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View Poll Results: 48÷2(9+3) = ???

288


134 
46.05% 
2


157 
53.95% 


07172012, 12:30 PM


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PEMDAS is not the correct order of operations, it is an acronym taught in school to help kids and has one major problem. It gives multiplication precedence over division and addition precedence over subtraction when they actually have equal value in the standard order of operations.
"Please Excuse My Dear Aunt Sally" = Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
Whereas standard order of operations is Parenthesis, Exponents, Multiplication and division(left to right), addition and subtraction(left to right).
Order of operations is not new, it's just that since computers/internet have become so common more and more people/places teach it by this standard whereas maybe in the past all areas were not equal as far as knowing the rule exactly correctly. That's JMO I guess, not sure why else you wouldn't have been taught standard order of operations when you were in school.
PEMDAS is not correct. It is close but has a mistake in it.
Implied multiplication(what you did to solve for 2) is not really wrong, but it does not follow the standard order of operations. Now it's not like jesus came down from the heavens and said everyone will obide by the standard order of operations, so what's "right" and "wrong" really depends on what you were taught and how you think it should be solved. Most of the math community around the world abides by the standard order of operations, which would give an answer of 288. Some people use implied multiplication which isn't wrong but also doesn't abide by these rules, so it just depends what is "right" and "wrong" in your opinion really.
If the equation was written more clearly then we could see what the person was trying to communicate.
It's somewhat open to interpretation, and much depends on how the equation is written. Think of it this way, if some one simply asked you "what is the meaning of the word post?" you might answer "an object, usually wood, that is buried in the ground and holds something up such as a fence" whereas I might answer "the act of mailing something such as a letter". The person who wrote the question didn't give enough information for us to 100% for sure say that our answer matches their intent. So it's open to interpretation.


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07172012, 01:21 PM

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Quote:
Order of operations is not new, it's just that since computers/internet have become so common more and more people/places teach it by this standard whereas maybe in the past all areas were not equal as far as knowing the rule exactly correctly.

There again the age difference comes into play  computers (as we know them today) did not exist when I was going to school & when I started college you were not allowed to have a calculator in class. Later that changed & at the 2nd univ. I went to you'd better darn well have a calculator or you couldn't keep up! But the professors' view was that a calculator only helped your speed  i.e., the calculator wasn't going to solve an equation for you that you didn't already know how to do on paper.
And I never heard of the "PEMDA Rule" before today  I just happened across it by copying the original equation we've been talking about & pasting it into the Google search bar  than all kinds of stuff came up!! Again, we were always taught to do the unfinished part of an equation 1st, then you'd end up with only one thing left to do, be it add, subtract, multiply or divide.
You'd go left to right if there are unfinished calculations on both sides of the operator, finishing the left side, then the ride side, then apply the operator between them & the answer is always the same that way. For example;
(3 x 6) ÷ (4  2) =
9 ÷ 2 =
4.5 (or 4 1/2)
And since we used to do a lot of fractions, you'd have to be able to write an equation both ways  my example would be
(3 x 6)
_______
(4  2)
or
9
__
2
= 4.5
or,
1
__
16
and 1 ÷ 16 mean exactly the same thing.
I also happened across an article which evidently started the whole deal  with a couple photos showing 2 calculators of the same brand, but different models, coming up with the two different results, 2 & 288. So it boiled down to what order of operations had been programed into the calculators!
But going back to doing it on paper (before calculators & computers existed), you'd always come up with 2 as the answer.


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07172012, 01:35 PM


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Quote:
But going back to doing it on paper (before calculators & computers existed), you'd always come up with 2 as the answer.

Not if you follow order of operations.
Your examples are different from the initial equation. They don't have division and multiplication next to each other.
How would you solve this:
4÷9÷2*7 = ?
Where's the "unfinished" part here? Would you rewrite that as:
4
_______________________
9
_________
(2*7)
which = ~6.25
or:
4
_________
9
_______________________
(2*7)
which = ~0.03
In this case, without order of operations telling you to go left to right you could do it either way. Which way is right, you tell me? This is what makes implied multiplication "wrong" IMO.
Bottom line is both 2 and 288 are "right" depending on what you want to think is right, but only 288 follows order of operations which is what I believe the question is really asking.


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07172012, 01:36 PM


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Well the post screwed up the way I wrote that but in the first example 4 is the numerator and in the second example 4/9 is the numerator.


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07172012, 02:45 PM

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Quote:
Originally Posted by snrusnak
Well the post screwed up the way I wrote that but in the first example 4 is the numerator and in the second example 4/9 is the numerator.

LOL !! Sometimes it is easier to write it with pencil & paper!
Now let's see if I can answer your question . . .
Quote:
How would you solve this:
4÷9÷2*7 = ?
Where's the "unfinished" part here?

Nothing in quotes, with an exponent, square root, etc. (unfinished) to do 1st in that one, so I'd just go in the order written, solving as I went:
4 / 9 = .444 (to infiniti) / 2 = .222 (to infiniti) x 7 = 1.555 (to infiniti). Which is, of course, why you'd want to use quotes  there wouldn't be any doubt what was meant if it was written
(4÷9) ÷ (2 x 7), or
(4/9) / (2*7) (same), or
4÷(9÷2)7, or
(4÷9)÷2 x 7,
but of course you'd come up with a different result depending where the parentheses were & what was inside them.
Also, every problem I can remember seeing along these lines could be boiled down to "find the value of x." You may have to figure out what the values of a, b, c, etc. are 1st & perhaps in different orders, but your final answer would always be x. And there would be only one correct value for x.
Now here's one I remember from clear back in grade school:
.999 (with a line on top of the 9's indicating on to infiniti) = 1.
Is that a true statement? .999 = 1
Most everyone would automatically say no  the values are very, very close, but not exactly the same.
But wait a minute!
1/3 + 2/3 = 3/3, which = 1.
1/3 = .333
2/3 = .666
________
3/3 = 1 = .999
So it is a true statement! Or is it?
You can do that with any set of fractions which represent an irrational number; 2/7ths plus 5/7ths, 11/13ths + 2/13ths & so on.
So does .999 = 1, or not?


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Last edited by ArtNJr; 07172012 at 02:49 PM.

07172012, 02:50 PM


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Quote:
but of course you'd come up with a different result depending where the parentheses were & what was inside them.

Yeah that was my point, without a standardized order of operations everyone would do this problem differently...


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07172012, 03:09 PM

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Quote:
Originally Posted by snrusnak
Yeah that was my point, without a standardized order of operations everyone would do this problem differently...

I came across an article on that which you may be interested in  what's the history behind order(s) of operations?:
http://mathforum.org/library/drmath/view/52582.html


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07172012, 07:28 PM


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Well if i could i would change my vote. The way it is written and order of operations it is 288. I'm in college calculus 2 and that even tripped me up because the teachers usually write the equations more specific. If the equation was written 48/(2(9+3)) then the answer would be 2 but the way it is written it is the same as (48/2)*(9+3) which would equal 288.



06182013, 08:18 PM

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The way I learned math was PEMDAS and you worked parentheses till they are out of the equation. 2(12)=24. Then you worked the remaining problem in this case as regular division. 48÷24=2


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07102013, 10:05 PM

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came up with 2, been years since i have had to think about anything like this.



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