48÷2(9+3) = ?

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Originally Posted By: Hokiefyd
I've seen things like 2(a+b) a lot. You distribute the 2, and it becomes (2a+2b). In this case, you have 2(9+3), and that becomes (2*9 + 2*3), or (18+6), or 24.

I was always taught to distribute first, if distribution is part of the expression. So you can distribute the 2 first and evaluate that, or you can do the 9+3 first and then evaluate the 2(12) before the division; either way, you end up with 2 as an overall result.


I agree and so do my 2 college students taking college algebra. My oldest daughter is going to ask her professor and also has sent an email to a couple of friends who are "math geeks" at UCLA. Stay tuned!
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Originally Posted By: d00df00d
Originally Posted By: Drew99GT
Originally Posted By: d00df00d
It's a matter of how you see what is presented.



No it's not. If you follow order of operations, you'll get the correct answer every time. Math isn't subjective. It's not "how you see it".

Sorry, I guess I wasn't clear. I didn't mean to say the correct answer was a matter of perception. I was trying to point out the reasons for why people were getting different answers.


I hear ya. The problem is, you're not supposed to use the division symbol when doing algebra. You're supposed to use the / symbol. If you use the division symbol, it reads 48/(2(9+3)) which = 2. If it's 48/2(9+3), it's 288.
 
Originally Posted By: Hokiefyd
I've seen things like 2(a+b) a lot. You distribute the 2, and it becomes (2a+2b). In this case, you have 2(9+3), and that becomes (2*9 + 2*3), or (18+6), or 24.

I was always taught to distribute first, if distribution is part of the expression. So you can distribute the 2 first and evaluate that, or you can do the 9+3 first and then evaluate the 2(12) before the division; either way, you end up with 2 as an overall result.


If you are going to do it that way then you should do:

(48/2*9 + 48/2*3)

You cannot only take 2 into the distribution. You should take the 48 as well.

a/b*(c+d) = a/b*c + a/b*d
 
Great thread. Especially since there's been so much confidence in the first 4 pages, in both answers. I suspect there never will be agreement on the "correct" answer, especially since two Texas Instruments calculators are each deliberately programmed to evaluate this expression differently. This is all contrary to a previous post or two about math being only black and white with absolutely no room for interpretation. In some respects, math is as much of a language as Greek or Latin is.
 
Originally Posted By: Hokiefyd
Great thread. Especially since there's been so much confidence in the first 4 pages, in both answers. I suspect there never will be agreement on the "correct" answer, especially since two Texas Instruments calculators are each deliberately programmed to evaluate this expression differently. This is all contrary to a previous post or two about math being only black and white with absolutely no room for interpretation. In some respects, math is as much of a language as Greek or Latin is.


Math does not and cannot have different interpretations. One of the Texas Instruments calculator was designed incorrectly or it's a hoax.

Fortunately, Microsoft doesn't hire illiterates to design their software. Excel formula =48/2*(9+3) gives the right answer 288
 
Originally Posted By: Drew99GT
Shouldn't the correct order of operations be 48/2 which equals 24. 24x9 = 216. 24x3 = 72. 216 + 72 = 288. That's how I was taught to do it!



that's different...right answer...but process???
confused.gif
 
Originally Posted By: Astro14
Originally Posted By: Drew99GT
Shouldn't the correct order of operations be 48/2 which equals 24. 24x9 = 216. 24x3 = 72. 216 + 72 = 288. That's how I was taught to do it!



that's different...right answer...but process???
confused.gif



It got me through college calculus with an A! Got me through some tough accounting classes!
lol.gif


That's exactly how we were taught to do it in high school algebra.
 
Originally Posted By: Hokiefyd
This website:

http://www.purplemath.com/modules/orderops2.htm

Indicates that you'd multiply the brackets by the 2 first, then divide 48 by that, resulting in 2.

Quote:

Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.
16 ÷ 2[8 – 3(4 – 2)] + 1
= 16 ÷ 2[8 – 3(2)] + 1
= 16 ÷ 2[8 – 6] + 1
= 16 ÷ 2[2] + 1 (**)
= 16 ÷ 4 + 1
= 4 + 1
= 5

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by".


