Why does PEMDAS do multiplication and division before addition and subtraction? - Printable Version +- HP Forums ( https://archived.hpcalc.org/museumforum)+-- Forum: HP Museum Forums ( https://archived.hpcalc.org/museumforum/forum-1.html)+--- Forum: Old HP Forum Archives ( https://archived.hpcalc.org/museumforum/forum-2.html)+--- Thread: Why does PEMDAS do multiplication and division before addition and subtraction? ( /thread-247393.html) |

Why does PEMDAS do multiplication and division before addition and subtraction? - Don Shepherd - 07-30-2013
One of the responses to the rather large thread on PEMDAS got me thinking about this. I teach middle school math, and we always teach order of operations to 6th graders. I have always explained that PEMDAS is just the set of rules for evaluating mathematical expressions; no student has ever asked me "why are these rules the way they are?" Is it just arbitrary that multiplication and division come before addition and subtraction in PEMDAS, or is there a reason? In algebra, when we get to 2-step equations (3X + 12 = 24), I have always suggested undoing addition and subtraction first, then undoing multiplication and division. But PEMDAS teaches "doing" multiplication and division first. No wonder many kids get confused.
When you
Re: Why does PEMDAS do multiplication and division before addition and subtraction? - htom trites jr - 07-30-2013
Evaluating an expression means you have to reduce it to lowest terms. You do this by taking apart the most complicated, highest, parts first (driving into the parenthesis and other groupings and evaluating them first, bringing back a number to combine with other numbers); then the middle parts (exponents being repeated multiplication, then multiplication being repeated addition and division repeated subtraction) are dismantled, and finally the parts you've found are summed.
It's like that tower of disks on the post puzzle. Add and subtract are on the bottom, multiply and divide on that, exponentiation on that, and parenthesis on the top. You can't take off the bottom disk until you have taken off the others.
Re: Why does PEMDAS do multiplication and division before addition and subtraction? - Thomas Klemm - 07-30-2013
We use polynomials a lot. Without PASMDE we'd still need to write the same expression. Only PEMDAS allows us to get rid of the parentheses and write: p(x) = ax.^{3}+bx^{2}+cx+d
In addition to that the distributive law of multiplication would look weird:
Maybe I didn't understand you correctly but IMHO
Division first, then subtraction: 3X + 12 = 24
Subtraction first, then division: 3X + 12 = 24
Kind regards Re: Why does PEMDAS do multiplication and division before addition and subtraction? - Harald - 07-30-2013
[quote]
You confused me there. I think you would rather have implied addition if addition had precedence over multiplication:
Re: Why does PEMDAS do multiplication and division before addition and subtraction? - David Persinger (US) - 07-30-2013
I just came across this on youtube. Interesting.
www.youtube.com/watch?v=y9h1oqv21Vs&feature=youtube_gdata
Re: Why does PEMDAS do multiplication and division before addition and subtraction? - Kimberly Thompson - 07-30-2013
Don
Interesting read on the http://mathforum.org/dr.math/faq/faq.order.operations.html
..continued at this url... http://mathforum.org/library/drmath/view/57289.html
SlideRule
Re: Why does PEMDAS do multiplication and division before addition and subtraction? - Thomas Klemm - 07-30-2013
Wouldn't that rather be Re: Why does PEMDAS do multiplication and division before addition and subtraction? - Harald - 07-30-2013
That is true ;)
Re: Why does PEMDAS do multiplication and division before addition and subtraction? - Pier Aiello - 07-31-2013
Guys! This forum is serious, wake up pls! a*bc = ab*c
while (a*b)(a*c)=a^2*bc
(deleted post) - deleted - 07-31-2013
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Re: Why does PEMDAS do multiplication and division before addition and subtraction? - robert rozee - 07-31-2013
this is the clearest of the explanations, and i'd hope would be the end of the matter. but what of the millions (or billions?) of pocket calculators made over the years, telling all who will listen that 1+2*3=9? yes, this is a loaded question; 1+2*3=9 because in the early years of the calculator, it was (from an engineering perspective) much easier to leave out operator precedence. yet long after the engineering issues were banished, manufacturers continued to build calculators that get it wrong. certainly for at least 30 years, there has been no excuse for 1+2*3 to equal anything other than 7.
so why do we still manufacturer and distribute to the mass population calculators that don't follow what we so desperately attempt to teach in schools?
Re: Why does PEMDAS do multiplication and division before addition and subtraction? - Pier Aiello - 08-03-2013
xD No, obviously the formatting options here are not user friendly.
I meant: a Re: Why does PEMDAS do multiplication and division before addition and subtraction? - Thomas Klemm - 08-03-2013
Distributive law of multiplication:
With
With
With
With
With
HTH |