What is the correct result?

[carey]

(04-12-2024 10:50 PM)Matt Agajanian Wrote:  Hi all.

Here’s a new one.

While following another of those 'What’s the answer' posts, from my post a FB poster stated that "Implied multiplication has no priority." Then, in another statement I made about PEJMDAS, the individual commented Casio and Sharp are, get this, incorrectly programmed and TI is the most reliable.

What do you make of this?

There is no mystery.

But before replying directly to the question, it seems important to recognize that operator precedence is a mathematical convention invented by people (as in Kronecker’s saying: ”God made the integers; all else is the work of man”). People did arithmetic before calculators and there was no universally agreed upon operator precedence before around 1920. As nicely detailed in this YouTube video by an Australian math video creator (starting around 6:45 in the clip) calculators created the recent chaos for math teachers, students and calculator users (but not for professional mathematicians).

As explained in the video (which includes material from Casio and TI managers) North American teachers prefer the (current) TI convention (PEMDAS) while elsewhere in the world PEJMDAS is preferred. (Mercifully, the video defines these terms! :)

Because of TI’s long-standing relationship with the National Council of Teachers of Mathematics (NCTM), the preference of N.A. teachers for the TI convention is not surprising and might be an example of the tail wagging the dog. Thus, the cited FB comment claiming that TI is more reliable and that Casio and Sharp are wrong appears to simply reflect a geography-based preference and not a universal truth.

An interesting sidenote is that at 11:35 in the video the operator precedence for the HP35s appears to throw the video creator for a loop!