Monday, March 13, 2017

PEMDAS Peace at All Costs

image credit:

mathmadegr8.blogspot.com
Today is Mathematical Monday at my blog. Even if the math is easy for you  (and especially if it's not) please don't stop reading

I've been trying to bend over backwards to make peace between relatives and friends at odds with one another over You Know Whom aka "45"... I don't like questions that don't have generally-agreed-upon answers, and that's one of the reasons I enjoy math.

Let's watch as, finding myself in the midst of mathematical mayhem, I try to make Everyone Feel OK About Themselves, No Matter How Wrong They Are:


Facebook Puzzle asks:
 4 - 4 x 7 - 3

...and gets 369 replies....and mine had floated to the Tippity Top of the "Top Comments List."


Irene Athena: Please Excuse My Dear Aunt Sally, for her mnemonic lacks reference to multiplication and division having the same rank, done in order from left to right; similarly, addition and subtraction sharing the next and lowest rank.

4 - 28 + 3 = -21


Pathogens Evading MDs, AntiSeptics!!!

Like · Reply · 3 · 23 hrs

Proud Angel:  I like it.
Unlike · Reply · 1 · 22 hrs

Somebody Else:  27 bodmas
Like · Reply · 1 · 21 hrs

Proud AngelIrene was correct with her answer of -21.

Some Other Somebody Else27.
Like · Reply · 1 · 13 hrs

Proud Angel:  It really is -21. 
Not sure how you can subtract 28 from any combination of 4 and 3 and come up with a positive number.
Unlike · Reply · 1 · 13 hrs


Irene Athena: I'm standing by -21. Thank you, Proud Angel, for Watching my Six while I was engaged in debate in other corners of Facebook. Speaking of Six, it is the sum of 27 and -21, thus the average of these answers is "3" which appears to be the answer winning the popular vote .

"3" is the answer when the problem is done left to right, without any regard to the order of operations. So if the Order of Operations is merely a social construct, rather than an axiom, doing arithmetic from left-to-right might be a convention acceptable in some circles. Who am I to judge?

I arrived at -21 by following the PEMDAS convention. There are no Parentheses or Exponents, or Divisions, so Multiplication is the first operation to execute; thus, 28 replaces 4 X 7, leaving 4 - 28 + 3.

Addition and Subtraction come next. These two operations are given the same priority, even though Addition precedes Subtraction in the PEMDAS mnemonic (I offered a more robust mnemonic; perhaps this group can come up with a better one.) Additions and subtractions are done in order from left to right.

Thus 4 - 28 is replaced by -24, and finally, -24 + 3 is simplified to -21.

The thought process employed by the "27" contingent is mysterious, but that may be because they're motivated spiritually by a desire to harmonize (by calculating the average value) the adherents to the rigid constraints of PEMDAS rule ("-21" folks like yours truly) with  those whose approach to arithmetic is more carefree, take-it-as-it-comes, the left-to-righters, who, at the end of their journey, arrive at the mystical number "3."

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