I wrote a (very long) blog post about those viral math problems and am looking for feedback, especially from people who are not convinced that the problem is ambiguous.
It's about a 30min read so thank you in advance if you really take the time to read it, but I think it's worth it if you joined such discussions in the past, but I'm probably biased because I wrote it :)
Funny how using parentheses gets you the same answer as if implicit multiplication doesn't have a higher order... It's almost like considering implicit multiplication as having an advanced order is an invalid assumption to make when looking at a maths equation.
Edit: I'm wrong, read below.
It's not invalid or even uncommon. It's just not necessarily correct. Implicit multiplication can be used intentionally to differentiate from explicit multiplication and context can suggest there is a difference in priority. For example, a/bc is likely to be read as a/(bc) because the alternative could be written less ambiguously as ac/b. If I wanted to convey to you that multiplication is associative, I might say ab*c = a*bc, and you'd probably infer that I'm communicating something about the order of operations. But relying on context like this is bad practice, so we always prefer to use parentheses to make it explicit.
It's only ambiguous if you don't read left to right. That's a literacy issue not a mathematics one.
It's definitely not a mathematics issue. This all concerns only notation, not math. But it's not a literacy issue either. It's ambiguous in that the concept of a correct order of operations itself is wrong.
Notation is read left to right, reading it in any other order is automatically incorrect. Just like if you read a sentence out of order you won't get it's intention. Like I said, if you actually follow the rules it's almost like implicit multipication having a higher order doesn't work, which makes it illigitimate mathematics.
It's not left to right. a+b*c is unambiguously equal to a+(b*c) and not (a+b)*c.
You determine processing order by order of operations then left to right. Always have. Even in your example, that is the left-most highest order operand, nothing ambiguous about it.
So it's "higher operands first, then left to right." I agree. But you presuppose that e.g. multiplication is higher than addition (which, again, I agree with). But now they say implicit multiplication is higher than explicit multiplication. You apparently disagree, but this has nothing to do with "left to right" now.
Just because they say one type of multiplication has precedence doesn't make it so. We've already shown how using parenthesis negates that concept, and matches the output of the method that doesn't give implicit multiplication precedence, ipso facto, giving ANY multiplication precedence over other multiplication or division doesn't conform to the rule of highest-operand left to right and doesn't conform to mathematical notation, and provides an answer that is wrong when the equation is correctly extrapolated with parenthesis, ergo it is utterly conceptually, objectively, and demonstrably, incorrect.
Edit: It was at this moment he realised, he fucked up. Using parenthesis doesn't resolve to one or the other because the issue is inherent ambiguity in how the the unstated operand is represented by the intention of the writer. They're both wrong because the writer is leaving an ambiguous assumption in a mathematical notation. Ergo, USE PARENTHESES, ALWAYS.
It's not that their words have magic power. It's that it's just an arbitrary notational convention in the first place.
Using parentheses doesn't "negate" or "match" anything. (a * b) + c and a * (b + c) are two different expressions specifically because of the use of parentheses, regardless of the relative order of the * and + without parentheses.
You're right, I had that epiphany and and updated my comment. Thanks for helping me educate myself.
No it isn't. It's the way we write factorised terms (and The Distributive Law is the reverse process to factorising).
Stop spamming me with uneducated nonsense
Maths textbooks are "uneducated nonsense". Uh, whatever.
How many math textbooks have you read?
Here's a more relevant question - how many Maths textbooks do you own? If it's more than zero, then take a picture/screenshot of any pages which you think support your argument. I'll wait.
A couple dozen
Still waiting.
Do something with your life.
I teach Maths. How about you?
I did for about 8 years until I quit academia during the pandemic. I would feel bad for your students if you weren't lying.
I see. So university, where they don't teach order of operations. Got it.
My students are doing just fine thanks
If you're not lying, then you've just doxxed yourself, as this is the single review for a high school math tutor on a UK tutoring website. Said tutor's credentials also do them no favors. Please delete the comment and this conversation is over.
How do you figure that? She had literally never passed Maths before, and with my tutoring she did. BTW order of operations was in the test.
Ok then, bye now.
There's no ambiguity - The Distributive Law applies to all bracketed terms.
You're responding to a 3 month old post without even reading all of what you're replying to. Are you retarded?
I read what you wrote when you said...
...and I responded by saying there's no such thing as ambiguity in Maths (and in this case it's because of The Distributive Law, and the paragraph before that was about "implicit multiplication" of which there is no such thing). I therefore have no idea what you're talking about in saying I'm replying to something I haven't read, when I quite clearly am responding to something I have read.
No, I'm a Maths teacher (hence why I know it's not ambiguous - I know The Distributive Law. In fact I teach it. You can find info about it here - contains actual Maths textbook references, unlike the original article under discussion here).
So you are retarded.
I see only one of us has read those textbook references.
I see only one of us is stupid enough to roll through a 3 month old thread chirping at everyone and trying to shill the fact that you're a teacher. Your social retardation is matched only by your unequivocally unearned ego.
Engaged in several proper conversations with people now, so it's active again, not "3 months old". Maybe you should try reading some of those conversations (since you don't seem to want to read textbooks).
I try to mention it as little as possible actually. It's only when I see something outrageously wrong mathematically that I point out they're trying to gaslight a Maths teacher, so that ain't gonna work.
🤡
Correct! "implicit multiplication" is NOT a rule of Maths. It's something made up by those who don't remember all the actual rules, which includes The Distributive Law and Terms.
It's not ambiguous - if you correctly follow all the relevant rules of Maths (which includes expanding brackets) then there is only 1 correct answer, 1.
L
...that's the actual definition given and used in Maths textbooks.
That's not the "actual definition" and is not even how the standard order of operations would interpret the expression.
Yes it is and yes it is 1917 (ii) - Lennes' letter (Terms and operators)
Only thing worth reading from you is the hashtag "#LoudlyNotUnderstandingThings"
So, you didn't understand it? Which part do you want me to explain further?
You are unhinged