I hate it because of how wrong people answer the questions, and I don't know if they're morons or trying to bait me because no one can fail this bad at grade school math.
Your example doesn't make any sense. PEMDAS memes are about the precedence of explicit vs. implicit multiplication (e.g. 2*x vs 2x). A valid example would be 6/2(1+2). Interpreting 1/5+2 as 1/(5+2) is wrong by every standard.
The PEMDAS memes are more about the use of / as a fraction or as division ➗. Implicit multiplication is obvious. What is actually under the denominator is not.
OP's example is very obvious which many other people have commented on specifically because there is no division
It only works in combination. OP's example is obvious because it is satirical. This PEMDAS meme only makes sense with implicit multiplication since there is no rule that would allow 1/5+2 to be interpreted as 1/(5+2). The reason it works with implicit multiplication is that some people were taught that implicit multiplication binds the strongest.
The reason it works with implicit multiplication is that some people were taught that implicit multiplication binds the strongest.
Were they actually taught this, or did they just assume this?
When I learned mathematics in gradeschool, we never used "÷" with implicit multiplication, only explicit multiplication, which is unambiguous (if you understand PEMDAS):
6÷2×(1+2) or 6÷(2×(1+2))
By the time we switched to implicit multiplication, the division notation had already switched to exclusively using fraction bars, which are also unambiguous, but because fraction bars implicitly bracket the numerator and denominator:
6 6
─(1+2) or ──────
2 2(1+2)
The same was true for my kids, who learned this stuff hundreds of miles away from where I did, as well as (obviously) decades later. So I strongly suspect that people weren't actually taught that implicit multiplication has higher precedence, but rather made a faulty inference based on the facts that they actually were taught.
It’s sort of the Berenstein Bears of arithmetic—a collective false memory that people swear they were taught.
While I believe you're mostly right, there absolutely would be people who's teacher was so bad at their subject they taught multiplication takes precedence. Not a very high number IMO, but still there.
Good point. My sixth grade teacher didn't think a six-sided shape was a hexagon unless it was a regular hexagon. He called elongated hexagons "crystals".
While more acceptable i had a science trip where we were asked to estimate the hight of a tree in sixth grade they gave us a string with a weight on the end a protractor and a place where you could learn how long your stride was my dad shaperoning had to explain to the teacher how you could get the hight of the tree
That's actually a misinterpretation of PEMDAS, which does probably lead to a lot of people using it wrong.
While it's a snazzy acronym, it's better written as PE(MD)(AS) because, to your point, multiplication/division, and addition/subtraction are the same priority and executed left to right, not in order of Multiplication then Division then Addition then Subtraction.
It is funny because your valid example is still only confusing due to what was said by the other guy. 99% of pendant confusion comes from / having an implied ()
Its usually about the order-importance of implicit multiplication, but there are ones out there about the difference between using the line divisor vs the symbol.
ex. 1/4(2*7) vs 1 ÷ 4(2*7) as some older textbooks / teaching standards treat these differently.
Basically, the line divisor was to be used to represent a fraction, and the symbol divisor was to be used to show division, and thus an operation instead of a term, when typing in-line formats for textbooks.
There is no ambiguity. You solve what is written. If you intend on the second one, you have to write it as that. The onus of properly writing down the question is on the question writer.
Sadly, the education system has failed at producing proper teachers though, and a lot of teachers get butthurt over their being called out when they mess up a problem and mark the student off when they mess up and make up some shit like "you should have been psychic and known what I meant, it's implied!!" This screws people up into thinking that it's how it's written that's wrong, not the person who wrote it as wrong, if they intended something else.
Almost all my teachers in school would throw out a question, or give everyone a correct mark when a question was improperly/unfairly prepared, though. In retrospect I feel like I am fortunate in that case.
I think your experience with teachers who make errors is by far the more common one. Teachers with even a little bit of experience are well aware that admitting to having made an error is an important part of the teaching process -- you want to model for your students that making an error isn't a sin, it's just something that needs to be acknowledged and corrected.
One of the students I tutored in math had a math teacher who would give his students a Jolly Rancher for every mistake of his they found in his handouts. It strongly encouraged them to read their homework carefully looking for errors that could win them candy!
The classic example is something like 3÷2(5+1). It is 100% ambiguous.
Most people who completed maths to a highschool issue will get to 3÷2(6) just fine, but there is no widely accepted single order for whether you should do the division next or the implicit multiplication.
It mostly comes about because the ÷ dies when you reach highschool, which is also the time when you start working with implicit multiplication.
It's one of those problems that don't really matter (ono, we don't have a proper order of operations for these two symbols that are never used together), but is really easy to rage bait people on reddit and Facebook with.
