48÷2(9+3) = ??
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The way I learned math, in the late 1960s I guess, if the answer was to be 288 it should be (48/2) (9+3) = 288. Without the second set of parentheses you'd do the stuff in parentheses first, then the adjacent multiplication, then the division, and get 2. That's how human beings used to do it.
Steady Eddy
Legend
If you're taking a class the answer your teacher will accept is 288. If you think it's 2, that's not your fault.
PEMDAS gives a false impression that multiplying comes BEFORE division, but the M and D are ties, as are the A and S. (In a sense, multiplying is dividing, b/c dividing by 3 can be expressed as multiplying by 1/3, just as subtracting is adding, subtracting 5 can be expressed as adding -5).
More teachers in the U.S. are now using GEMAL; grouping, exponents, multiplication, adding, left-to-right. The improvement is that a false distinction between multiplying and dividing is not implied.
P.S. I bought a British book and it stated the rule for the order of operations as BEDMAS. The B is for brackets, and they put the D before the M.
P.P.S. Whenever you see the awful "÷" symbol, replace the subsequent factor with it's reciprocal. In this thread's example, that would mean to re-write it as 48(1/2)(9+3). Write these 3 factors on any order you wish, you'll always get the correct answer of 288!
PEMDAS gives a false impression that multiplying comes BEFORE division, but the M and D are ties, as are the A and S. (In a sense, multiplying is dividing, b/c dividing by 3 can be expressed as multiplying by 1/3, just as subtracting is adding, subtracting 5 can be expressed as adding -5).
More teachers in the U.S. are now using GEMAL; grouping, exponents, multiplication, adding, left-to-right. The improvement is that a false distinction between multiplying and dividing is not implied.
P.S. I bought a British book and it stated the rule for the order of operations as BEDMAS. The B is for brackets, and they put the D before the M.
P.P.S. Whenever you see the awful "÷" symbol, replace the subsequent factor with it's reciprocal. In this thread's example, that would mean to re-write it as 48(1/2)(9+3). Write these 3 factors on any order you wish, you'll always get the correct answer of 288!
dr325i
G.O.A.T.
WOW, go back to the 3rd grade... Ah wait...calling the whole forum "Idiots" then turning out to be one probably means that you didn't even make it to the 3rd grade yet...
I just asked my 9-yo, and she knew it...
48/2*(12) (as you wrote it) = 24*12 = 288
Parenthesis in this case mean nothing except in the previous line to "protect" the addition.
If you meant to put the 2*12 below the division line, then you need to put it like (2*12).
Multiplication has no priority over the division...
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Steady Eddy
Legend
Yes, definitely.
Breaker
Legend
According to this thread if you didn't get 288 you are a failure who has no education and is what is wrong with America - even if you aren't from America! :lol:.
By the way I put it into my TI-85 and it came out as 2, so there's definitely some reason to believe it's 2.
mightyrick
Legend
The answer is 42.
tenis1
Banned
Did you take this question from elementary school kid's textbook? My cousin asked me the similar question last week. I think they get the answer right.
tenis1
Banned
Whats the answer???
Don't worry. You got it right. If he says differently he is mistaken.
tennismonkey
Semi-Pro
i have learned today that math is not very exciting and i have learned that people on these forums will argue about literally anything.
thanks tw!
thanks tw!
Steady Eddy
Legend
I don't know about the TI-85, but I know that it would say "2" on a TI-82. On the new TIs, if you want to divide 12 by (2*3) without using parenthesis, you have to go 12/2/3, then you'll get 2, while 12/2*3 yields 18.
The new ones don't work like your calculator anymore.
Geez it’s been so long since I took Algebra, but could the confusion here is cause by a subtle difference between algebra and programming language?
In algebra if you write 48 / 2(9+3) you mean to say 48 / 24 = 2
If you write (48/2) (9+3) you mean to say 24 * 12 = 288
If you don’t specify with a bracket, the grouping of 2 * (9+3) takes precedence before the whole operation is taken place which yields the answer of 2. I remember our professor kept drilling us with the use of brackets to clarify what we mean and something about the precedence of implicit grouping.
