I don’t think I ever used a divide symbol like that beyond elementary school. In practice always use fraction style notation for division because it’s not ambiguous or a gotcha.
SBA #119 maths
Submitted 3 weeks ago by agent_nycto@lemmy.world to [deleted]
https://lemmy.world/pictrs/image/d1323e05-5526-4cf3-bbf7-f41c35afe0d5.jpeg
Comments
pennomi@lemmy.world 3 weeks ago
neatchee@piefed.social 3 weeks ago
This is the correct answer and it drives me crazy how often this comes up.
As another user commented, division and subtraction are just syntactic flavor for multiplication and addition, respectively. Division is a specific type of multiplication. Subtraction is a specific type of addition.
And so there is a reason mathematicians do not use the division symbol (➗): it is ambiguous as to which of the following terms are in the divisor and which are part of the next non-divisor term.
In other words, the equation as written is a lossy representation of whatever actual equation is being described.
tl;dr: the equation as written provides insufficient information to determine the correct order of operations. It is ambiguous notation and should not be used.
Sadbutdru@sopuli.xyz 2 weeks ago
division and subtraction are just syntactic flavor for multiplication and addition
Can you tell me a bit more about how you mean this? I searched a bit but only basic primary school level resources about the relationship between addition and subtraction came up.
Do you mean like subtraction is just adding a negative number, and division is just multiplication by the inverse of a number? In that case I don’t really see how it simplifies things much because negatives and inverses still need as much definition. Or are you talking about bit-wise operations like a computer would use to do these things?
otter@lemmy.ca 3 weeks ago
Yup, I found an old comment of mine but unfortunately that post was deleted. The numbers are different but its the same riddle
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
AHemlocksLie@lemmy.zip 2 weeks ago
The P in PEMDAS just means resolve what’s inside the parentheses first. After that, it’s just simple multiplication with adjacent terms, and multiplication and division happen together left to right.
6÷2(1+2)
6÷2(3)
3(3)
9
mic_check_one_two@lemmy.dbzer0.com 2 weeks ago
This is actually a generational thing. Millennials were taught “PEMDAS”:
- Parenthesis
- Exponent
- Multiplication
- Division
- Addition
- Subtraction
But younger generations have been taught “BEDMAS” instead:
- Brackets
- Exponent
- Division
- Multiplication
- Addition
- Subtraction
Notably, Division and Multiplication are swapped on PEMDAS and BEDMAS, to make this “both happen at the same time” more straightforward. But that only applies if the entire operation can happen at the same time.
For instance, let’s say
6/2(3)compared to6÷2(3). At first glance, they both appear to be the same operation. But in the former, the6dividend would be over the entire2(3)divisor. Which means you would need to simplify the divisor (by resolving the multiplication of2•3) before you divide. So the former would simplify to6/6=1, while the latter would divide first and become3(3)=9.Technically, if you wanted to be completely clear, you would write it using multiple parenthesis as needed. For instance, you would write it as either:
(6÷2)(3)=9or6÷(2(3))=1to avoid the ambiguity. Then it wouldn’t matter if you’re using PEMDAS or BEDMAS.AHemlocksLie@lemmy.zip 2 weeks ago
But in the former, the
6dividend would be over the entire2(3)divisor.I have never heard of or seen an example of anyone using / and ÷ in different ways. If you want multiple terms in your divisor, either write it as a large fraction with all relevant terms in the dividend or divisor, or use parentheses. This just seems like sloppy notation to me.
Mistic@lemmy.world 2 weeks ago
Usually, no sign before the bracket means juxtaposition.
