The linked article is wrong. Read this - has, you know, actual Maths textbook references in it, unlike the article.
SmartmanApps
joined 1 year ago
your response is “Following my logic, there is no confusion!”
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 there’s 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 isn’t “correct”
It is correct - it's The Distributive Law.
it’s 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.
there’s a mutual agreement that it’s 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.
“2(3)” is the same as “2 x 3”
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).
Fair enough, but my point still stands.
...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, 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).