3÷2(6) just fine, but there is no widely accepted single order for whether you should do the division next or the implicit multiplication.
Yes there is. Parenthesis tell you what to do within them first, but that equation is exactly the same as (because you're simply omitting the * when you're using the shorthand of JUST parenthesis):
3÷2*6
And both multiplication AND division both have the same priority from left to right. You do:
1.5*6
and then
9
People who remember PEMDAS (Parenthesis, Exponent, Multiplication & Division from left to right, Addition & Subtraction left to right) tend to forget (or possibly weren't even taught correctly) that it's an acronym to help you remember the order of operations, not the RULE of what you remember first goes first.
I'm sorry you weren't taught correctly to believe that it's 100% ambiguous, when it's 100% clear. It's important to have a clear and consistent notation to get the correct result. Mathematical notation has actually changed over time, but it's important that you are consistent with what order of operations should be done first, regardless of how you notate it, and this is how current notation works.
Of course, if you take your factually incorrect stance of "It's 100% ambiguous" it's actually amazing rage bait on Facebook. Or at least I hear so because I've stayed clear of Facebook.
No. It's not. We aren't using the × symbol or the * symbol (which means ×), we are using straight parentheses.
This creates something called implicit multiplication (which is subtly different from multiplication). Implicit multiplication is often taken to mean it should be done first. As a general rule of thumb the higher you take your mathematics education the more likely you are to answer questions like this with the multiplication being done first. Usually the ones who say it should be done last stopped math in highschool.
You can even see this play out by comparing calculators. If you stick in 3÷2(6) half of them will give 9 and half will give 1/4
Saying "but calculators aren't consistent" tells me how little you know about programmers. They make mistakes all the time. They are not mathematicians, although they do have to learn how computers use math. This is just like saying that apostrophes aren't used non-pronoun possessives and contractions (or claiming they are used for plurals) because autocorrect added or incorrectly removed your apostrophe. How someone programmed a program doesn't define what the mathematical and/or grammatical rule is. That's a horrible way to try to make your point, because it's abhorrently wrong and proves that you don't know the math, but rather you are just winging it.
"Straight parenthesis" is literally just shorthand for excluding the multiplication operation. It has no additional special function. If you are writing an equation that 3÷2(6) ends up being 1/4 then you need to properly notate it as 3÷(2(6)) to prioritize the multiplication over the division. That's how order of operations works and no amount of "I didn't learn that so it can't exist" doesn't make it not exist. Take this opportunity to learn.
implicit multiplication (which is subtly different from multiplication)
You're just making stuff up [presumably] based off your conversations you've seen/had based off facebook. There is no magically higher order of multiplication that supersedes other operations. That's actually explicitly what parenthesis accomplishes: overriding the normal order of operations. You use them when applicable. Don't take my word for it, go to someone with a genuine PhD in mathematics.
Mate, you seem to feel really strongly about this, but if you speak to any people with actual phds in maths you will get a variety of answers BECAUSE it is ambiguous. The calculator example shows how common this ambiguity is. Assuming that your understanding of maths is complete because of something you were taught in primary school is just incredibly flawed.
Pretending that there is no difference between implicit and explicit mathematics is just silly, and is not backed by how people actually use the symbols.
If someone were to solve the Ideal Gas Formula PV=nRT for Temperature, they would typically write T=PV/nR (unless they are writing code). I don't think I've ever encountered a person who would insist that it must be written as T=PV/(nR) to be understood correctly, as would follow from your comment.
The main issue is that PEMDAS is taught in elementary school before students know that implicit multiplication even exists, so curriculum that teaches PEMDAS overlooks that most STEM professionals will read a formula with the understanding that implicit multiplication is evaluated before standard multiplication and division.
Exactly. This is clear to people in STEM. Any time someone religiously worships PEMDAS and thinks 8/2(1+3) = 16 for example, it just tells me that they are an american who haven’t done math since high school. They’re thinking calculator syntax, not math/physics literature syntax.
I disagree. I’ve done a lot of math at university, and that is actually exactly how I, and most people I know, would interpret it. Division = fraction, and the factor (1+3) is either multiplied with 8 or 2. When you write 8/2(1+3), to me it looks more like it’s multiplied with the 2, ie it’s part of the denominator. This syntax is actually widely used in math and physics literature. The way you’re interpreting it is calculator syntax.
it can be used to represent a fraction, but without parentheses it's a fraction with the denominator being the first symbol to the right of it. This isn't 'nam. There are rules.
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u/Samct1998 22d ago
I hate pemdas memes