💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @ SmartmanApps @programming.dev

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2 yr. ago

I wanted to compile a list of points that show as clear as humanity possible that there is no consensus here, even amongst experts

And I wrote a bunch of fact checks pointing out there is consensus amongst the actual experts - high school Maths teachers and textbook authors, the 2 groups who you completely ignored in your blog post.

What’s especially wild to me is that even the position of “it’s ambiguous” gets almost as much pushback as trying to argue that one of them is universally correct.

That's because following the rules of Maths is universally correct.

arguing vehemently that implicit multiplication having precedence was correct and to do otherwise was wrong, full stop

He was using the wrong words, but he was correct - the actual rules are The Distributive Law and Terms ("implicit multiplication" is a rule made up by those who have forgotten these 2 rules).

Yes, unfortunately there are some bad teachers around. I vividly remember the one I had in Year 10, who literally didn't care if we did well or not. I got sick for an extended period that year, and got a tutor - my Maths improved when I had the tutor (someone who actually helped me to learn the material)!

why that’s actually ambiguous.

It isn't actually ambiguous. You have remembered what you were taught in school, unlike the author of the blog post, who manages to write the whole thing without ever once checking a Maths textbook (which would reveal the only correct answer to be 1).

It treats division like a fraction

Which is why it gives the wrong answer.

Also you shouldn't be adding a dot between the 2 and the brackets - that also changes the answer.

TI calcs give the wrong answer, and it's in their manual why - they only follow the Primary School rule ("inside the brackets"), not the High School rule which supersedes it (The Distributive Law).

It is a funny little bit of notational ambiguity

It's not ambiguous - it's The Distributive Law. You got the correct answer, you just forgot what the rule is called (as opposed to people who forget the rule altogether).

You would've done dividing by fractions in high school, which requires both. Fractions and division aren't the same thing.

But stating the division as a fraction completely changes my mind now about how this calculation works

But division and fraction aren't the same thing - the former separates terms, the latter is a single term.

(140-age)(kg) / 72(SCr) vs (140-age) X kg ➗72 X SCr

The different answers for these two isn't because of / vs ➗, but because in the second one you have added extra multiplications in, thus breaking up some of the terms, and SCr has consequently been flipped from being in the denominator to being in the numerator. i.e. AK/72Scr vs. AK/72xSCr.

academic arguments

The "academic arguments" can be ignored since this is actually high school Maths - it's taught in Year 7-8.

Especially when said person keeps making incorrect statements about Maths and ignores completely what is taught in high school.

Unfortunately, demonstrably, a lot of people don't know what to do.

The blog post claims it is popular in academy

The blog post also completely ignores what is actually taught in high school - as found in Year 7-8 Maths textbooks - which indicates how much credibility you should attach to the blog post - none.

I read the equation and was shocked that anyone would get an answer other than 9

As a Maths teacher, I'm shocked whenever anyone ever gets an answer other than 1. I'm not sure how you came up with 9 when you previously said you've only ever seen strong juxtaposition? You can only get 9 with so-called "weak juxtaposition" (which is wrong).

I’d actually say that the weak juxtaposition is just the simple one schools use

Schools don't teach "weak juxtaposition" - they teach the actual rules of Maths! As per what's in Maths textbooks. It's adults who've forgotten the rules who make up the "weak juxtaposition" rule. See Lennes.

We do teach children how to solve this. It's not children who get it wrong - it's adults that get it wrong! Cos they've forgotten the rules of Maths (in this case The Distributive Law and Terms).

WA interprets both symbols as having equivalent meaning

The wrong meaning. It interprets them both as a fraction bar, thus giving the wrong answer.

Division doesn't mean fraction. Division is 2 terms, a fraction is 1 term. Terms are separated by operators and joined by grouping symbols. If you change the division to a fraction you change the number of terms and change the answer (and you also would've just done division before brackets, which violates the order of operations rules).

And WolframAlpha did division before brackets (turned 6/2 into a fraction, thus making it a single term instead of separate terms, all before doing brackets), thus violating the order of operations rules.

They're arguing about whether Distribution is Multiplication or not. Spoiler alert: it isn't, it's Brackets.