With programming language, it is literally from left to right. Then again, with different programming languages, the syntax can be slightly different especially with older languages like Cobol or C.
But what do I know?
Just another way to look at it.
How about 48/1 divided by 2/1 multiplied by (9+3)/1? That becomes 48/1 multplied by 1/2 multiplied by 12/1. At that point, you've obeyed PEMDAS and it's all multplication. The answer is 288.
Engineer by virtue of my undergrad education.
How about 48/1 divided by 2/1 multiplied by (9+3)/1? That becomes 48/1 multplied by 1/2 multiplied by 12/1. At that point, you've obeyed PEMDAS and it's all multplication. The answer is 288.
Engineer by virtue of my undergrad education.
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jonnythan
Professional
The correct answer is 288 as written. There can be no argument about this.
Order of operations requires that the 9+3 is added first. After this is done, all that remains is multiplication and division which are done at the same time left to right. Period.
There is no rule saying do multiplication before division.
Order of operations requires that the 9+3 is added first. After this is done, all that remains is multiplication and division which are done at the same time left to right. Period.
There is no rule saying do multiplication before division.
jhick
Hall of Fame
in algebra or programming
48/2(9+3) = 48/2*(9+3) = 24*(9+3) = 288
if you mean to say 48/(2(9+3)) you need the (), it's that simple. If there is no () then there is no grouping
BobFL
Hall of Fame
Why so aggressive? After you get 12, parenthesis becomes irrelevant and basically disappears and you go L --> R!! Maybe this is more appealing for you:
PS I cannot believe '2' is getting more votes
Polaris
Hall of Fame
No, there isn't. Either you entered it wrongly, or your TI-85 is wrong.
SirGounder
Hall of Fame
Lol this thread as entertained me for the last 15 minutes or so and I'm not a big fan of math. Good ol PEMDAS always causing headaches.
jonnythan
Professional
Actually, depending on the calculator, it does come up with 2 as the answer. If entered exactly as the OP posted it, my Casio fx-7700GE comes up with 2..but that doesn't mean it's correct.
The problem is if this were an SAT/ACT type question they would expect you to know the order of operations and rules without the parentheses to clarify. It's tricky no doubt.
athiker
Hall of Fame
http://www.mathgoodies.com/lessons/vol7/order_operations.html
Rule 1: First perform any calculations inside parentheses.
Rule 2: Next perform all multiplications and divisions, working from left to right.
Rule 3: Lastly, perform all additions and subtractions, working from left to right.
I originally voted 2 b/c I had stuck in my head multiplication take precedence over division for some reason but realize otherwise now and realize the answer is 288. The most reasonable explanation I've heard is division is the same as multiplication in the sense that dividing by 2 is the same as multiplying by 1/2. Learn something new (most) every day! FWIW my HP 12C says 2 though!
Rule 1: First perform any calculations inside parentheses.
Rule 2: Next perform all multiplications and divisions, working from left to right.
Rule 3: Lastly, perform all additions and subtractions, working from left to right.
I originally voted 2 b/c I had stuck in my head multiplication take precedence over division for some reason but realize otherwise now and realize the answer is 288. The most reasonable explanation I've heard is division is the same as multiplication in the sense that dividing by 2 is the same as multiplying by 1/2. Learn something new (most) every day! FWIW my HP 12C says 2 though!
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Photoshop
Professional
I'd never heard of PEDMAS (or other variations) until yesterday. Not something I was told to memorize in grade school. But isn't that common sense? Parenthesis, exponents, multiple/division, then add/subtract.
Then again I'm sure there's other common sense knowledges that I lack... such as the order of planets in solar system
I can't name the last few 
jmverdugo
Hall of Fame
Yes, but I am sure that I would had known this if I were to take the SAT...
