Diablo® III

48÷2(9+3) = ? cont.

90 Tauren Shaman
17170
Standard Order of Operations

If one strictly uses the standard order of operations to solve mathematical expressions, the answer to the problem would be 288, which is also the same solution provided by WolframAlpha[17] and Google.[18]

By convention, the order of precedence in a mathematical expression is as follows:

Terms inside of Brackets or Parentheses.
Exponents and Roots.
Multiplication and Division.
Addition and Subtraction.

If there are two or more operations with equal precedence (such as 10÷2÷5 or 7÷2*9), those operations should be done from left to right.

Therefore, the problem “48÷2(9+3) =” would be solved like this:
48 ÷ 2 * (9+3)=
48 ÷ 2 * (12)=
48 ÷ 2 * 12=
24 * 12=
288
PEMDAS

Solving for the answer 2 is sometimes a result of doing multiplication before division. Much of the confusion can be blamed on PEMDAS (sometimes known as, “Please Excuse My Dear Aunt Sally”) and other similar mnemonics used to teach order of operations in schools.

As an example, PEMDAS stands for:

Parentheses
Exponentiation
Multiplication
Division
Addition
Subtraction

Whereas BEDMAS stands for:

Brackets
Exponentiation
Division
Multiplication
Addition
Subtraction

The former can lead to the implication that addition always comes before subtraction, and that multiplication always comes before division. The latter can lead to the implication that addition always comes before subtraction, and that division always comes before multiplication.

If one uses multiplication before division (PEMDAS being especially popular in the United States), the problem would be solved like this:
48 ÷ 2 * (9+3)=
48 ÷ 2 * (12)=
48 ÷ 2 * 12=
48 ÷ 24=
2

However, solving the problem like this would be considered erroneous because multiplication and division hold equal precedence.[19]

It is helpful to remember that division and multiplication are inverse operations, and thus represent the same operation written in a different way. Division is the same as multiplication of the reciprocal, and multiplication is the same as division of the reciprocal. This is similar to how addition is the same as subtraction of the negative, and how raising to the nth power is the same as taking the 1/nth root.
Implied Multiplication

However, the answer 2 could be justified by the principle of implied multiplication. For example, consider the problem "2/5x."

If one strictly follows the standard order of operations, the correct interpretation would be “(2/5)*(x).”

But many calculators and textbooks state that a higher value of precedence should be placed on implied multiplication than on explicit multiplication:

Because “5x” is implied to be "5*x," it gets higher priority than "2/5." In this case, "2/5x" would be interpreted as "(2)/(5*x)."

Returning to the original problem, if one utilizes the principles of implied multiplication, then “2(9+3)” gets higher precedence than the explicit “48/2,” and would be solved like this:
48 ÷ 2(9+3)=
48 ÷ 2(12)=
48 ÷ 24=
2

However, there is a lack of consensus on the value of implied multiplication.

from http://knowyourmeme.com/memes/48293
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Yes like what i quoted...

where

2x÷2x = 1

(2x)÷(2x) = 1

is where the brackets are, this is implied multiplication

not

2(x)÷2(x) = x^2

But when you are given the brackets already similar to the x^2 solve, there is no implied multiplication, its already multiplication.

TLDR 48 ÷ 2(9+3)=288
Edited by Maazer#1103 on 6/12/2012 8:53 AM PDT
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why is this so confusing??
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No you need added grouping symbols to force (a+b) into the denominator. Thus x/y*(a+b) is (x/y)(a+b) and x/[y(a+b)] is with it in the denominator.


but it's a question for x/y(a+b) and not x/y*(a+b). You can't just add in a * when there is no *. I can't see a way to remove the parentheses if I don't do x/(ya+yb).

if a+b = z, it'll still be x/y(z) and i'd still stuck with
x
-
y(z)

unless the equestion is (x/y)(a+b) or x/y*(a+b) then, yeah.. it'd be your answer, but it's not. it's just x/y(a+b). No implied symbols whatsoever.