So 2(1+2) is really (2+4)
Compare 2/2x and 2/2*x where x is (1+2)
The first is 2/(2+4)=1/3, the second is (2/2)*(1+2)=3
Also, there’s no real rule about solving left to right due to associative and commutative properties: 123 = 1*(23) = (12)3 = 312 = 21*3 = 6
rapchee@lemmy.world 2 weeks ago
wiuld you say the same thing if the division was written out like a line under 2(3) and under that 6
idk how this’ll come out but something like this:
2(1+2)6AHemlocksLie@lemmy.zip 2 weeks ago
In that case, I’d say the answer is 1. Top and bottom are each resolved to the fullest extent possible before dividing top by bottom. It’s equivalent to (top)÷(bottom), but it’s clearer and preferable if you can easily format that way in my opinion, just harder on a computer.
Reyali@lemmy.world 2 weeks ago
I think that’s why people are complaining about the division sign.
It’s been decades since I took a math class so I am definitely not the right person to explain things, but I am using technology to confirm my understanding of the various notations:
So yeah, if you put 6 over a denominator of 2(1+2), the answer is different (1) because the equation is different. But if you write it out literally, it would be 6 over 2 times (1+2).
What you wrote swapped the denominator to make it 2(1+2)÷6, which will always be 1.
HeHoXa@lemmy.zip 3 weeks ago
The ÷ symbol is a bane of mankind
YiddishMcSquidish@lemmy.today 3 weeks ago
I’m my head cannon, I imagine it as a /. Where the left is the top of a fraction, and the right the bottom. This only works in very simple equations though.
DaleGribble88@programming.dev 2 weeks ago
That’s actually what the dots represent, values in a ratio when written in a sensible notation
remon@ani.social 3 weeks ago
Well, Patrick IS an idiot … so it checks out?
agent_nycto@lemmy.world 3 weeks ago
It is one though, you gotta do multiplication first
LORDSMEGMA@sh.itjust.works 3 weeks ago
No. After you do the parentheses, multiplication and division are done left to right.
ChairmanMeow@programming.dev 3 weeks ago
It can be both depending on how you handle operator precendence.
PEMDAS definitely doesn’t result in 1, but in 9, since under PEMDAS multiplication and division have the same priority (and thus should resolve left-to-right). So, you should resolve to 9 (6/2(2+1) => 6/2(3) => 6/23 => 33 => 9).
However, there’s also PEJMDAS, which suggests that implied multiplication has an operator precedence greater than regular multiplication/division (J for Juxtaposition). This version says you should do 6/2(2+1) => 6/(22 + 21) => 6/(4+2) => 6/6 => 1.
The issue is that there is no universal agreement on which is correct. Most textbooks don’t even use the / operator, but instead rely on writing out the full fraction like ⁶⁄₂₍₂₊₁₎ or ⁶⁄₂(2+1). This removes any ambiguity there might be, and thus they don’t touch on which one is actually correct.
Most (but not all) calculators these days will treat implied multiplication the same as regular multiplication, so you get 9 in the given example. Most programming languages do the same, or outright disallow implied multiplication because it only confuses people. Academics won’t ever use the ambiguous notation and will make sure to remove any ambiguity by either adding parentheses or using a notation like ⁶⁄₂₍₂₊₁₎, which makes things much more clear.
Neither 9 nor 1 is wrong, the question is just stupid.
remon@ani.social 3 weeks ago
No you don’t, decision is on the left, so it comes first
probablymissing@lemmy.world 3 weeks ago
KC_Royalz@lemmy.world 3 weeks ago
I hate math, my teacher taught is as first in last out and to this day I still get confused. The answer is 9 right?
remon@ani.social 3 weeks ago
Yes, at least by the most common agreed on convention. Almost any mathematician, programming language, search engine or spreadsheet software will say it’s 9. It is for all intents and purposes the right answer.
yermaw@sh.itjust.works 3 weeks ago
We discovered mathematics, the unflinching language of reality itself, and then managed to make it ambiguous.
If i was an alien id give humanity a big hair-tussle like a dog.
jambudz@lemmy.zip 2 weeks ago
Use unambiguous notation
Clent@lemmy.dbzer0.com 3 weeks ago
No mathematician would write an ambiguous equation like that.
