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I didn't want to read the whole thing, but as an engineer, here's my thoughts.
48÷2(9+3) = 2
The reason...
÷ = What's to the right of it is the denominator
(9+3) is assumed to be in the denominator because it's shown multiplying 2 in a way that is commonly used in algebra 2(9+3).
If (9+3) were in the numerator, the equation should have been written this way
48(9+3)÷2 or this way (48÷2)(9+3)
As an engineer, I've taken LOTS of math classes.
and you are never going to find a book that shows that equation in that way implying that
48÷2(9+3) = (48÷2)(9+3)
Actually it's 288. It's a very simple elementary problem. You do what's in parentheses first, then divide the other, then multiply 24(12)... VERY simple. Let's not argue over common sense.
By doing that, you kicked the (12) that was multiplying 2(12) to the numerator.
48÷2(9+3) = 48÷2(12) <= At that point, there's nothing saying that (12) is in the numerator.
Instead, by saying that (12) is multiplying 2, it says that it is in the denominator.
By doing that, you kicked the (12) that was multiplying 2(12) to the numerator.
48÷2(9+3) = 48÷2(12) <= At that point, there's nothing saying that (12) is in the numerator.
Instead, by saying that (12) is multiplying 2, it says that it is in the denominator.
Hmmm, I think you could have just said multiplication before division... then it would be 48 / 2 x 12. I forgot order of operations. The answer is 2 then.
Hmmm, I think you could have just said multiplication before division... then it would be 48 / 2 x 12. I forgot order of operations. The answer is 2 then.
Multiplication does not come before division -- they are in fact the same operation. (More accurately, one is the inverse of the other; but one does not take precedence over the other.)
Rather, what's causing most of the commotion is the use of the "÷" symbol. There's a reason why this symbol is not used in algebra. This thread is a perfect illustration of that reason.
I didn't want to read the whole thing, but as an engineer, here's my thoughts.
48÷2(9+3) = 2
The reason...
÷ = What's to the right of it is the denominator
(9+3) is assumed to be in the denominator because it's shown multiplying 2 in a way that is commonly used in algebra 2(9+3).
If (9+3) were in the numerator, the equation should have been written this way
48(9+3)÷2 or this way (48÷2)(9+3)
As an engineer, I've taken LOTS of math classes.
and you are never going to find a book that shows that equation in that way implying that
48÷2(9+3) = (48÷2)(9+3)
The question posed by the OP has made the circles in many other online Forums. If you search Engineering Forums, you will find it there, too. And, you will find those "engineers" arguing the case for 288 and 2 as well.
Quote:
Originally Posted by Dopo
By doing that, you kicked the (12) that was multiplying 2(12) to the numerator.
48÷2(9+3) = 48÷2(12) <= At that point, there's nothing saying that (12) is in the numerator.
Instead, by saying that (12) is multiplying 2, it says that it is in the denominator.
I agree that (12) "should" be in the denominator, as I pointed out in an early post, but as Drover mentions, it is really about how one reads the division sign.
As I also mentioned in an early post, this is a typical are you smarter than a 5th grader question. Look at it like this: in elementary school, we learn the basic functions of the English language, yet ask a college educated adult to pick out the adverb in a sentence and you will find them scratching their heads. Even though they [may] have better command over language use and rules, such a fundamental building block no longer holds concern since the impetus on proper structure and syntax has become second nature that the basics have long been forgotten.
Yet, a 5th grader who is fresh from the study of fundamental English language rules would be in a better position to recall such a thing since it is still fresh.
Dover is correct. The ÷ in basic arithmetic would indicate this to be a simple left-to-right order of operations (after the parenthesis, of course), which would give the answer of 288. However, as pointed out, the ÷ is not used in algebra for that very same reason. The / sign also indicates division, but using / would place the (12) with the denominator, so you get 2; which is why in another early post I said that you can get both answers depending on how you read the question. I, like many, see ÷ as /, yet honestly the question posed uses ÷, so I suppose I will concede that by pure usage of the division sign, this is basic left-to-right arithmetic, not algebra, and the answer is 288....although I want it to be 2
I didn't read through all 23 pages of this thread, so excuse me if this has already been said, but IIRC from high school math class, there is an easy way to remember the ORDER OF OPERATIONS. Just remember the following phrase: Please Excuse My Dear Aunt Sallie
We now have our answer (obviously the last two components also don't apply here since there aren't any).
The only way I see this coming out to 288 is if it were written as follows:
(48/2)*(9+3)
24*12 = 288
This is as I seem to remember, any equation written as such: 2(12) is a multiplication of 2 and 12, and multiplication comes before division in the order of operations.
However, I did plug the equation into a spreadsheet (it made me put the multiplication symbol between the 2 and the opening parentheses) and it did come out to 288. So either I missed something, or there is a special exception to the rule here somewhere?
Your error is the bolded part. Multiplication does not have a higher precedence than division.
Dover is correct. The ÷ in basic arithmetic would indicate this to be a simple left-to-right order of operations (after the parenthesis, of course), which would give the answer of 288. However, as pointed out, the ÷ is not used in algebra for that very same reason. The / sign also indicates division, but using / would place the (12) with the denominator, so you get 2; which is why in another early post I said that you can get both answers depending on how you read the question. I, like many, see ÷ as /, yet honestly the question posed uses ÷, so I suppose I will concede that by pure usage of the division sign, this is basic left-to-right arithmetic, not algebra, and the answer is 288....although I want it to be 2
This part is wrong. Obelus and Slash are interchangeable in math. There is no problem with the operator symbol.
The issue here is that the way the expression is written confuses people and causes them to make a simple, yet not so obvious mistake and result in the answer 2.
Iit has been argued) that the expression is ambiguous. If you take into consideration that many people have weak math skills, then it can be argued that the expression is poorly written for many to understand properly. But the expression in itself is not ambiguous.
For example, in C, one could write x=++a+(c++)-(++b) and it would be completely legit, yet confusing to most people.
The expression is just confusing. Not incorrect; Not ambiguous.
Last edited by FreedomThroughAnarchism; 07-20-2011 at 09:23 PM..
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Let's not argue over common sense.