I'd never heard of PEDMAS (or other variations) until yesterday. Not something I was told to memorize in grade school. But isn't that common sense? Parenthesis, exponents, multiple/division, then add/subtract.
Then again I'm sure there's other common sense knowledges that I lack... such as the order of planets in solar system
I never heard about PEDMAS either I guess we have another word in spanish but do not remember it either ... I guess if you do not use it you lose it.
Kobble
Hall of Fame
Rule 1.5: Do exponentiations right to left
2^3^4 = 2^(81) = some big number
(2^3)^4 = 8 ^ 4 = some small number
First is the way to do it.
Addition and subtraction are left-associative.
a+b+c = (a+b)+c -> doesn't matter actually
a-b-c = (a-b)-c not a-(b-c) = a-b+c -> matters
Exponentiation is right-associative.
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BreakPoint
Bionic Poster
But
48/2(9+3) = 48/2(12) Which is not the same as 48/2 * 12
48/2(12) = 2 because you multiply the 2*12 in the denominator first due to the parentheses.
The answer is 2.
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BreakPoint
Bionic Poster
Of course 12 is in the denominator!
48/2(9+3) = 48/2(12) means the 12 inside the parentheses is in the denominator.
If the 12 was in the numerator, it would be written: (48/2)(12) or (48/2)*12
Actually it is. For the last time the only thing encapsulated by the parentheses is the 12. As the all the actual qualified math people here have tried to explain.
The way to visualize this is:
48/1 * 1/2 * (9+3)/1 =
I think I give up
Djokovicfan4life
Legend
Guys, even I know it's 2. I hate math.
Paranthesis applies only to what is inside it. What is outside is irrelevant. What you say would have been true if it was 48/(2(9+3))
But yes the first reflex is to club it that way, especially since the multiplication sign was omitted. But strictly speaking, it is left to right as 24*12=288
Ash_Smith
Legend
We use BODMAS - Brackets of Division, Multiplication, Addition, Subtraction in the UK school system (or at least we did all those years ago).
That would mean brackets first (9+3) = 12
Division second 48/2 = 24
Multiply thrid 24x12 = 288
Cheers
Ash
P.S. Despite having done maths A-Level that is the sinlge thing I can remember, apart from the fact that I hated it!
That would mean brackets first (9+3) = 12
Division second 48/2 = 24
Multiply thrid 24x12 = 288
Cheers
Ash
P.S. Despite having done maths A-Level that is the sinlge thing I can remember, apart from the fact that I hated it!
BreakPoint
Bionic Poster
But what's inside the parentheses is in the denominator, not the numerator.
48/2(12) = 2
(48/2)(12) or (48/2)12 = 288
Thus, the way it's written, the answer is 2.
(Note: I have scored in the Top 1% or 2% in the country in every standardized math test I have ever taken, and have engineering and MBA degrees from Ivy universities.)
Yes I also learnt it as BODMAS in childhood, being schooled in the British tradition.
Unfortunately, "of" is no longer used in US school textbooks. We had problems like half of 12, which is no longer taught in terms of a separate operator called "of". Such a thing is unknown to most American students. Also, BODMAS doesn't address exponentiation.
Another problem of BODMAS is that it teaches division first, which just happened to work here because division was on the left.
The new way is the computer language way which are taught in American schools - that D and M have the same prioriity, and we should simply go left to right. That is how all programming language compilers implement it.
It does appear that way, doesn't it? Many physics books will show a formula and interpret it like the way you did, i.e. add an implicit paranthesis to identify the denominator.
However, programming languages don't do it like that.
If you write
x = 48/2*12;
in C,
x will turn out to be 288.
In this case, 12 is not in the denominator. krz actually laid it out pretty well by taking each of the numbers/groups individually and placing them over 1.
48/2(9+3) broken out looks like...
48/1 divided by 2/1 multiplied by (9+3)/1 which becomes....
48/1 multiplied by 1/2 multiplied by 12/1 which becomes
48 * 0.5 * 12 which equals...
288.
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