People who argued over these are displaying an incorrect memory of a math education that is simply not a good look.
Division and multiplication have the same precedence, equations are evaluated left to right, so equation is divide then multiple. Division and subtraction are syntactic sugar for multiplication and addition.
These are fun little experiments showing how social media makes people more stupider and how proud the ignorant behave amongst themselves.
DaleGribble88@programming.dev 2 weeks ago
It also pulls double duty by making math look hard, ambiguous, and untrustworthy. Anti education, poor reasoning skills, and an implicit distrust of mathematical models and statistics.
FishFace@piefed.social 3 weeks ago
It’s not unheard of to find, in an exercise, “Simplify 4x²/2x”. The answer is almost guaranteed to be 2x. (There are some interesting exceptions, but they’re not really important). More often such a question would use fraction notation, but not always, to prevent exercises taking up too much space.
What’s going on is that the multiplication of the 2 and x, because they are written without a symbol in between, is seen as morally being something you should do first.
And in such exercise contexts, it’s unlikely to be misunderstood. But it’d still be better to be clear about it.
Sadbutdru@sopuli.xyz 2 weeks ago
Division and subtraction are syntactic sugar for multiplication and addition.
Can you tell me a bit more about how you mean this? I searched a bit but only basic primary school level resources about the relationship between addition and subtraction came up.
Do you mean like subtraction is just adding a negative number, and division is just multiplication by the inverse of a number? In that case I don’t really see how it simplifies things much because negatives and inverses still need as much definition. Or are you talking about bit-wise operations like a computer would use to do these things?
FishFace@piefed.social 2 weeks ago
When you set up arithmetic from absolute first principles you typically say that there is an operation called addition, an operation called multiplication, that they are related by the distributive law, and then you assert that there are identities for these operations, which do nothing: adding zero does nothing, and multiplying by one does nothing, so zero and one are the additive and multiplicative identities.
Next you add that each element has an inverse under these operations. The additive inverse of a number is its negative, so the inverse of 2 is -2. The multiplicative inverse of a number is its reciprocal. The defining feature is that the inverses cancel the operation leaving just the identity, so 2 + -2 = 0, and 3 × 1/3 = 1. The exception is that 0 does not have a multiplicative inverse.
With this, the operation of subtraction is defined in terms of addition and additive inverse, and division is defined in terms of multiplication and multiplicative inverse.
Saying that one is “syntactic sugar” for the other is standard in higher mathematics, but of course you could go through the same procedure starting with subtraction and division, and defining inverses in terms of those operations - the result is no different. The reason starting with inverses is preferred though is because there are lots of structures which have an operation and an identity for it, in which you can ask the question “are there inverses” because inverses are defined purely in terms of an operation and its identity. You can’t ask the question “can you divide in this structure” if the only way to even have a concept of division is to start with one.
This topic is the beginnings of abstract algebra which starts with group theory and builds from there.
Clent@lemmy.dbzer0.com 2 weeks ago
But hard to write this with the limitations of text but essentially it can be written as multiplication of fractions.
2 ÷ 2 ÷ 2 ÷ 2
2 x ½ x ½ x ½
Personally, I think the second form is easier to visualize and reason about, it can also can be simplified to use an exponent.
janakali@lemmy.4d2.org 2 weeks ago
it’s ambigious
AHemlocksLie@lemmy.zip 2 weeks ago
Only if you forget that multiplication happens left to right and that a(b) is simply a different way to write a×b with no other extra steps or considerations. The P in PEMDAS just means resolve what’s INSIDE the parentheses first.
janakali@lemmy.4d2.org 2 weeks ago
That only works if everyone agrees with you, which is clearly not true. In academic math, there’s a thing called juxtaposition. It mostly exists because math people are lazy, so instead of putting parentheses around statement e.g.
