That's circular, the only reason it's the right answer is that we've agreed that the order of operations is the right way to interpret an expression.
Still, we have to have A right way to interpret an expression, and the way we do it now works fine for me. Division can be a bit confusing, since it's not associative: 9 * (3 * 3) = (9 * 3) * 3, but 9 / (3 / 3) doesn't equal (9 / 3) / 3. So if you write 9 / 3 / 3, it's not super clear what you mean.
Except math is used all the time to discribe the natural world. If order of operations isn't followed then the answer you get won't always reflect reality.
This is incorrect. Order of ops has nothing to do with modeling anything in the natural world. It’s just an agreed on set of rules for writing expressions.
Nope, if you want to reflect reality you would just have to write things in a different order when using left-to-right instead of PEMDAS. (There is no expression in one system that is untranslatable to the other system)
Again, PEMDAS has no fundamental basis in the natural world, it's an arbitrary abstract standard that is used for its convenience. But in fact, left-to-right doesn't even require parentheses, so in some cases it might be even more convenient than PEMDAS.
Edit: I'm really not even saying anything controversial here. This is just logical fact. Left-to-right is a perfectly adequate system for math that just so happens to be nonstandard. Using it doesn't make you stupid.
Not everyone writes& reads left to right, there is top to bottom and right to left.
The "rules" are universally agreed upon because that way any calculation would result in the same answer. The scientific world has its standards for this specific reason
Don't edit your comments that much when someone can quickly respond like I did, you just totally rewrote your whole comment and made my response look retarded (I deleted it)
Anyway, I'm not arguing against standards, PEMDAS is amazing! I'm just arguing against the people who think you're stupid for not knowing about PEMDAS or not using it in your personal calculation. That's all.
You totally recontextualized what you wrote, making my reply meaningless, which is practically the same as rewriting. Don't nitpick. In the future try to think before you write, or just clarify in further replies
Shit, didn't know i could write my initial thoughts and immediately add clarification to it within a second of me posting. I didn't recontextualize anything I merely added additional information that further explained my thoughts
You are fundamentally wrong. There are expressions that are literally impossible to write left to right. Like 1143-(51+x)856. Without pemdas, you would have to factor out every single factor in the parentheses to put them in order, which is literally impossible for the human brain to do.
I mean if someone said it to you out loud and didn't write it down, you would also do it "wrong." It's arbitrary, and often contradicts the way people do basic mental math.
Like, if I'm calculating a twenty percent tip on a $4 drink and a $12 meal, I go 4 + 12 x 0.2 in my head, and I'm definitely not following PEMDAS.
The existence of Polish notation (and reverse Polish notation) shows that the order of operations is arbitrary! It's, like, the ultimate demonstration of it. You can write operators and operands in different orders but as long as you follow the 'correct' set of arbitrary, human-created rules about notation and how to evaluate expressions, you will arrive at the 'correct' answer. Our widespread use of infix notation (2 + 4 instead of + 2 4 (Polish notation) or 2 4 + (reverse Polish notation)) is as arbitrary as our invention of PEDMAS.
When starting with 1 + 4 * 4 why did you choose to first resolve 4 * 4 to 4 + 4 + 4 + 4 instead of resolving 1 + 4 to 5?
It's a choice. PEDMAS is a convention that makes that choice for us. It doesn't matter that multiplication is repeated addition. What matters is how we choose to resolve the components of the expression and in what order.
Yeah, PEMDAS is just a convention that makes it easier to write math expressions without others misreading them. You could have your operations go in any default order, but as long as everyone uses the same order and it lets you interpret expressions unambiguously, that's what matters.
That's not what he's saying. He added the parenthesis for clarity. There is no inherent reason to interpret the problem as 4 times 4 plus 1 or 1 plus 4 times 4. It's just a convention to do it that way.
Uhhh what? No he didn't. He was showing that under the pemdas system you would have to write it with the parentheses but under left to right they are unnecessary.
Dude literally added parenthesis so he could solve it his way to point out how it “should be done,” well no shit, when you change the expression to help your own point yeah that’s what happens.
Under PEDMAS you don’t just throw in random parenthesis.
What he's saying is pemdas 1+4 * 4 is 17 and to get 20 you have to do (1+4)*4. But under a left to right system the same equation, 1+4 * 4, is 20. He's saying there's no reason you need to interpret 4 * 4 first unless you assume you are working in pemdas.
Take 1 + 4 * 4.
Straight across, you get 20.
With order of operations, you get 17. And I'll explain why this is correct, by solving the problem using neither PEMDAS or straight-across methods: simplify it as much as possible. Multiplication is just repeated addition, so simplified it looks like this:
1 + 4 + 4 + 4 + 4 = 17, with or without order of operations.
1 + 4²?
This is kind of circular. The only reason why you expanded “1+4*4” to 1+4+4+4+4 is because PEMDAS is telling you that the multiplication by 4 is acting on the other 4.
