6Γ·2(1+2)
π‘πππΊππππΊπ π°ππππ± @ SmartmanApps @programming.dev Posts 22Comments 591Joined 2 yr. ago
π‘πππΊππππΊπ π°ππππ± @ SmartmanApps @programming.dev
Posts
22
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591
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2 yr. ago
did you stop after realizing that it was saying something you found disagreeable
I stopped when he said it was ambiguous (it's not, as per the rules of Maths), then scanned the rest to see if there were any Maths textbook references, and there wasn't (as expected). Just another wrong blog.
What will you tell your students if they show you two different models of calculator, from the same company
Has literally never happened. Texas Instruments is the only brand who continues to do it wrong (and it's right there in their manual why) - all the other brands who were doing it wrong have reverted back to doing it correctly (there's a Youtube video about this somewhere). I have a Sharp calculator (who have literally always done it correctly) and most of my students have Casio, so it's never been an issue.
trust me on this
I don't ask them to trust me - I'm a Maths teacher, I teach them the rules of Maths. From there they can see for themselves which calculators are wrong and why. Our job as teachers is for our students to eventually not need us anymore and work things out for themselves.
The truth is that there are many different math notations which often do lead to ambiguities
Not within any region there isn't. e.g. European countries who use a comma instead of a decimal point. If you're in one of those countries it's a comma, if you're not then it's a decimal point.
people donβt often encounter the obelus notation for division at all
In Australia it's the only thing we ever use, and from what I've seen also the U.K. (every U.K. textbook I've seen uses it).
Check out some of the other things which the βΓ·β symbol can mean in math!
Go back and read it again and you'll see all of those examples are worded in the past tense, except for ISO, and all ISO has said is "don't use it", for reasons which haven't been specified, and in any case everyone in a Maths-related position is clearly ignoring them anyway (as you would. I've seen them over-reach in Computer Science as well, where they also get ignored by people in the industry).
"The obelus is treated differently,β Church said. "It could mean ratios, division or numerator and denominator, and these all tweak the meaning of the symbol.β
This is the only symbols I've ever seen used (but feel free to provide a reference if you know of any where it isn't - the article hasn't provided any references)...
Ratio is only ever colon.
Division is obelus (textbooks/computers) or slash (computers, though if it's text you can use a Unicode obelus).
Fraction is fraction bar (textbooks) or obelus/slash inside brackets (computers). i.e. (a/b).
read the article instead of βscanningβ it.
I stopped reading as soon as I saw the claim that the right answer was wrong. I then scanned it for any textbook references, and there were none (as expected).
You clearly donβt even understand the term βimplicit multiplicationβ if youβre claiming itβs made up
Funny that you use the word "term", since Terms are ONE of the things that people are referring to when they say "implicit multiplication" - the other being The Distributive Law. i.e. Two DIFFERENT actual rules of Maths have been lumped in together in a made-up rule (by people who don't remember the actual rules).
BTW if you think it's not made-up then provide me with a Maths textbook reference that uses it. Spoiler alert: you won't find any.
Implicit multiplication is not the controversial part of this equation
It's not the ONLY controversial part of the equation - people make other mistakes with it too - but it's the biggest part. It's the mistake that most people have made.
shitty blog
So that's what you think of people who educate with actual Maths textbook references?
Read. The. Article.
Read Maths textbooks.
The first step in order of operations is solve brackets. The first step in solving unexpanded brackets is to expand them. i.e. The Distributive Law. i.e. the ONLY time The Distributive Law ISN'T part of order of operations is when there's no unexpanded brackets in the expression.
The examples I gave were that the expansion of brackets would be done differently if the order of operations was βPESADMβ
Yep I read it, and no it wouldn't. Expanding Brackets - or in the case of this mnemonic Parentheses - is done as part of B/D (as the case may be). i.e. expanding brackets isn't "multiplication" (no multiplication sign), but solving brackets (there are brackets there), which always come first in all the mnemonics.
reverse polish notation exists
...but is not taught in high school.
your level of qualification on this topic is not above mine
Maybe not, but it means it's not an "appeal to authority" (as per screenshot). Maths teachers ARE an authority on Maths. The most common appeal to authority I see from people is claiming that someone (not them) is a University professor, and "they would know". No, they wouldn't - this topic isn't taught at university - it's taught in high school.
why you were so engaged in this.
I'm a teacher. You say you're on the same level as me - don't you like to teach people what's correct?
3 month old post
Which will show up in search results for all eternity (it's how I found it - I was looking for something else!).
probably wonβt be a lot of engagement in this thread from this point on
Got another 12 responses after yours. But the point is I'm not even LOOKING for responses, just to correct misinformation. As a teacher (a Maths teacher?) have you not had people say to you "But Google says"? I certainly have. It's the bane of my professions.
it seems like youβre on your own
Did you read my thread? Maths textbooks, calculators, proofs, etc. Also, someone else said what you just did, asked a Maths teacher, and was told I was correct, then was man enough to go back and edit his posts and admit I was correct and specifically said "SmartmanApps is not on his own with this".
clear examples against what you are saying
Which are where, exactly? You haven't presented any. You haven't, for example, shown how one can make (2+3)x4=14.
re: appeal to authority
I believe youβre conflating the rules of maths with the notation we use to represent mathematical concepts.
You think a Maths teacher doesn't know the difference?