5+(2*x)they’ll just write5+2x.This is fine as long as you know the context of that expression. If you take it out of the context and just ask any person what is the right order of operations - it becomes ambiguous. Because some people know PEMDAS. And other people know that PEMDAS is just a simplification for middle school, when real math notation is messy, non-standard and requires a lot of local domain knowledge.
Noodle07@lemmy.world 2 weeks ago
I was taught not to write like this so we dont have to deal with this shit 😊
TotallyWorthLife@lemmy.world 2 weeks ago
I was taught to do
- Brackets
- Division and multiplication left to right
- Addition and subtraction left to right
FishFace@piefed.social 3 weeks ago
Uh oh, here we go! Before the Fediverse’s favourite mathematical charlatan comes to play, let’s lay out a few facts:
- This is an unusual way of writing down this expression: you would not normally mix in-line division (written with ÷) and multiplication written without a symbol. It’s written this way on social media to for engagement bait.
- Because of this, a perfectly valid reply is to ask “can you put in some brackets to make it clear” :)
- A strict, standard reading of the order-of-operations as abbreviated by PEMDAS, BODMAS, etc, is to perform multiplication and division in the order that they occur. This would mean the evaluation goes like this:
- 6÷2(1+2)
- Perform addition inside the brackets: 6÷2(3)
- Perform the first multiplication or division: 3(3)
- Perform the remaining multiplication: 9
- Occasionally, PEMDAS is interpreted as indicating that multiplication must be done first because the M occurs before the D. This is not usually how it is taught, but rarely it happens. This would give you 1 but, to be clear, in most places this is wrong. I myself was taught BODMAS and, in fact, do division first in all circumstances.
- Much more commonly, though, the actual practical order in which mathematicians, teachers and students all evaluate expressions is a little different, in that it evaluates symbol-less multiplication (also known as “juxtaposition” which just means “writing two things next to each other” or, in discussions about this topic in particular, “implicit multiplication") before anything else. This is done because writing two things next to each other creates a tightly-bound visual unit.
It’s rare for this last point to be mentioned explicitly as a violation of the order-of-operations. It usually only becomes relevant well after those conventions are spelled out (which is typically done in late primary school or early high school) after children start learning algebra and how to write algebraic expressions: using letters to represent unknown quantities, omitting the × symbol. Exam boards and textbooks are usually quite careful to avoid writing problems in which this unstated rule actually matters.
It’s important to realise that the order in which we evaluate a mathematical expression is a matter of convention. After establishing how to add, multiply, subtract or divide two numbers, it is a separate question which operations should happen first when more than one is written together. This is why we need to teach students the order of operations - they can’t just work it out themselves. Having said that, it certainly makes a lot more sense to do multiplication before addition, and exponentiation before multiplication, because each of these operations is (typically: you can define them in different ways if you’re a masochist) defined in terms of the previous one. This means that if you have an expression involving all three, and you first turn all the exponentiation into multiplications, you are left with a simpler expression that means the same thing. This only happens if evaluating exponentiation is the first thing you’re supposed to do. However, it would be a mistake to think this means that there is any mathematical necessity about this: what a sequence of squiggles on paper means is entirely up to the people reading and writing the squiggles; as long as they agree, the person reading the squiggles will get the same answer as intended by the person writing them. There’s a good, lengthy write-up here
This means that while what I was taught is “wrong” according to how it is usually taught (including today in the same country), this wrongness is better understood mathematically as “unusual” - something that needs to be worked out by communication and consensus rather than by dictating one right and another wrong.
You do get some people with very strong opinions about this, which is not always correlated with their actual knowledge. If the aforementioned charlatan turns up, I’ll explain…
justOnePersistentKbinPlease@fedia.io 3 weeks ago
The US education system is in such tatters that what they teach anymore is largely irrelevant to the rest of the world.
FishFace@piefed.social 3 weeks ago
Not sure where that comes in…
panda_abyss@lemmy.ca 3 weeks ago
It’s ambiguous either this resolves to
6 / (2(1+2))or(6/2) * (1+2), and therefore both answers must be accepted.By convention, the division sign is not to be used in equations. It is not a standard operation.
