48÷2(9+3) = ? --> How smart are you?

[Mr. Magoo]

It has it's moments. 

where did you go to law school?

[coltrane]

dayton

[pellius]

48/2(9+3)
48/2(12)
24(12)
288

Once again you show what an utter retard you are yet you still persist in interjecting your ignorance in subjects you know nothing about. I majored in mathematics at UCLA and you are wrong as you are in just about anything not having to do with drugs and gay sex.

48/2(9+3)
48/2(12)
48/24
= 2

[OneMoreRep]

Once again you show what an utter retard you are yet you still persist in interjecting your ignorance in subjects you know nothing about. I majored in mathematics at UCLA and you are wrong as you are in just about anything not having to do with drugs and gay sex.

Don't insult GAY men that way!

Pilipino Caba?  Bakla Caba?

"1"

[jwb]

Pellius,


Do you consider 48/2(9+3) to be the same question as 48/2*(9+3)?

[jwb]

This doesn't apply to PEMDAS for this equation since there are no radicals but it is food for thought as to whether teachers should just be teaching the correct order of operations and not a learning crutch.

PEMDAS: Terminate With Extreme Prejudice
Wednesday night, I walk into a lecture room for my first evening algebra class of the spring. And what do I see on the chalkboard? Some guy has oh-so-carefully written out the PEMDAS acronym, with each associated word in a column sequence. In fact, that's the only thing he's got on the board after a presumably 2-hour lecture.

So, now it's time for my official AngryMath "Kill the Shit Out of PEMDAS" blog posting.

It's a funny thing, because I'd never heard of the PEMDAS acronym until I started teaching community college math. None of my friends had ever heard of it; artists, writers, engineers, what-have-you, from Maine or Massachusetts or Indiana or France or anywhere. But for some reason these urban schools teach it as a memory-assisted crutch for sort of getting the order of operations about halfway-right (PEMDAS: Parentheses, Exponents, Multiplying, Division, Addition, Subtraction.)

But the problem is, it's only half-right and the other half is just flat-out wrong. Wikipedia puts it like this ( http://en.wikipedia.org/wiki/Order_of_operations ):

In the United States, the acronym PEMDAS... is used as a mnemonic, sometimes expressed as the sentence 'Please Excuse My Dear Aunt Sally' or one of many other variations. Many such acronyms exist in other English speaking countries, where Parentheses may be called Brackets, and Exponentiation may be called Indices or Powers... However, all these mnemonics are misleading if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order addition first, subtraction afterward would give the wrong answer..."

In my experience, none of the students who learn PEMDAS are aware of the equal-precedence (ties) between the inverse operations of multiplication/division and addition/subtraction. Therefore, they will always get computations wrong when that is at issue. (Maybe prior instructors managed to scrupulously avoid exercises where that cropped up, but I'm not sure how exactly.)

Here's a proper order of operations table for an introductory algebra class. I've taken to repeatedly copying this onto the board almost every night because it's so important, and the PEMDAS has caused so much prior brain damage:

1. Parentheses
2. Exponents & Radicals
3. Multiplication & Division
4. Addition & Subtraction

Notice that each operation (after parentheses) is linked with the exact opposite (inverse) in equal precedence. Of course, you have to emphasize that (a) "parentheses" means "stuff inside the parentheses", and (b) in each stage you'll go left-to-right in the expression doing either the operation or its inverse in any order. In contrast, PEMDAS gets parentheses right (and that's pretty much it); but among its flaws are (1) leaving out radicals as the inverse of exponents, (2) overlooking that multiplication & division are tied, and (3) overlooking that addition & subtraction are tied.

An example I use in class: Simplify 24/3*2. Correct answer: 16 (24/3*2 = 8*2 = 16, left-to-right). Frequently-seen incorrect answer: 4 (24/3*2 = 24/6 = 4, following the faulty PEMDAS implication that multiplying is always done before division).

If you're looking at PEMDAS and not the properly-linked 4-stage order of operations, you miss out on all of the following skills:

(1) You solve an equation by applying inverse operations (i.e., cleaning up one side until you've isolated a variable). If you don't know what operation inverts (cancels) another, then you'll be out of luck, especially with regards to exponents and radicals. Otherwise known as "the re-balancing trick", or in Arabic, "al-jabr".

