real-world measurement will actually end up dictating the order, but if this distinction needed to be made, you would separate as necessary with more parentheses.
But also, all maths are commutative, so you can just mush all the numbers together using any means you desire and you’ll always get the right answer.
My math teachers all kicked me out because I was so advanced.
All maths is not communtative. Most of linear algebra and number systems above the complex numbers (i.e. quaternions and above) are not commutative.
But yes, all maths in most peoples everyday life is commutative.
Forgot my “/s,” but I’m happy to double down.
No, literally all maths is commutative. In fact, you can arbitrarily substitute any number with another number and get the right answer. See?
4+4=8
5+3=8
9+1=8Same for multiplication and sublimation. 5x2=8.
I could go on, but I’m pretty sure that I’ll injure myself.
Also the (2+2) bit isn’t relevant to the confusion.
The parentheses are what make people accept the missing multiplication symbol.
Right, good point
We were taught BEDMAS in Canada which has the division and multiplication switched. Which still equals one.
Addition / subtraction and multiplication / division are interchangeable, so that’s still functionally identical in all aspects.
PEJMDAS. Juxtaposition is a distinct stage.
Edit: This makes it consistent with
x = 2 + 2
y = 8 ÷ 2xI agree, which is why I don’t see why people are saying the answer is 16. You add in the parentheses, you multiply, then you divide. The answer is 1.
This left-to-right business linked below is complete nonsense when it comes to equations. That’s how westerners read books, but not how math is communicated. Am I that old? Like Mr. Incredible said, did they change math!?!
Input from a published Berkeley professor: PEMDAS does NOT cover this, it’s ambiguous and there’s no ‘correct’ answer
https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html
16
The green party has entered the chat.
Nope. One of those is just wrong. That symbol applies to the numbers around it, not to any random group of things you pick by taste.
And someone being proven objectively wrong has always led to an amicable resolution.
You’re right. I’m just saying that doesn’t matter.
Both are right, depending on who you ask:
most people see:
8 / 2 * (2+2) = 16math people see “juxtaposition” instead of multiplication, it has precedence over multiplication and division:
5 / 2a = 5 / (2 * a)Math notation just sucks and is not standard in general, everyone just tries to avoid ambiguity like in this equation.
The entire issue here stems from the division symbol, which is not taught well and is often confusing. Which is why we don’t use it as mathematicians
This is just another layer. Order in
8/2(2+2)is still not clear if you understand the division symbol correctly.https://en.wikipedia.org/wiki/Order_of_operations#Mixed_division_and_multiplication
I also find multiplication bothersome, so I don’t do it either.
That’s why everyone should learn Reverse Polish Notation. Then it’s either
8 2 / 2 2 + *or8 2 2 + 2 * /. Unambiguous, easy, superior.As much as I love my RPN calculators, that just looks awful. Maybe I’m just not used to it
¼ 4 *or8 4 2 * /‽Not sure why you got “worth reading” over mines.
I’m decent at math, versed in PEMDAS / BOMDAS, and confess that I arrived at 1 until I read this mathematician’s take on the topic: https://mindyourdecisions.com/blog/2019/07/31/what-is-8-÷-22-2-the-correct-answer-explained/ (hint: it’s as much about typography and changing interpretations as it is about math).
I am a strong believer in PEBKAC myself.
They seem to be saying that however a calculator would calculate it is ipso facto correct.
Which is odd because I had at least one, maybe more, teacher show us this as a reason not to blindly trust your calculator
Oops! That page can’t be found.
I can summarize: The equation is ambiguous, because there are two equally valid ways to interpret the relationship between the 2 and the parentheses. Pre-computer written math would have assumed that the 2(x) was a unit, as the 2 could be distributed across the parenthetical expression. With the advent of calculators and computers, equations written this way are executed left to right, and so the 8 ÷ 2 would go first, and then that result would be multiplied by the result of the parentheses.
It’s worth noting that both interpretations follow the PEMDAS rule, so such debates are irrelevant. It is a question of grouping terms and solving the holistic equation, vs solving step by step left to right.
The real solution is to shoot the person who wrote it, because they should have used more parens.
That’s odd. I tried the URL in a couple of different browsers and it loaded correctly. Anyone else have problems loading it?
The argument in that article is basically “Most calculators do it this way now, so that must be our convention to use, so 16 is the correct answer. Please ignore that this goes against the conventions established before calculators became transistorized.”
It’s 16 btw. Anyone saying anything else is just wrong. There is no interpretation in math.
Don’t be fooled by them writing long explanations. They’re still wrong.
BODMAS. 16.
$ python3 -c “print(8 / 2 * (2+2))”
16.0CASIO gives priority to implicit multiplication (without the × symbol) so it says 1, but TI doesn’t so it says 16. So if you get used to saving keypresses and shoddy notation, you might get surprised when the TI says that 1÷2π is 1.5708 and not 0.1592. Should have used a fraction (if supported) or brackets!
Also, my android phone calculator says 16
So for my intents and purposes, this is ambiguous and dumb but the answer is 16 :)
EDIT: I own a TI calculator
Neither interpretation is wrong.
PEMDAS (or whatever you call it) is not a law and makes no mention of implicit multiplication. My Casio calculators rates implicit multiplication higher than explicit multiplication and division by the way.
Here’s another ambiguity:
Is 2½ equal to 1 or 2.5?
Depending on how you enter it, my Casio calculator returns either.
- If you create a normal fraction and then put a number in front (by going left with the arrows) it will result in 1
- Only if you use the dedicated “fraction with number in front” button will it result in 2.5
8 / 2(2 + 2) = 8 / 4 + 4 = 2 + 4 = 6
Excuse me what
Hah, good joke yes
It’s obviously 11. What’s the controversy?
The implicit multiplication between the two and the summed twos takes precedence over the division operation. They are more tightly grouped.
That’s my thinking too. But apparently others don’t pick up on or agree with the implied grouping. So what, we need more parentheses like 8 / (2(2+2))? or just
8
2(2 + 2)