It is may be used for representing the operation of division as a symbol, but never as an operator itself.
Anyone using the division sign is using it entirely for trolling purposes.
FishFace@piefed.social 3 weeks ago
This is not true. It typically falls out of use in high school and rarely shows up after, but it’s not like it’s banned or anything like that.
panda_abyss@lemmy.ca 2 weeks ago
It’s not in the modern standard for notation. I never once saw it used in university. I even had prof who typed their homework on a typewriter and he didn’t use it (he actually typeset everything pretty nicely).
0ops@piefed.zip 3 weeks ago
I wouldn’t say that it’s ambiguous, you’ll only get one answer evaluating in PE(M|D)(A|S) order left to right (your second one), enter it into any calculator and you should get 9.
For sure, how it’s written is unconventional and easy to misread if I’m in a hurry, but honestly that’s an issue of misleading typography, not ambiguous notation. The ÷ symbol takes a lot of space (plus it looks sort of like a +) and the implicit multiplication against the parentheses doesn’t, so when I read too fast my brain might instinctively calculate each side of the division first because they sort of look like two terms. But doing that violates the left-to-right rule.
Mistic@lemmy.world 2 weeks ago
enter it into any calculator and you should get 9
Have you tried it, though? My Casio says it’s 1
That’s because it treats 2(1+2) as 2x and not 2*x
That’s called juxtaposition and is the reason why people find this notation ambiguous. Some people account for it, some not. Same with calculators. The scientific ones are most likely to give you an answer of 1
Hiro8811@lemmy.world 2 weeks ago
Huh why would you add additional brackets? It’s simply 6:2*(1+2) then you solve it in order since division and multiplication are same level of operation.
AdolfSchmitler@lemmy.world 2 weeks ago
Oh christ the math memes are leaking from facebook
SaltyIceteaMaker@lemmy.ml 2 weeks ago
ChaoticNeutralCzech@feddit.org 2 weeks ago
CASIO calculators say 1, and I think it’s more intuitive with “÷2π” being equivalent to “÷(2×π)” rather than “÷2×π”. It took me a while to figure out why my results were almost but not quite one order of magnitude wrong after I was forced to switch to TI.
morphballganon@mtgzone.com 2 weeks ago
you still go left to right
Unless there’s implied multiplication, which there is. Then you do that before the explicit division.
HasturInYellow@lemmy.world 2 weeks ago
Incorrect. Multiplication and division happen in whichever order they appear left to right. They have the same priority.
tomi000@lemmy.world 2 weeks ago
Who taught you that? They shouldnt have.
phaneuf@lemmy.zip 2 weeks ago
Look at you looking so confidently incorrect. Embarrassing.
brown567@sh.itjust.works 2 weeks ago
6 2 ÷ 1 2 + ×
Or 6 2 1 2 + × ÷ for Patrick
ryathal@sh.itjust.works 3 weeks ago
Math should be taught with postix or reverse Polish notation. It removes this ambiguity as the order of operations is left to right.
FishFace@piefed.social 3 weeks ago
But it’s not so great for polynomials and other more complicated expressions which you’re not just evaluating, but rather manipulating algebraically:
3 y × 3 ^ 4 y × 2 ^ + -2 y × + 3 +
kek_kecske_31@lemmy.world 3 weeks ago
This is pure braindeath for the 100th time still. We, mathematicians always come up with small abuse of notations to make life easier. No mathematician is like, this is the only way you could go you charlatan. That being said, write equations and formulas in a way that the people you wrote them for (even if yourself) will understand. That’s what matters. If the formula is ambigous for the intended reader, than it is a bad formula or the notations are not presented clearly enough.
akwd169@sh.itjust.works 3 weeks ago
They taught it to us in Ontario, Canada as BEDMAS where the B is brackets
AI_toothbrush@lemmy.zip 3 weeks ago
Guys, just use proper notation for devision, it clears up so much confusion.
vathecka@lemmy.radio 3 weeks ago
If I need to use anything other than p you need to rewrite the equation
kayohtie@pawb.social 2 weeks ago
The real answer is “what’s the fucking context for how these numbers are being used?”