(2) Operations on powers all follow a downshift-one-operation shortcut. Examples: (x^2)^3 = x^6 (exp->mul), sqrt(x^6)=x^3 (rad->div), x^2*x^3 = x^5 (mul->add), x^5/x^3 = x^2 (div->sub), 3x^2 +5x^2 = 8x^2 (considering a shift below add/sub to be "no operation"). If you don't see that, then you've got to memorize what looks like an overwhelming tome of miscellaneous exponent rules. (And from experience: No one succeeds in doing so.)

(3) Distribution works with any operation applied to an operation one step below. Examples: (x^2*y^3)^2 = x^4*y^6 (exp across mul), (x^2/y^3)^2 = x^4/y^6 (exp across div), 3(x+y) = 3x+3y (mul across add), sqrt(x^2*y^6) = x*y^3 (rad across mul), etc. However, the following cannot be simplified by distribution and are common traps on tests: (x^3+y^3)^2 (exp across add), sqrt(x^6-y^6) (rad across sub), etc.

(4) All commutative operations are on the left, all non-commutative operations are on the right (the way I draw it). Also, any commutative operation applied to zero results in the identity of the operation immediately below it. Examples: x^0 = 1 (the multiplicative identity), x*0 = 0 (the additive identity), x+0 = x (no operation), etc. The first example is usually forgotten/done wrong by introductory algebra students.

(5) The fact that each inverse operation generates a new set of numbers (somewhat historically speaking). Examples: Start with basic counting (the whole numbers). (a) Subtraction generates negatives (the set of integers). (b) Division generates fractions (the set of rationals). (c) Radicals generate roots (part of the greater set of reals).

(6) Finally, per my good friend John S., perhaps the most important oversight of all is that PEMDAS misses the whole big idea of the order of operations: "More powerful operations are done before less powerful operations". I write that on the board, Day 1, even before I present the basic OOP table. It's not a bunch of random disassociated rules, it's one big idea with pretty obvious after-effects. (See John's MySpace blog.)

So as you can see, PEMDAS is like a plague o'er the land, a band of Vandals burning and pillaging students' cultivated abilities to compute, solve equations, simplify powers, and see connections between different operations and sets of numbers. If you see PEMDAS, consider it armed and dangerous. Shoot to kill.

[MindSpin]

Once again you show what an utter retard you are yet you still persist in interjecting your ignorance in subjects you know nothing about. I majored in mathematics at UCLA and you are wrong as you are in just about anything not having to do with drugs and gay sex.

48/2(9+3)
48/2(12)
48/24
= 2

You majored in mathematics?  That's awesome.  Anyone who came up with 288 just got pwn3d!!!

[tbombz]

Once again you show what an utter retard you are yet you still persist in interjecting your ignorance in subjects you know nothing about. I majored in mathematics at UCLA and you are wrong as you are in just about anything not having to do with drugs and gay sex.

48/2(9+3)
48/2(12)
48/24
= 2

 

i was responding to smm=

But how does that change anything? The numbers between parenthesis will be computed first always. So the answer is always 2. It never gets to 288.

SUCKMYMUSCLE


and right after that i posted=

the reason why it is two is because multiplication and division have equal priority in simplifying expressions, and thus you have to work from left to right, with the division happening before the multiplication, but after the addition that was done in the parenthesis.

but congragulations for majoring in math. a subject with virtually no practical application  for 99% of people including you beyond its 10th grade level.

[el numero uno]

.

[OTHstrong]

Once again you show what an utter retard you are yet you still persist in interjecting your ignorance in subjects you know nothing about. I majored in mathematics at UCLA and you are wrong as you are in just about anything not having to do with drugs and gay sex.

48/2(9+3)
48/2(12)
48/24
= 2

I do not feel like being ignorant towards you in any way, but your dead wrong. the way you have it written above will give you 2 but the way it is written in the thread title will give you 288, there is a difference in the 2 equations. the calculator proved it so your major is more proof then a calculator...ah no.

[tu_holmes]

Implied parenthesis is the issue... It's really a mal-formed equation.

[OTHstrong]

.

The picture of the calculator and now this proves 288 the people with the answere 2 haven't showed us jack. thread closed

[pellius]

i was responding to smm=

But how does that change anything? The numbers between parenthesis will be computed first always. So the answer is always 2. It never gets to 288.

SUCKMYMUSCLE


and right after that i posted=


but congragulations for majoring in math. a subject with virtually no practical application  for 99% of people including you beyond its 10th grade level.

