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
see my earlier post. great minds thing alike..
see #520. we are not alone...
48/2(9+3)
48/2(12)
48/24 [oops, broke left to right rule]
2
You arbitrarily turned 48/2(9+3) into 48/(2(9+3)), which breaks associative rules. You also have unbalanced parenthesis in your equation.
The correst parse:
48/2(9+3) parsed from left to right is
24(9+3)
24(12)
288
You are incorrect. The correct order of operation is:
terms inside brackets
exponents and roots
multiplication AND division
addition AND subtraction
In the absence of parentheses, multiplication and division are performed left to right.
So it would be:
48/2(9+3)
48/2 * 12 <-— this is now left -> right!
24 * 12
288
See post 401. This is from PurpleMath.com and explains what happens with the parentheses. Using their logic, the correct answer is 2.
Sorry, that would be post 429, not 401. 429 was in response to 401.
Linky-dinky-doo to the purplemath.com reasoning behind why the answer is 2. The equation in question (from post 429), and the logic behind it, is at the bottom of the page.
The “juxtaposition” theory does not seem to be very well accepted, given how all of the computer programs, etc. don’t use it.
If someone is really following that theory, I can accept their answer. It’s the rest of the nonsense and ignorance used to get to “2” that is questionable.
Did you read his final note? His way breaks the order of operations in my opinion.
I'm pretty much in agreement that it's how you learned that makes the difference.
In school, I would have come up with 2, as that is how I learned it from my Algebra teacher - himself a math geek.
In programming, I would have come up with 288. However, if I wanted to come up with two as a programmer, I would have clarified the equation with an extra set of parentheses around the 2(9+3) - (2(9+3)).
The real issue is that the equation should have been better clarified, and if I got the wrong answer (depending on if the instructor was looking for 2 or 288), I would easily be able to state my case for the opposite, using cites from this here interweb thingy.
You mis-stated the original problem. There was no multiplication sign in the original problem. 2(9 + 3) is one number and that number is 24.
48 ÷ 2(9 + 3) =
48 + 24 = 2
You must use the distributive property prior to division. The 2 is distributed to the 9 and 3.
No reason for you to not accept the obvious.
And those who see “/” as a mathematical operation between expressions on either side of it.
The former force implied parentheses into their evaluation.
The latter do not.
I think both sides are forcing an implied parentheses into their evaluation.
The 288 crowd are implying a parenthesis like this:
(48/2)(9+3)
The 2 crowd are implying a parenthesis like this:
48 / [2(9=3)]
The mathematical expression is written ambiguously.
Where is the rule stated that you must use the distributive property?
Can’t you add 9 and 3 together? That resolves what is inside the parentheses. Then you go on to division and multiplication.
An extra set of parentheses is not needed because of the distributive property must apply prior to division.
Thank you for that and also see my posts #469 and #440 in this thread.
I guess the Windows-centric worldview leads to that confusion since the backslash character in Gatesware used for the directory component separator. Real operating systems (and URLs) use the proper slash (or virgule) as set forth from the beginning of The Epoch.
No, if you follow the rules of the order of operations, as stated all over the internet and without the “juxtaposition” theory, there is no ambiguity. Try it.
Do what is in the parentheses. 48/2(12)
Resolve left to right, since mult and div have same priority
24(12)
288
I don’t need to add any implied parentheses, just follow the rules.
Purplemath.com is just one source.
Someone also posted that if you go to algebra sites and enter the problem exactly as presented, the answer is 2.
If you change the problem to 48/2(9+3), the answer is 288. If that was indeed the problem, the answer is clearly 288, but that is not the problem.
Where is it written you must use the distributive property? When you can simply add 3 and 9?
The distributive property is one of the rules and you can’t pretend is doesn’t exist. If it doesn’t apply in a case like this, why have it at all?
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