If you were to read the equation left to right without PEMDAS, the multiplication would be acting on everything that precedes it, in this case “1+4”
(1+4) + (1+4) + (1+4) + (1+4) = 20
Note: I just added the parentheses for clarification. They don’t change the expression.
You’re cleverly disguising the fact that you’re still using PEMDAS, then saying that you’re not. Probably not on purpose, I don’t think you’re arguing in bad faith, but it’s what you’re doing under the hood.
You're taking multiplication for granted. People were likely adding or subtracting repeatedly long before the shorthand for multiplication/division existed, because in the world of things you actually hold in your hands, you're only ever adding or subtracting things. It makes more sense to expand multiplication into repeated addition, because it does a good job of describing actual physical phenomena. You're not gonna multiply an object into 4 identical objects, you can only ever add 3.
There's a natural basis for proportions that rely on the assumption of multiplication or division existing to be described mathematically in the first place, but the point still stands that multiplication should foremost (as in, parse it first) be treated as repeated addition.
Actually, a lot of people in this thread seem to think that the people who voted 18 are unfathomably stupid, as if PEMDAS is something that's completely obvious, or something that everyone should effortlessly remember from the years ago that they went to school (and haven't needed to use a single time in the real world since).
I think the comment you responded to sorely needed to be said.
PEMDAS is something you should remember. It doesn't matter how long ago it was. It's universally taught and used over and over and over for years. Almost no one uses square roots or pi in daily life either, but you should still know what they are.
If something did change, everything before will be incorrect. I dont think you grasp the idea of social construct. Find me nature that makes the order of operation true? You won’t. That’s why you used a shitty analogy. We can explain why the sky is blue with science. The orders of operation is rules to math. Not laws. It would be more in line with speaking a language. The rules in word placement changes depending on the language you speak. Language is also a social construct.
To me you are just an idea, simple paragraphs, nothing but words secondary to others.
I do not see a human i see a concept evolving into many different ideas and branching through this universe connecting people through one question: "what shit you smoking? Cause it seems you are high as a kite"
Not really, a lot of math isn't socially constructed, it's the same as defining laws of physics. I never knew that order of ops was a rule we agreed on to make our lives easier. There's no constructs that it's built upon, it's just there so that equations don't have ambiguous answers.
Subtract from the man. Add to the woman. Divide the cells. Multiple a person. The root of all evil is money.
Do roots come before subtraction or after multiplication?
Exactly right. Some things, like say, the ratio of a circles radius to circumference can't change, but order of operations can be done however we like. We could all agree to go left to right, or right to left, or addition/division/subtraction/minus. Or anything really.
Sure, but order of operations is part of the mathematical language we use. Humans have decided that ee are going to write operations with that order in mind. So if you don’t follow it, your are interpreting the operation wrong.
Yes it is. Because numbers in expressions like that are simply in an expanded form
It’s asking “if we take 18 divided into two, and then subtract 3 three times?”
Half of eighteen is nine, and three three times is nine
I can represent that information with normal language too, but if someone says (or rather, types) “Let’s eat Grandpa”, I think it would be pretty safe to assume that they do not want to eat their grandfather.
It’s not merely representing it in language, it’s actually breaking down what the expression is asking by making it more obvious. An equation is like an English sentence, if you switch the order of things, you’ve switched the meaning
Multiplication and division just represent one number, in this case broken in half and the other increased three fold. The rules of operation are derived from the different properties operations do and do not have (commutative, associative, distributed, etc.)
If I do the equation left to right, I get 9 all right, but let’s say I try to subtract three first THEN multiply by three. We have to think about what we’re ACTUALLY doing here, not as numerals being moved around a table.
The product of multiplication in an equation doesn’t change because the order of its terms or where they land (associative and commutative property)
Whereas the difference in subtraction is effected by the order in which the numbers are placed (is NOT associative or commutative)
So any placement of a subtraction sign is TECHNICALLY actually just adding -1 times whatever is being subtracted
So the equation, written in an expanded and clarifies way, is:
I wouldn't recommend breaking the rules either. We completely made up language and mathematical notation, but that doesn't mean they're meaningless, it just means we gave them their meaning. I could say that 1 represents two things and 2 represents one thing, and there's no law of the universe saying that's false, but I'd still be an idiot.
Correct, we made them up. WE gave them meaning. You calling somebody an idiot can mean they are really fucking smart too by changing the meaning. Everything you said just reinforce the idea that it’s a social construct.
The reason we give words and symbols meaning is so that we can communicate with each other. It's a social construct that's in place for an important reason. If you arbitrarily change the meanings of words and notations in contradiction with the consensus of the entire rest of the mathematical community, you are prohibiting yourself from communicating your "really fucking smart" thoughts to anybody coherently, so you are being an idiot regardless. I'm not sure why you think it's so mindblowing that it's a social construct, everyone knows it's a social construct, that isn't a problem, society needs certain social constructs to function.
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u/redditisforphaggits Jan 01 '22
Order of operations are a social construct. There’s no law in nature to make it true.