I might get downvoted for that, but I think Europe should start working closer with China.

Here you are: https://jsfiddle.net/2o97k6vz/6/

Exactly. The only real unit is football fields.

It's not really hard to implement at all but would just trade pest for cholera. We could just burn a lot of coal again, the dustier and dirtier the better. But that's pretty bad for air quality but it would seriously cool the planet.

All sounds files are "raw bytes" 😉

Totally agree with that and I don't think anybody would see that as controversial. LLMs are actually good in a lot of things, but not thinking and typically not if you are an expert. That's why LLMs know more about the anatomy of humans than I do, but probably not more than most people with a medical degree.

Thank you for taking the time reading it.

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You are right the manual isn't very clear here. My guess is that parentheses are also considered Type B functions. I actually chose those calculators because I have them here and can test things and because they split the implicit multiplication priority. Most other calculators just state "implicit multiplication" and that's it.

My guess is that the list of Type B functions is not complete but implicit multiplication with parentheses should be considered important enough for it to be documented.

Thank you so much for taking the time and reading the post. I just fixed the typos, many thanks for pointing them out.

There is nothing really to be embarrassed about and if you look at the comment sections of such viral math posts you can see that you are certainly not the only one. I think that mnemonics that use "MD" and "AS" without grouping like in "PE(MD)(AS)" are really to blame here.

An alternative would be to drop the inverse and only use say multiplication and addition as I suggested with "PEMA" but with "PEMDAS" one basically sets up students for the problem that they think that multiplication comes before division.

"when in doubt" is a bit broad but left to right is a great default for operations with the same priority. There is actually a way to calculate in any order if divisions are converted to multiplications (by using the reciprocal value) and subtractions are converted to additions (by negating the value) that requires at least a little bit of math knowledge and experience so it's typically not taught until later to prevent even more confusion.

For example this: 6 / 2 * 3 can also be rewritten as 6 * 2⁻¹ * 3 and because multiplication is commutative you can now do it in any order for example like 3 * 6 * 2⁻¹

You can also "rearrange" the order without changing the meaning if you move the correct operation (left to the number) with it (should only be done with explicit multiplication)

6 / 2 * 3 into 6 * 3 / 2 (note that I moved the division with the 2)

You can even bring the two to the front. Just remember that left to the six is an "imaginary" (don't quote me ^^) multiplication. And because we can't just move "/2" to the beginning we have to insert a one (empty product - check Wikipedia) like so:

1 / 2 * 6 * 3

This also works for addition and subtraction

7 + 8 - 5

You can move them around if you take the operation left to the number with it. With addition the "imaginary" operation at the beginning is a plus sign and the implicit number you use is zero (empty sum - check Wikipedia)

8 - 5 + 7

or like this

0 - 5 + 8 + 7

because with negative numbers you can use the minus sign to indicate negative numbers you can even drop the leading zero like this

-5 + 8 + 7

That's not really possible with multiplication because "/2" is not a valid notation for "1/2"

Same priority operations are solved from left to right. There is not a single credible calculator that would evaluate "6 / 2 * 3" to anything else but 9.

But I challenge you to show me a calculator that says otherwise. In the blog are about 2 or 3 dozend calculators referenced by name all of them say the same thing. Instead of a calculator you can also name a single expert in the field who would say that 6 / 2 * 3 is anything but 9.