LOL! Expertise in mathematics is a requirement in any technical field and how I am able to work as an engineer.

What UC school did you claim to be accepted to and what is your major?

[dr.chimps]

LOL! Expertise in mathematics is a requirement in any technical field and how I am able to work as an engineer.

What UC school did you claim to be accepted to and what is your major?

*Gets popcorn*     

[pellius]

Pellius,


Do you consider 48/2(9+3) to be the same question as 48/2*(9+3)?

Yes, but the "*" is superfluous. Strictly speaking it should be written 48/[2(9+3)] but, like many things, such as in grammar, it is just understood.

[Fury]

LOL! Expertise in mathematics is a requirement in any technical field and how I am able to work as an engineer.

Not only that, but businesses love mathematics majors. If they can handle advanced mathematics then they're usually more than capable of handling anything a firm can throw at them. But it's not "practical" to Getbig's wunderkind.

[Mr. Magoo]

*Gets popcorn*     

x2

[jwb]

Everyone needs to take a deep breath.

We can all agree that 48÷2(9+3) is a lousy way to ask this question.

From reading around some more I have found out that people have been taught two different conventions.

And these different conventions affect what you think you are being asked by 48÷2(9+3)

To the PEMDAS crowd a/bc is the same as a/b*c

To the other crowd a/bc is the same as a/(bc) since bc is not the same as b*c at least to them.

Why have conventions changed and therefore older calculators give 2 and newer ones give 288?

It appears teachers didn't think kids were bright enough to remember the correct order of operations which is

1. Parentheses
2. Exponents and Radicals
3. Multiplication and Division
4. Addition and Subtraction

and wanted to use PEMDAS even though it leaves out radicals and doesn't make it clear to all about equal weighting of MD and AS.

The simple fact is there is no way that half of all the millions of people debating this online are doing WHAT THEY WERE TAUGHT incorrectly.

so what is the answer? what is the question?

[pellius]

I do not feel like being ignorant towards you in any way, but your dead wrong. the way you have it written above will give you 2 but the way it is written in the thread title will give you 288, there is a difference in the 2 equations. the calculator proved it so your major is more proof then a calculator...ah no.

Ha! Ha! Touche my friend, touche! In studying mathematics the "÷" is so seldom used (I don't even have the symbol on my lap top and had to copy and paste it from the original post). The "/" symbol for division is so ingrained in me that even when I see "÷" I still think "/". That's why I copied it that way. I doubt it would ever be written as it written in the original post in real life. My windows calc also doesn't have the "÷" symbol.

[kiwiol]

this thread is still going??

It's joined the ranks of unsolvable questions in Getbig, like "Bear vs Gorilla" and "Dorian vs Ronnie"

[MindSpin]

I love that this thread is 11 pages...lol.

[OTHstrong]

48÷2(9+3) IS THE SAME AS 48÷2X(9+3) WHICH IS THE SAME AS 48   1  (9+3):
                                                                                                   ---X--X-------
                                                                                                    1    2     1

48X1X(9+3)     48X12    576
-------------- = ------- =  ----  = 288
 1X2X1                 2         2

WE CANNOT ASSUME WE MUST MULTIPLY THE 2 WITH THE (9+3) FIRST BECAUSE WE ARE DEALING WITH MATH.. ITS EITHER BLACK OR WHITE...WRONG OR RIGHT WE HAVE TO CALCULATE THE PROBLEM EXACTLY THE WAY IT IS GIVEN...FOR THE ANSWER TO BE 2 IT MUST READ 48÷[2(9+3)] AND BASED ON ORDER OF OPERATIONS WHATS IN THE BRACKET MUST BE CALCULATED FIRST BUT SINCE THE PROBLEM WAS NOT WRITTEN THAT WAY PROPERS ORDER OF OPERATIONS MUST BE FOLLOWED AND THE ANSWER IS UNDENIABLY 288

[jwb]

Onetime were you taught about implicit multiplication?

[OTHstrong]

Onetime were you taught about implicit multiplication?

No, I'm not familiar with that term.

[jwb]

No, I'm not familiar with that term.

That is my point it isn't taught anymore because the conventions have changed.

To people it was taught to 48/2(9+3) is not the same as 48/2*(9+3) but it is now considered the same.

Does that affect the answer? No it doesn't provided you fit the question to the convention.

what you see as 48/2(9+3)=288 would have been written as