OVERK1LL, this is how I read your rule earlier, and how I would have completed the formula as well. I get 2 from the OP's formula.


It's not a matter of "your" rule or not.

In order, PEMDAS, work the Parens, then the Exponents, but Multiply and Divide are equal, so you work them L - R and Add and Subtract are equal, so you work them L - R...

you get 288.

Unless...is there a Hokie approach? My son is a Hokie...we might have to talk!
grin.gif
 
In the example where you distribute the polynomial, that's fine, but it's simple. When you have a complex polynomial (or arithmetic expression) you have to use the order of operations....
 
Originally Posted By: CivicFan
Math does not and cannot have different interpretations. One of the Texas Instruments calculator was designed incorrectly or it's a hoax.


It's not a hoax. The picture was posted with this exact expression, and the webpage I found that explains that TI calculators will evaluate expressions like this differently corroborates BigMike's photo he posted. Again, from that website:

Quote:
In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently.


If it was absolutely black and white, there would be no "general consensus" and teachers wouldn't view things differently.

Tons of discussion on the same expression here:

http://forum.bodybuilding.com/showthread.php?p=659753333

Many people think it's 288, and many think it's 2. Heck, the thread title is "Conclusive Proof that the answer is 2".
 
Glad I saw this thread because I never liked the implied multiplication sign immediately outside the parens,
and now I can claim its because of the ambiguity and not OC disorder. I even know what to call it now: "multiplication by juxtaposition".

Maybe the solution to all this is for everything to be written in postfix notation.
lol.gif
 
Originally Posted By: Astro14
It's not a matter of "your" rule or not.


In speaking to OVERK1LL, I said "your rule" in reference to the way he described the order of operations. I read it differently than he meant it. And interestingly, the way I read "his rule" is the way I was taught to do it.

Proud graduate of the Fairfax County Public School system.
 
Originally Posted By: bigmike
I found this pretty funny:

headasplode.jpg



Where did you find this image? Even the name of the image is funny, it is called "headasplode"! I did not know "asplode" was a word :-)
 
Originally Posted By: Hokiefyd
Even Physics forum members disagree:

http://www.physicsforums.com/showthread.php?t=488334


Now that doesn't surprise me!

Pecking order of the sciences:
Biologists answer only to Chemists.
Chemists answer only to Physicists.
Physicists answer only to Mathematicians.
Mathematicians answer only to God.

Sorry... some math humor from a mathematician.
 
Originally Posted By: addyguy
The fact that there are people who CAN'T get the right answer for that equation scares me!

....c'mon, that is pretty freaking basic math!

:P


Originally Posted By: addyguy
EXACTLY....there ISN'T another way to see this...there is one way to do this correctly!

Geeeze, school standards have slipped, if people has been taught that there is more than one way to see this!


OK addy, you've shared your thoughts on the thread but not on the answer?
grin.gif
 
Originally Posted By: CivicFan


If you are going to do it that way then you should do:

(48/2*9 + 48/2*3)

You cannot only take 2 into the distribution. You should take the 48 as well.

a/b*(c+d) = a/b*c + a/b*d


I was going to say you are wrong but then realized that the notation of writing a/b*c as a "linear" expression (that is to write in a single line on a type writer without subscript or superscript is inherently ambiguous. Often, if I am doing this on the calculator, I will enter it as "a / b / c" if I am treating it as "a/bc". If you think about it, "a/bc" is ambiguous too and I should have said "a/(bc)". If I really meant "a / b * c", then I should have written it as ( a / b )* c

Being software engineer by trade, when you write similar construct, you write it so that there should be no question about misinterpretation. There are cute ways of saving some keystrokes using "C" language but if your aim is to write maintainable program, you learn NOT to use them. There are times when you might be the guy who ends up having to fix that code and you really don't want to end up with "What was I thinking!!"

- Vikas
 
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