If it’s “just as written on a test” I think asking for clarification on order would be accepted.
If it’s an actual context of some kind then that alone dictactes the way you solve it.
Can’t quickly come up with a word problem for this one though.
Buddahriffic@lemmy.world 2 weeks ago
I guess the joke is that it wasn’t an ambiguous expression in the first place and that pedmas/bedmas wasn’t the issue, or rather using just it here is the problem?
When you have multiplication expressed as numbers joined without a symbol, that takes precedence at the current layer, where layers are created using brackets, fraction symbols, superscript exponents and concatenated multiplies.
I’m not sure this resolves all ambiguity, but it simplifies the rule to just doing multiplication/division before addition/subtraction. It seems simple enough in my mind, so I’d need to see a counter example if it does break down.
Though I hate how mainstream math problems/puzzles always end up being an order of operations problem, which I’d argue isn’t even math but more of a metamath thing. If you’re using math to solve a real problem, the correct order of operations will be determined by logic, not any conventions.
Like if it takes you 5 seconds to get in your car and 12 seconds per km traveled, and 5 seconds to get out of your car, if you multiply the 10 seconds to get in or out by the distance, you’ll have a wrong answer. It’ll always be distance traveled in km times 12 seconds/km plus the 10 seconds, and the math works on the units as well as the numbers to show you did it in a way that makes sense.
GeorgimusPrime@lemmy.world 2 weeks ago
BODMAS
- Brackets
- Of
- Division
- Multiplication
- Addition
- Subtraction
ne0n@lemmy.world 2 weeks ago
I can’t tell if this is trolling or not, but O = Orders lol
CetaceanNeeded@lemmy.world 2 weeks ago
You’re right but when I was taught this in grade four we were taught Of, I guess Orders was probably a bit above 10 year Olds.
Mistic@lemmy.world 2 weeks ago
Let me just, ahem
1-2+3/(3+3)2+36/3 = 1-2+3/(3+3)2+16 = 1-2+3/(3+3)*2+6 = 7-2+3/(3+3)*2 = 7-2+3/(6+6) = 7-2+(1/2+1/2) = 5+(1/2+1/2) = 5+1=6
Mmm, yes, DMAMDSBA :P
Let’s just say BODMAS/PEMDAS isn’t all be-all end-all. They’re good, but there’s also better
Janx@piefed.social 3 weeks ago
It’s…a shitpost because Patrick and you are wrong?
cattywampas@lemmy.world 3 weeks ago
It’s 9 if you actually understand PEMDAS
Reyali@lemmy.world 3 weeks ago
I’m guessing confusion is coming from those taking PEMDAS literally as that order? Rather than PE(M|D)(A|S), like it’s supposed to be?
cattywampas@lemmy.world 3 weeks ago
It’s also convoluted by the notation of the multiplication. When it’s written like this, many assume that you need to resolve that term first since it involves parentheses.
FishFace@piefed.social 3 weeks ago
It’s also because writing multiplication without a symbol creates a tightly bound visual unit that is typically evaluated before other things. If you see an exercise like, “what is 4x²/2x” most people answer “2x” not “2x³”. But this convention is rarely taught explicitly, so it’s ripe for engagement bait.
purplemonkeymad@programming.dev 3 weeks ago
Well implicit multiplication would be done before the other operators anyway, but after exponents. Pemdas is incomplete.
BurntWits@sh.itjust.works 2 weeks ago
I was taught BEDMAS in school, so slightly different order. I was also taught that DM and AS are not specifically in that order, but rather left to right of the equation, in the same lesson. I’m not sure why some schools aren’t doing it that way.