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[–] 1 pt (edited )

This is an age old 'mess with people' question, something we should teach tom.

https://math.berkeley.edu/~gbergman/misc/numbers/ord_ops.html

Been on the internet as a brain teaser for a long time, farther back than 2011 for sure. And way before the internet.

[–] 1 pt (edited )

Here is the real problem:

https://www.purplemath.com/modules/orderops2.htm

Note that different software packages will process this expression differently; even different models of Texas Instruments graphing calculators will process this expression differently. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations

Some older software would accordingly treat the implicit multiply as though it were also in an implicit surrounding parentheses, similar to interpreting 4(2) as 4 to the power of 2, which would have a high precedence. In this particular case some humans would also accordingly interpret the conjoined symbols as implying they were all part of the denominator, if you can imagine for a huge number of people that write that way only because they were unable to write the non-horizontal format in that moment, like on a computer. In C and JS et al, of course replacing the implicit multiply with just multiply would yield 16 every time.

The nuance from the past is gone, for mundane tasks, and every online calculator will do 16. Is probably something computers ruined for at least high school math. Was a progression of academics, coders, and users battling it out for horizontal equation syntax that was understandable and supportable for modern (last 20 years) calculators. Most academics would not write horizontally normally for anyting serious.

I ended up with a HP 28S for Christmas one year myself. Many hours. Good fun. I honestly can't remember how it would have treated 20/5(2*2).