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
And if you do use the distributive property, why distribute 2 instead of 48/2?
48/2 is the term that precedes the (9 + 3), isn’t it?
Gee, I don’t know. The speed limit doesn’t apply while I’m sitting on my couch. Doesn’t mean I think speed limits don’t exist.
Where in the order of operations does it say that you have to apply the distributive property before doing mult or div?
It doesn’t. You’re mixing apples and oranges.
The distributive property exists to help simplify algebraic expressions, not to do simple math.
Regardless, I’ve already shown how applying the distributive property properly (that is, distributing 48/2 to both addends) yields the proper answer.
You choose, for no reason, to assume that the “/” makes everything to its right part of its denominator, then you insist that only the “2” needs to be distributed.
That’s just flat wrong.
If I asked what “10/2 + 3” is, what would be your answer?
You don’t have to use it if you are willing to accept the wrong answer.
You have to distribute the 2 to the 9 and the 3. Do that and the result is 24.
48 ÷ 24= 2
To get the result you want, the problem would have to be expressed as:
48 ÷ 2 x (9+3)= 288, but that is not the problem.
The problem is 48 divided by 2(9+3); it is not 48 divided by 2 and then that result being multiplied by 12.
The numerator is 48 and the denominator is 2(9+3)n or 24.
Write it down on a piece of paper and your will see the answer is 2.
I only meant that for programming purposes.
You are simply wrong. The division operator does not automatically make everything to its right part of the denominator.
What is 9 / 3 * 3?
Consulted my Presidential Award winning Calculus teacher wife. Please Excuse My Dear Aunt Sally. Multiplication before Division.
Answer is 2. TI has a problem. She buys molto calculators from them and is now on the warpath.
You teacher wife needs to go back for a refresher. Multiplication and division have the same priority.
http://en.wikibooks.org/wiki/Algebra/Order_of_Operations
I agree with that observation. A computer can’t really be programed to understand the distributive property and if it could be; it’s probably simpler to just insert the extra parentheses.
BING images for 48÷2(9+3): http://www.bing.com/images/search?q=48%c3%b72(9%2b3)&qpvt=48%c3%b72(9%2b3)&FORM=IGRE#x0y0
Go to the link in post #528 and scroll down to the illustration of a calculator screen and you will see that you are wrong.
Why do you choose to argue with an award-winning math instructor?
Of course it could be. But it's entirely irrelevant to this problem.
The older TI calculator followed the "juxtaposition" theory. That means the times 2 outside the parentheses (without an explicit *) was considered a higher priority than any regular mult or div.
The newer TI corrected to follow the established rules and not this juxtaposition theory.
Distribution has nothing to do with it.
No, it’s not.
I swear I saw something that looked like 48/2(9 + 3).
If you don’t know what the “/” operator is, that would explain a lot. It doesn’t magically make everything to its right part of a denominator unless you explicitly tell it to by adding parentheses.
I can’t help you any further than that.
Prior to calculators, any competent 4th-grader could easily solve this problem and the answer would be 2.
Go and continue to wallow on your ignorance. If you could not follow the example at the link which I had copied in post #429, you are beyond help. And to claim you are more lnowledgable than an award-winning math teacher is just plain stupid.
She says that the tie goes to the multiplication, not the division. Someone has to win, and the convention is that multiplication wins. That situation was forced upon the engineering community by linear processors. It’s not an ‘order’ if an operation has the same priority as another.
Her words, “Do you really want to leave an equation open to interpretation if you are trying to put a man on the moon safely and get them back? AOS was created to minimize the need for interpretation. Clearly, TI has forgotten that.”
What enforced PEMDAS was the advent of computerization. M comes before D because a linear processor can’t process the operations simultaneously.
What used to aid PEMDAS was IOWA (In the Order in Which they Appear). Problem with that was subroutines and recursion. Calls to subroutines can provide results that shift the order in which important resultants can appear - sometimes early in one use of a subroutine, and later in another.
PEMDAS works because there is one unambiguous rule governing AOS, and AOS was created to avoid this VERY situation. M before D.
It’s clear people are still using PEMDAS and IOWA together, including TI. The CRC tables aren’t clear on AOS, but they also don’t mention IOWA.
You’re giving me wikibooks as a definitive source?
I’ve asked two of my professors so far(one has math and compsci masters degrees, other has a PhD in physics) and both have said 288. To be fair, the physics PhD did recognize the ambiguity between whether to do the division or multiplication first.
Nonsense. You don’t go do all the multiplication first, then go do all of the division. You go from left to right. IOWA, if you must.
Does she agree that 48/2 is the same as 48*0.5?
Then what makes 48*0.5*(9 + 3) = 2?
Ask your wife if addition now trumps subtraction as well?
Is 1 - 1 + 1 = -1?
Is 9 / 3 * 3 = 1?
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