By placing the 2 directly in contact with the () the designer of this problem has therefore ordered that this is "as if" it were in another set of parenthesis. This operation must be performed first before the left to right ordering. So if the problem was written 48÷2x(9+3) I would agree, but when the problem is written 48÷2(9+3) you must solve for 2x() first then move left to right.
You Guys Are Smart wrote:
The letter why, why is 48÷2(12) not equivalent to 48÷2x12?
If "x" is a variable, writing something like 3x/2a is definitely ambiguous. If you were the kind of person who dealt with numbers often (I can see that you're not), you would know that it's common practice to write this without parenthesis as shorthand, when what you really mean is (3x)/(2a). If someone wants to write 3(x/2)a, they'll write 3xa/2.
It's a rule that you learn in 5th grade, but one that you bend later on in life. I'm sure you can think of other rules, like being nice to idiots on the internet, that you've learned early on in life that aren't typically followed due to social conventions?
instead of 3xa/2, it's also common to write 3x/2*a
the question is ambiguous. no mathematician worth their salt would write the expression that way.
it would be either
48/(2(9+3)) = 2
or
(48/2)(9+3) = 288
depending on what was wanted.
There is no direct contact rule that says "2(9+3)" is some kind of higher precedence implied parenthetical grouping different than "2x(9+3)".Operators of the same precedence must be resolved left to right, one at a time.Your instinct is right to agree with "48÷2x(9+3)". You just need to realize that the two equations are not different.
scottdye wrote:
By placing the 2 directly in contact with the () the designer of this problem has therefore ordered that this is "as if" it were in another set of parenthesis. This operation must be performed first before the left to right ordering. So if the problem was written 48÷2x(9+3) I would agree, but when the problem is written 48÷2(9+3) you must solve for 2x() first then move left to right.
I give up. Go ask a mathematician what he thinks.
old and in the way wrote:
the question is ambiguous. no mathematician worth their salt would write the expression that way.
The one that gets a lot of people is simply -3^2
mileageGuy wrote:
The one that gets a lot of people is simply -3^2
This is either 7th or 8th grade level math. I teach 7th grade math. The reason it "gets a lot of people" is because it's rarely used outside of the math courses you take in middle school and high school. I could probably count on one hand the number of times I've had to find the opposite of a square in my daily life outside of teaching.
I have never seen so much FAIL on one thread before.
zip zero nada wrote:
This is a dumb question, as it is ambiguous. You need a set of parentheses to distinguish between (48/2)(9+3) and 48/(2(9+3))
The problem is not ambiguous at all. The rules of the order of operations are standard. If you want to vary from those rules then you have to explicitly alter those rules via nested cells (parenthetics).
You would be right, except of course that the five pages of this thread indicate that you are wrong.
As has been stated numerous times, no reasonable person would ever write a problem this way, just as no one would ever write -3^2. You would always write either -(3^2) or (-3)^2.
The question isn't "is this a reasonable expression" the question is "What does 48÷2(9+3) equal?"
The answer is 288.
A teacher would write a problem this way to teach the rules.
In fact the only reason why you write this in any manner is to teach.
Actually this is the best way to phrase the expression.
You could put parentheses around the 48 and the 2 to clarify what you mean but that would be wasteful.
Why add parentheses when they are not needed to produce the result?
rekrunner wrote:
There is no direct contact rule that says "2(9+3)" is some kind of higher precedence implied parenthetical grouping different than "2x(9+3)".
Operators of the same precedence must be resolved left to right, one at a time.
Your instinct is right to agree with "48÷2x(9+3)". You just need to realize that the two equations are not different.
scottdye wrote:By placing the 2 directly in contact with the () the designer of this problem has therefore ordered that this is "as if" it were in another set of parenthesis. This operation must be performed first before the left to right ordering. So if the problem was written 48÷2x(9+3) I would agree, but when the problem is written 48÷2(9+3) you must solve for 2x() first then move left to right.
Actually the rules of math would say you solve the 2(9+3)as if it is in parenthesis. Just as if you were given an equation as such:
x(x+x^2) would equal x^2+x^3
Whatever else is part of the equation factors in after you have simplified the parenthetic equation.
If you are using a calculator you will not get the correct answer because it does not follow this rule. All you know-it-alls should know that.
Well according to PEMDAS which most people learned in 6th grade math. The answer comes out to 2. However after looking around on google, the answer seems to be 288.
laxmack117 wrote:
Well according to PEMDAS which most people learned in 6th grade math. The answer comes out to 2. However after looking around on google, the answer seems to be 288.
Perfect example of why you don't believe everything you read on google.
This is so ridiculous. The answer is 2 according to PEMDAS because that is what is correct. This is math and that means it follows strict laws. None of this "well I can interpret it like this blah blah blah." No! Just because you think you are smarter than everyone and you think you can argue that a Zebra has spots doesn't mean you are correct.
The answer is 2, not 288!
As an engineer I multiply stuff out all the time and thus have a pretty good grasp on order of operations. The only way to get 2 is to add an extra set of parentheses around the 2*(9+3) term, but the problem doesn't indicate we should do that.
The tipoff that you guys are wrong is that people who actually know math are all telling you that you're wrong. Meanwhile, the other side is arguing based on a middle school mnemonic device.
In fact, I just typed this problem exactly as written into my TI-89. Answer: 288.
No, the math people are saying it is ambiguous. The only people taking a firm stance have no idea what they are talking about.
laxmack117 wrote:
Well according to PEMDAS which most people learned in 6th grade math. The answer comes out to 2. However after looking around on google, the answer seems to be 288.
I think that you're making the same mistake that was pointed out before regarding PEMDAS. PEMDAS isn't parentheses, exponents, multiplication, division, addition, subtraction. It is parentheses, exponents, multiplication and division, addition and subtraction.
I don't see any math people saying it's ambiguous. It isn't ambiguous as written. It's possible to look at it and think the person may have meant to write 48/(2*(9+3)), but since we can't ask the author we have to take the problem at face value. The answer is 288.
It is 288. I thought that the first time I looked at it. I've been teaching algebra for years and not in the US which makes me knowledgable.