The Problem with PEMDAS: Why Calculators Disagree

An exploration of how different calculators parse implicit multiplication and why some brands switched from PEJMDAS to standard PEMDAS.

Some calculators say 6/2(1+2) = 1 and others say it equals 9 (similarly 8 divided by 2(2+2) can be 1 or 16 depending on the calculator). How did this disagreement on the order of operations come to be? My first PEMDAS video focused on how mathematicians, scientists and engineers interpret expressions; this video focuses on how calculators treat them. It turns out that the rule that juxtaposition comes before division is much older than "PEMDAS", and has been widely used for decades. So why did some calculator brands switch from this rule (which I call "PEJMDAS") to treating juxtaposition as the same priority level as division? And what can we do about the ambiguity? See my first PEMDAS video here: youtu.be/lLCDca6dYpA See also David Linkletter's article: plus.maths.org/content/pemdas-paradox References: Sass' article: math.ucdenver.edu/~jloats/Student%20pdfs/4_Order%20of%20Oper… First year algebra: archive.org/details/firstyearalgebra00well/page/18 also p85 First course in algebra: archive.org/details/firstcourseinal01toutgoog/page/n23 (p10) also p74 (page 90 of the pdf) Second course in algebra: archive.org/details/secondcourseinal00wellrich/page/4 also p64 Lennes' article, 'Relating to the Order of Operations in Algebra': jstor.org/stable/2972726 Sharp EL-512 manual: manualslib.com/manual/1177727/Sharp-El-512.html?page=9#manua… (p14) TI 81 manual: manualslib.com/manual/325929/Texas-Instruments-Ti-81.html?pa… (p1-8) TI website's comment on the issue: epsstore.ti.com/OA_HTML/csksxvm.jsp?nSetId=103110 AMS Guide for Reviewers May 2000 web.archive.org/web/20000815202937/http://www.ams.org/author… APS Physical Review Style and Notation Guide cdn.journals.aps.org/files/styleguide-pr.pdf p21 AIP style guide: web.mit.edu/me-ugoffice/communication/aip_style_4thed.pdf p23 (page 26 of the pdf)