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a/bc is equally as ambiguous as a/b*c

It's not ambiguous at all. By the definition of Terms - ab=(axb) - a/bc is 2 terms and a/bxc is 3 terms. If we were to write it in fraction form (to illustrate the difference), in the former c is in the denominator, but in the latter it's in the numerator, hence a different answer. dotnet.social/@SmartmanApps/110846452267056791

you seem to take the position that the operations are resolved from left to right... but I haven’t seen this defined in mathematics anywhere

It applies to operators, or more precisely division. When doing the divisions, you have to do them left-to-right, but other than that each of the operators can be done in any order. i.e. it doesn't matter what order you do the multiplications in, as long as you do them before the additions and subtractions. Unfortunately I've seen many people misremember left-to-right as an overarching rule, rather than only applying to division.

It's not ambiguous. People who say it is have usually forgotten The Distributive Law or Terms, or more commonly both!

Seems this whole thing is the pedestrian-math-nerd’s equivalent to the pedestrian-grammar-nerd’s arguments on the Oxford comma.

Not even remotely similar. Maths rules are fixed. The order of operations rules are at least 400 years old.

mathematical notation is just as flexible as any other facet of written human communication

No, it isn't. The book "A history of mathematical notation" is in itself more than 100 years old.

The meme refers to the problem of handling implicit multiplication

There's no such thing as implicit multiplication. dotnet.social/@SmartmanApps/110925761375035558

I don’t see the problem actually.

Everything between ()

You recreated the problem right there - ignored The Distributive Law. a(b+c)=(ab+ac). i.e. 2(1+2)=(2x1+2x2). After step 1 - solving brackets - all that's left is 6/6. dotnet.social/@SmartmanApps/110819283738912144

Excel and Google are both wrong. In fact, Microsoft excels 😂in this area, with Excel, the Windows calculator, and MathSolver all getting it wrong in different ways! dotnet.social/@SmartmanApps/111164851485070719

Starting a new comment thread (I gave up on reading all of them). I'm a high school Maths teacher/tutor. You can read my Mastodon thread about it at Order of operations thread index (I'm giving you the link to the thread index so you can just jump around whichever parts you want to read without having to read the whole thing). Includes Maths textbooks, historical references, proofs, memes, the works.

And for all the people quoting university people, this topic (order of operations) is not taught at university - it is taught in high school. Why would you listen to someone who doesn't teach the topic? (have you not wondered why they never quote Maths textbooks?)

#DontForgetDistribution #MathsIsNeverAmbiguous

Because as a high school Maths teacher as soon as I saw the assertion that it was ambiguous I knew the article was wrong. From there I scanned to see if there were any Maths textbooks at any point, and there wasn't. Just another wrong article.

Without parentheses around (2×3)

But there is parentheses around (2x3). a(b+c)=(ab+ac) - The Distributive Law. You can't remove them unless there is only 1 term left inside. You removed them when you still had 2 terms inside, 2x3.

6/2(1+2)=6/2(3)=6/(2*3)=6/6=1

OR

6/2(1+2)=6/(2+4)=6/6=1

2(1+2) is the same as (1+2)+(1+2)

You nearly had it. 2(1+2) is the same as (2x1+2x2). The Distributive Law - it's the reverse process to factorising.