I always do what's related to the brakets first, so in this case 48 is divided by the 2(9+3) group
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From what I can tell is that we are looking at 2...although I can see some saying 288.
If we go from the original equation, 48÷2(9+3), we work the equation from left to right, being that we are going 48/2 = 24 then the 2nd proble, 9+3 = 12...so then we have 24*12 which is 288.
Where we are now is this also, as some have postulated that this is actually equal to 2.
Here is how they come up with that. If we have an implied Multiplication number between the 2 and the (9=3), then we come up with 48 ÷ 2*(9+3) or 24. Now we have 48 divided by 24 = 2
so who is right in this equation? If we follow the PEMDAS notion (Parenthesis -> exponents > multiply -> divide -> add -> subtract, then we solve 9+3 first = 12, next we work the multiplication...2*12 = 24, then we finish with the division, which is 48/24 which is 2
But if you do your basic left to right configuration we would have 48 divided by 2 = 24 multiplied by 12 which is 288.
So to sum up
PEMDAS is 2
L2R is 288
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There's no good answer to a bad question. The equation is incorrect to begin with. If you're going to use the ÷ symbol, you need to place parentheses where needed. There is no correct answer to this problem.
definitely agree that parenthesis are the best method, particularly in programming, for consistency.
But this is an exercise in order of operations, and there is a correct answer. Which way do you lean?
2 because of distributive property of multiplication we know that 48/2(9+3) is the same as 48/(2*9 + 2*3) which simplifies to 48/24 which is 2. The way I was taught while in both problems 2*(9+3) and 2(9+3) you multiply by 2 in either equation they are NOT completely the same. I was taught if the number is right next to the parenthesis it is to be treated as one problem kind of like this [2(9+3)] where as if you put a multiplication sign between the 2 and the parenthesis the brackets are removed and it would look like this 2*(9+3).
Last edited by 99xjproject; 04-08-2011 at 03:45 PM..
To be clear, let's add a multiplicative symbol in there:
48 / 2 * (9+3)
Parenthesis are first, so this simplifies to:
48 / 2 * 12
Multiplication and division are the same level in the order of ops heirarchy, and they are done from left to right, so it's:
24 * 12 = 288
Agree with most that it could be written more clearly as (48/2)*(9+3).
To clarify... PEMDAS heirarchy specifies 1) parenthesis, 2) exponents, 3) multiplication and division left-to-right, 4) addition and subtraction left-to-right.
Winnar
Quote:
Originally Posted by 99xjproject
2 because of distributive property of multiplication we know that 48/2(9+3) is the same as 48/(2*9 + 2*3) which simplifies to 48/24 which is 2. The way I was taught while in both problems 2*(9+3) and 2(9+3) you multiply by 2 in either equation they are NOT completely the same. I was taught if the number is right next to the parenthesis it is to be treated as one problem kind of like this [2(9+3)] where as if you put a multiplication sign between the 2 and the parenthesis the brackets are removed and it would look like this 2*(9+3).
I really don't see the distinction between adding and not adding the multiplication symbol. Brackets are not implied in the case of omitting said symbol, they are added to change the order of operations.
Otherwise calculators would always add brackets with numbers next to parentheses. Most that I have used do not. Punch said result directly into a calculator and report what you get.
Got a simple question but don't want to ask because: You don't want to clutter the forum with threads; You feel silly asking it; You tried to search to no avail.
The way I was taught if there is a problem like the first was to treat 2(9+3) like one problem where as in the second you wouldn't. I only used the brackets to help illustrate the way I was taught. I very well could be wrong though trick questions like this always get you thinking! I read on one of the links listed this was discussed for 93 pages! I guess the way I am thinking is what is said below. which I took off the last page of the second link.
Originally Posted by tak08810
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.
Is this wrong??
Last edited by 99xjproject; 04-10-2011 at 06:53 PM..
The way I was taught if there is a problem like the first was to treat 2(9+3) like one problem where as in the second you wouldn't. I only used the brackets to help illustrate the way I was taught. I very well could be wrong though trick questions like this always get you thinking! I read on one of the links listed this was discussed for 93 pages!
1st of all, I was told that there wasn't going to be a test today...........
Well, it's Friday so applying the beer theory will certainly clear things up.
If the final result is equal the number of free beers you will receive, which would you rather have?
2?
288? etc.....
It also works when substituting watts for beers considering this is a Caraudio forum.
Bret Mason
PPI-ART COLLECTOR
"It's amazing how good things sound in print."-Anon
It's Friday so applying the beer theory will certainly clear things up.
If the final result is equal the number of free beers you will receive, which would you rather have?
2?
288? etc.....
It also works when substituting watts for beers considering this is a Caraudio forum.
48/2(9+3) = 48/2(12) = 24(12) = 288
Parenthesis first, and then left to right. If you need to, put a dot in between 2 and the sum of 9 and 3, makes it easier to see the true answer
There is obviously a standard folks. Try any calculator based on said standard ( most if not all, I've tried 7 hand calculators since I saw this post, lol) and you will get 288, plain and simple. Parenthesis first, then move left to right because division and multiplication are on the same level in the hierarchy of order of operations.
Interestingly enough, Matlab won't even return an answer if there is no multiplication sign between the 2 and the quantity (9+3). Surely that is saying something to you guys. It just so happens that most common calculators assume you meant to multiply.
Quote:
Originally Posted by superjay
please excuse my dear aunt sally
48/2(9+3)
48/2(12)
48/24
2
that's the answer...you guys are morons
Go punch the equation directly into a calculator capable of displaying quantities, such as a graphing calculator or a nice scientific calculator. If you get 2, snap a pic and prove it to us
Quote:
Originally Posted by superjay
look at it like this 48 is one part of the equation
2(9+3) is the other part of the equation...distributive law
You can't apply distributive law in that manner. 48 is part of the equation and can't simply be dismissed. It must be included when answering the question.
Got a simple question but don't want to ask because: You don't want to clutter the forum with threads; You feel silly asking it; You tried to search to no avail.
In the third link in one of the posts a person put it into two different calculators. One got 2 the other got 288.
Originally Posted by tak08810
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.
In the third link in one of the posts a person put it into two different calculators. One got 2 the other got 288.
Originally Posted by tak08810
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.
Is this wrong??
Like I said, most if not all. Also notice that the 2 came from an older calculator of the series.
I sent a text to my math buddy, who has a masters in math from Cal Poly. He sent me "Order of opps stupid, 288
I suppose it could depend on who you ask. I think that most of us would agree that the question is poorly written and should include parenthesis for clarity.
Got a simple question but don't want to ask because: You don't want to clutter the forum with threads; You feel silly asking it; You tried to search to no avail.