There is absolutely nothing stopping us from choosing to interpret a+bΓc as (a+b)Γc
Yes there is - the underlying Maths. 2x3 is short for 2+2+2, which is therefore why you have to expand multiplications before doing additions. If you "chose" to interpret 2+3x4 (which we KNOW is equal to 14, because 3x4=3+3+3+3 by definition) as (2+3)x4, you would get 20, which is clearly wrong, since 20 isn't equal to 14.
We donβt even have to write it like that at all
No that's right, because it IS written differently in different languages, but regardless of how you write it, it doesn't change that 2+3x4=14 - the underlying Maths doesn't change regardless of how you decide to write it. Maths is literally universal.
Γ before + is a very convenient choice
It's not a choice, it's a consequence of the fact that x is shorthand for +. i.e. 2x3=2+2+2.
it is still just a choice
It is a consequence of the definitions of what each operator does. If x is a contraction of +, then we have to expand x before we do +. If it were the other way around then we'd have to do it the other way around. Anything which is a contraction of something else has to be expanded first.
I was making a joke.
Fair enough, but my point still stands.
if we instead all agreed that addition should be before multiplication
...then you would STILL have to do multiplication first. You can't change Maths by simply agreeing to change it - that's like saying if we all agree that the Earth is flat then the Earth is flat. Similarly we can't agree that 1+1=3 now. Maths is used to model the real world - you can't "agree" to change physics. You can't add 1 thing to 1 other thing and have 3 things now, no matter how much you might want to "agree" that there is 3, there's only 2 things. Multiplying is a binary operation, and addition is unary, and you have to do binary operators before unary operators - that is a fact that no amount of "agreeing" can change. 2x3 is actually a contracted form of 2+2+2, which is why it has to be done before addition - you're in fact exposing the hidden additions before you do the additions.
the brackets do nothing
The brackets, by definition, say what to do first. Regardless of any other order of operations rules, you always do brackets first - that is in fact their sole job. They indicate any exceptions to the rules that would apply otherwise. They perform no other function. If you're going to no longer do brackets first then you would simply not use them at all anymore. And in fact we don't - when there are redundant brackets, like in (2)(1+2), we simply leave them out, leaving 2(1+2).
The linked article is wrong. Read this - has, you know, actual Maths textbook references in it, unlike the article.
your response is βFollowing my logic, there is no confusion!β
That's because the actual rules of Maths have all been followed, including The Distributive Law and Terms.
there clearly is confusion in the wider world here
Amongst people who don't remember The Distributive Law and Terms.
The blog does a good job of narrowing down why thereβs confusion
The blog ignores The Distributive Law and Terms. Notice the complete lack of Maths textbook references in it?
6/2=3
3(1+2)=9
You just did division before brackets, which goes against order of operations rules.
For me to read the whole of 2(1+2) as the denominator in a fraction
You just need to know The Distributive Law and Terms.
But it isnβt βcorrectβ
It is correct - it's The Distributive Law.
itβs one of two standard ways of doing it.
There's only 1 way - the "other way" was made up by people who don't remember The Distributive Law and/or Terms (more likely both), and very much goes against the standards.
The ambiguity in the question is
...zero.
Hooray! Correct! Anyone who downvoted or disagrees with this needs to read this instead. Includes actual Maths textbooks references.
you provided so many great references
Except for any actual Maths textbooks. Try this instead.
thereβs a mutual agreement that itβs only approximately correct.
No there isn't. I've never seen a single Year 7-8 Maths textbook that is in the slightest bit ambiguous about it. The Distributive Law has to literally always be applied (hence why it's a law). dotnet.social/@SmartmanApps/110819283738912144
The answer still lies in the ambiguity of the way the problem is written though
But it's not ambiguous, as per the reason you already gave.
If the author used fractions instead of that stupid division symbol
If you use fractions then the whole thing is a single term, if you use division it's 2 terms.
9 is definitely not the clear and only answer
1 is definitely the only answer.
those calculators because that is a badly written equation
It's not badly written, and the reason Texas Instruments gets it wrong is right there in their manual (disobeys The Distributive Law).
modern rules of math
The order of operations rules haven't changed in at least 100 years, and more likely at least 400 years. Don't listen to Youtubers who can't cite a single Maths textbook.
β2(3)β is the same as β2 x 3β
No, it's the same as (2x3), as per The Distributive Law and Terms.
it shows how there is no consensus
Used to not be. Except for Texas Instruments all the others reverted to doing it correctly now - I have no idea why Texas Instruments persists with doing it wrong. As you noted, Sharp has always done it correctly.
There really is no agreed upon standard even amongst experts
Yes there is. It's taught in literally every Year 7-8 Maths textbook (but apparently Texas Instruments don't care about that).
BWAHAHAHA! Ok then, what EXACTLY does it relate to, if not brackets? Note that I'm talking about The Distributive LAW - which is about expanding brackets - not the Distributive PROPERTY.
a(b+c)=(ab+ac) actually - that's one of the common mistakes that people are making. You can't remove brackets unless there's only 1 term left inside, and ab+ac is 2 terms.
No, never. ab+c is 2 terms with no further simplification possible. From there all that's left is addition (once you know what ab and c are equal to).
Yep, they're a grouping symbol. Terms are separated by operators and joined by grouping symbols.