No, no, no. Lets put it this way. Here's the problem.

x(3+9) let x = 48/2

The coefficient in front of (3+9) is 48/2 (9+3) is not in the denominator.
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I would think that juxtaposed multiplication would show that 48/2 should be multiplied by 9 and 3 before they are added together, that would give the correct answer of 288.
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i will try my best to explain why 288 is wrong.

48÷2(9+3) lets replace 9 and 3 with A and B.
48÷2(A+B) i assume everyone here knows we have to solve inside the bracket first right?

so if you solve it as below, you're doing it wrong and u will get 288 as an answer because the way you're doing it you didnt solve the A+B inside the bracket first. you are actually multiplying 24 with A and B separately.

24(A+B)
24A + 24B ---> is wrong because u just ignored/did not solve the A+B inside the bracket.
24(9) + 24(3)
216 + 72 = 288

the correct way to do it :
48 ÷ (2A+2B) because we have to solve inside the bracket first.
48 ÷ (18+6)
48 ÷ 24= 2

editted for further clarification... feel free to correct me if im wrong @_@
Edited by TheConquest#1191 on 6/12/2012 9:06 AM PDT
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06/12/2012 08:56 AMPosted by Windscar
I would think that juxtaposed multiplication would show that 48/2 should be multiplied by 9 and 3 before they are added together, that would give the correct answer of 288.


also this
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I think the majority of people are comfortable with the answer 288.

the answer 2 can only be acceptable using the notation 48/2(9+3) which is ambiguous and quite possibly interpreted as 48/[2(9+30].
Otherwise using 48 ÷2(9+30) can only be interpreted as 48 ÷2*(9+3)

Multiplication and division have same priority. PEMDAS is an incorrect mnemonic.
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48÷2(9+3) or 48/2(9+3) are ambiguously written.

If you mean (48÷2)*(9+3) you need to write it like that. Conversely 48/(2(9+3)) is unambiguous.

I feel that (48÷2)*(9+3) is implied, but can understand how someone might write the original meaning 48/(2(9+3)).

Ambiguity is the enemy of math.
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i will try my best to explain why 288 is wrong.

48÷2(9+3) lets replace 9 and 3 with A and B.
48÷2(A+B) i assume everyone here knows we have to solve inside the bracket first right?

so if you solve it as below, you're doing it wrong and u will get 288 as an answer because the way you're doing it you didnt solve the A+B inside the bracket first. you are actually multiplying 24 with A and B separately.

24(A+B)
24A + 24B
24(9) + 24(3)
216 + 72 = 288


This is NOT wrong. The coefficient in front of (A+B) is 48/2 or 24 if you will.
48/[2(A+B)] is what you are trying to force 48/2(A+B) to be and it is not. THEY ARE NOT THE SAME.

48/2(9+3) = 288

48/[2(9+3)] = 2

Adding grouping symbols to force (9+3) into the denominator is needed to get the answer of 2.
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i will try my best to explain why 288 is wrong.

48÷2(9+3) lets replace 9 and 3 with A and B.
48÷2(A+B) i assume everyone here knows we have to solve inside the bracket first right?

so if you solve it as below, you're doing it wrong and u will get 288 as an answer because the way you're doing it you didnt solve the A+B inside the bracket first. you are actually multiplying 24 with A and B separately.

24(A+B)
24A + 24B
24(9) + 24(3)
216 + 72 = 288


Technically there's nothing wrong with that solution.
for example:

4*(5+3)

It is infact:

4*5 + 4*3 = 32
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85 Orc Warrior
12025
06/12/2012 08:52 AMPosted by Powerlad
there is a lack of consensus on the value of implied multiplication.


there absolutely is not a lack of consensus between actual mathematicians. the answer is 288. there is only one order of operations. you cannot prioritize multiplication or division over the other, regardless of what acronym you use. this is because they are inverse functions. for example:

50 / 2 = 50 * 0.5

any statement with division in it can be re-written inversely to be a multiplication and vice-versa.

the same applies to addition and subtraction.

this is why they are prioritized equally and are done in the order that they appear.

please stop spreading this fallacious garbage to make it sound as if someone who works this out to be 2 is actually doing something valid other than being retarded. the correct answer is 288. there is no ambiguity. the expression is perfectly valid.

specifically: at the end of your post you stated implied multiplication. you do not know what you're talking about. it is called the distributive property and it has rules that govern its use. it cannot be applied here
Edited by jordan#1710 on 6/12/2012 9:03 AM PDT
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Isn't this just a matter of convention?

This question that takes advantage of the OCD of intelligent mathematicians and theorists (presumably you) who enjoy being precisely correct. Because the usage of the division operator is taught in elementary school, it is thought to be elementary, so any implied deviation from what you learned is "obviously stupid." However, the method in which it was taught was ambiguous. If you think an elementary school teacher would recognize and address the notation's ambiguity before a class of students who generally do not care, then you deserve to be whacked upside the head. The notation is replaced in higher education for those who actually care about the subject; therefore ambiguity is much less likely to exist.

Since I (and others before me) have demonstrated that the question as delivered is created explicitly to troll others due to its intended ambiguity and abuse of cultural knowledge (what is taught, often incorrectly, in elementary schools), could this thread be left to die for other, more intelligent, threads to bubble to the surface? We all agree that order of operations barely constitutes "Technology and Science." Let's leave it that way.

Finally, I know that this post only contributes to the problem by bumping it to the top. But seriously??? 9 pages of worthless time and debate over something intentionally ambiguous is much dumber than any one person who has contributed to this subject.

EDIT: Not going to bump this up again. Not to be narcissistic, but the voices of reason just can't speak loudly enough. And now another thread exactly like this has cropped up. Stuff like this is why I dropped my math major to a math minor. I can't help but wonder if this is tl;dr, in spite of all the disgusting-looking notation thrown around this thread.
Edited by criex10#1768 on 6/12/2012 9:15 AM PDT
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Here is a very simple and authoritative description of the topic from another discussion I think many of you could benefit from:

I am your college professor that you requested, with a doctorate in Mathematics. I will break this down as simply as possible and end this debate as approx. 10 students have already asked me this today.
The problem as it is written is 6÷2(1+2) , the ÷ cannot be substituted with a fraction bar because they have different ranks on the order of operations. It is an illegal math move to do this. The bar ranks with parentheses, ÷ is interchangeable with *. therefore the problem must be solved as 6÷2(1+2) NOT 6 (over) 2(1+2) we do the parentheses first, so 6÷2(3), the parentheses are now no longer relevant, because the number inside is in it's simplest form. Every single number has implied parentheses around it.
6÷2(3)
(6) ÷(2)(3)
6÷2*3,
or even converting the division to multiplication by a reciprocal (a legal math move)
(6)(1 (over) 2)(3)
are all correct ways to write this problem and mean exactly the same thing. Using pemdas, where md and as are interchangeable, we work from left to right, so (3)(3) or
3*3= 9

Just because something is implied rather than written does not give it any special rank in the order of operations.

The problem in it's simplest form, with nothing implied would look like this:
(1+1+1+1+1+1 (over) 1) ÷ (1+1 (over) 1) * ((1(over) 1) + (1+1 (over) 1))
From here, nothing is implied, This again, works out to 9.

If the symbol '/' was used this whole debate would be ambiguous since that symbol can mean "to divide by" or it could mean a fraction bar.

HOWEVER, because the ÷ symbol is used, it can not be changed to mean a fraction bar because that would change the order of operations and thus the whole problem, you can't change a symbol to mean something because you want to, in doing so you are changing the problem.

Once and for all, the answer is 9.

Hopefully some of my students see this so I can stop answering this question.

End of debate... hopefully.
Source(s):
Doctorate, 9 years teaching experience.
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i will try my best to explain why 288 is wrong.

