Posted on 04/12/2011 1:32:09 PM PDT by grundle
Texas Instruments TI-85 says:
48÷2(9+3) = 2
But Texas Instruments TI-86 says:
48÷2(9+3) = 288
That’s cause you are begging the question. Let me show you:
48/2(9 + 3) = 288 — original
48/x (9+3) = 288 — substitute x for 2
48(9 + 3)=288x -— multiply both sides by x
48(12)=288x -— do the parenthetical addition
576=288x — multiply 48 and 12
2=x -— divide both sides by 288
QED
So that makes for at least two award winning calculus gals telling Dave he doesn’t know what he is talking about. Heck, I only got all As in college calculus, but I suppose Dave is smarter than all of us.
Keep reading.
You are misleading yourself.
I can't help but wonder how many of the 2ers are also little endian advocates and if the 288ers are on the big endian side.
Of course, we must also consider that although three's company, two's complement.
...now running quickly away and ducking for cover!
You are not smarter than a 5th-grader.
At least I can read well enough to know grateful was on the 288er side. She said she would agree it was equal to 2 IF the parentheses that the 2ers imagine were actually there.
The other teacher believes that multiplication is always done before division, which is simply ignorant. She is about as far away from my child as she can be, so I am not worried.
SeaHawkFan: Since 2007-04-16
SoothingDave: Since 1998-06-04
The seniority system...it ain't just fer unions! :-)
288
Not if I stated it without parenthesis. If I say parenthesis, they would have to use the PEMDA rule.
You’d be wrong again. I first signed up under a different screen name on 1998-04-17.
Can’t say if SoothingDave had an earlier screen name, but based on your assumption (which could be wrong), I would be the winner.
I was at the MFJ on 10-31-98 and carried the Washington State Flag during the opening ceremony.
Okay, go ahead and use the parentheses. You would say: “Forty-Eight divided by two times open-parentheses twelve close parentheses equals?.”
I guess you are claiming that any number attached to the immediate outside of a parentheses with a multiplier or divisor is done before all other multipliers or divisors. Is that what you're stating? What exactly is that rule called? It's not the P in PEMDA because that's for components inside the parentheses.
288 is the correct answer.
I’m a theoretical physicist and deal with stuff like this all the time. Your math problem is too ambiguous and needs to be re-written for clarification.
However, that being said, the correct order of operations for solving this is “(BP)(ER)(MD)(AS)” (Be PERMeD AS):
That is to say:
1) Brackets and Parenthesis are solved first, followed by;
2) Exponents and Roots, followed by;
3) Multiplication and Division, and finally;
4) any Addition and Subtraction left over.
Once all those steps have been followed, the resulting equation is solved left to right.
Therefore, the proper procedure for solving your ambiguous equation would be step 1, followed by step 3:
48÷2*(9+3) = 48÷2*(12)= 48÷2*12 = 24*12 = 288
Because multiplication and division hold equal weight in the sequence BP ER MD AS, anyone who comes up with an answer of 2 is falling into the trap of not solving sequentially from left to right once the problem in parenthesis (9+3) has been solved.
Obviously, the TI 85 was programmed incorrectly and added more weight to solving multiplication before solving division while the TI 86 was correctly programmed to give equal weight to multiplication and division so as to correctly solve in a left to right fashion.
Cheers
LOL, this has been a fun thread to watch and participate in.
So, let me throw another loop in, or rather, an observation:
In my office I have two admins, both 20. One is uber smart in mathematics and one is average, like me. The uber smart guy said straight up linear equation it equals 288, but the use of the (divide by symbol not the slash) made it appear as a fraction (nominator divided by denominator), he said the equation was "crap" because it wasn't defined clearly.
Now my other admin, she took one look at it and said 2. That they were still teaching in school that multiplication functions come before the division functions, so she had no idea that they were considered "equal weight" and to process from left to right. (This is in Houston, TX btw)
We all agreed that the use of one extra parenthesis would have made a HUGE difference.
So I did a google search at lunch because I wanted to see what else was being said about the equation... the hits were many and varied. So much fun to read through them. That being said, I can't argue the logic of the 288ers, but based on the way the equation was written in the title of the thread, and they way I was taught many years ago, my answer is still 2. Nominator divided by denominator, with a desperate need for one extra set of parenthesis.
:-)
48÷2*(9+3) = 48÷2*(12)= 48÷2*12 = 24*12 = 288
DoctorBulldog is from Missouri, the "Show Me" state. Q.E.D.
Because the answer is 288 because the math problem is incorrectly written which leads to an ambiguous answer.
Besides, even your award-winning math instructor admits on the same page that you link that his method is not the end all be all:
“please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!”
Ergo, 288!
:)
Cheers
A smilie? Really? I'm stuned!
Can't you tell this is a hughly series thread? Has there been anything even remotely approaching humor in a jugular vein or lightheartedness in this ponderous discussion of massive import with the greatest minds of the (known) universe participating.
"Academic politics is the most vicious and bitter form of politics, because the stakes are so low." -- Sayer's Law
they were still teaching in school that multiplication functions come before the division functions, so she had no idea that they were considered "equal weight" and to process from left to right.
This is what happens when teachers' colleges teach pedagogy and don't teach the fundamentals.
That being said, I can't argue the logic of the 288ers, but based on the way the equation was written in the title of the thread, and they way I was taught many years ago, my answer is still 2. Nominator divided by denominator, with a desperate need for one extra set of parenthesis.
Unfortunately, with the way single-line expressions are parsed, you do indeed need those parentheses if you want the answer to be 2.
It's not something I made up, it's how every programming language I've ever seen has parsed operators.
LOL. (nods) Oh absolutely, hughly series thread.
And what's worse, is that I see the logic, get the logic, then I remember how Sister Mary in school taught it and then my brain exploded.
Although with using the PEMDAS method, my female admin was taught that because M came before D, then the multiplications come first. So that is still being taught in schools, or at least taught here.
Now the funny visual aide that Sister Mary taught us back in the OLD days was this:
2(9+3) should mean that you implicitly assume (yeah I know, assume) that each should have a parenthesis around them, making that part of the equation (2)(9+3) and the )( looks like an X which is (was) the symbol for multiplication that way you KNEW that you should multiple 2 by whatever result was in the other parenthesis.
It's enough to make a girl want a martini.. oh wait, I already poured myself one. :-)
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