48÷2(9+3) lets replace 9 and 3 with A and B.
48÷2(A+B) i assume everyone here knows we have to solve inside the bracket first right?

so if you solve it as below, you're doing it wrong and u will get 288 as an answer because the way you're doing it you didnt solve the A+B inside the bracket first. you are actually multiplying 24 with A and B separately.

24(A+B)
24A + 24B
24(9) + 24(3)
216 + 72 = 288


LoL.

the main problem comes from people adding brackets that do not follow the order of operations

48÷2(9+3)

48÷(2(9+3)) WRONG

(48÷2)(9+3) RIGHT

48÷(2*12) WRONG because ur doing multiplation before divison

(48÷2)*12 is right because doing it in the right order anyway.

Really there's no need to add brackets anyway, but you are free to add them just to clarify what is already determined by order of operations, which is useful for plugging these type of problems into really crappy scientific calculators.
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but it's a question for x/y(a+b) and not x/y*(a+b). You can't just add in a * when there is no *. I can't see a way to remove the parentheses if I don't do x/(ya+yb).

if a+b = z, it'll still be x/y(z) and i'd still stuck with
x
-
y(z)

unless the equestion is (x/y)(a+b) or x/y*(a+b) then, yeah.. it'd be your answer, but it's not. it's just x/y(a+b). No implied symbols whatsoever.


No, no, no. Lets put it this way. Here's the problem.

x(3+9) let x = 48/2

The coefficient in front of (3+9) is 48/2 (9+3) is not in the denominator.


hmm, wouldn't a linear mathematical question than be posted as (48/2)(9+3)? I mean, it is quite sadistic otherwise as 48/2(9+3) as a linear question would make it as the coefficient as 2, as it is not implied otherwise.... :( there is only one set of bracket used after all.
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06/12/2012 09:01 AMPosted by Chedwick
there is a lack of consensus on the value of implied multiplication.


there absolutely is not a lack of consensus between actual mathematicians. the answer is 288. there is only one order of operations. you cannot prioritize multiplication or division over the other, regardless of what acronym you use. this is because they are inverse functions. for example:

50 / 2 = 50 * 0.5

any statement with division in it can be re-written inversely to be a multiplication and vice-versa.

the same applies to addition and subtraction.

this is why they are prioritized equally and are done in the order that they appear.

please stop spreading this fallacious garbage to make it sound as if someone who works this out to be 2 is actually doing something valid other than being retarded. the correct answer is 288. there is no ambiguity. the expression is perfectly valid.

specifically: at the end of your post you stated implied multiplication. you do not know what you're talking about. it is called the distributive property and it has rules that govern its use. it cannot be applied here


Good to see you back. These idiots keep growing in numbers.
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No, no, no. Lets put it this way. Here's the problem.

x(3+9) let x = 48/2

The coefficient in front of (3+9) is 48/2 (9+3) is not in the denominator.


hmm, wouldn't a linear mathematical question than be posted as (48/2)(9+3)? I mean, it is quite sadistic otherwise as 48/2(9+3) as a linear question would make it as the coefficient as 2, as it is not implied otherwise.... :( there is only one set of bracket used after all.


Only one set of brackets are needed. That's what we've been trying to say. If you wanted to force (9+3) into the denominator then you have to add brackers otherwise (9+3) is in the nominator.

48/[2(9+3)] -----> (9+3) is in denominator

48/2(9+3) -------> (9+3) is in nominator
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[quote]Through out all my education (I'm in my last year of grad school for math) I have never heard of this principle of implied multiplication.


What is your thesis or dissertation on?
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06/12/2012 09:08 AMPosted by Speusippus
[quote]Through out all my education (I'm in my last year of grad school for math) I have never heard of this principle of implied multiplication.


What is your thesis or dissertation on?


I'm not getting my Ph.D. I'm stopping at my master's and I chose to go the comps route rather than write a thesis/dissertation.
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