Half of you will get this wrong: 48÷2(9+3) = 288 or 2?

[control101]

Guy on the physics forums said it best in this 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. ' and its absolutely true. Sure we know that there is a multiplication sign in there when it says 2(9+3) but there has to be a distinction that says 2x(9+3) to follow the left to right rule. If the 2 is next to the parenthesis then the operation is generally assumed to be done before solving the other operations. Built you can argue that it is written like this (even though it isnt) 48÷2*(9+3) that it indeed equals 288, but its not. Since the 2 is attached to the parenthesis it's generally assumed that the operation should be done together. All in all comes down to how its written. I understand the point about if it were written like 48÷2*(9+3), but since that attachment to the parenthesis says that operation is to be done together by general consensus. Distributive Property says it all.


rofl. comes down to interpretation of the person who wrote the problem really. Really there should be a second set of parenthesis in there either way, thats why its poorly written. funny tho!

 

[myCATpowerlifts]

Guy on the physics forums said it best in this 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. ' and its absolutely true. Sure we know that there is a multiplication sign in there when it says 2(9+3) but there has to be a distinction that says 2x(9+3) to follow the left to right rule. If the 2 is next to the parenthesis then the operation is generally assumed to be done before solving the other operations. Built you can argue that it is written like this (even though it isnt) 48÷2*(9+3) that it indeed equals 288, but its not. Since the 2 is attached to the parenthesis it's generally assumed that the operation should be done together. All in all comes down to how its written. I understand the point about if it were written like 48÷2*(9+3), but since that attachment to the parenthesis says that operation is to be done together by general consensus. Distributive Property says it all.

 

[Built]

Obviously it's not doing much for you, because you still are incorrect.

PEMDAS

/thread

I'm enjoying a rather delicious thought: posters who could have sworn they were right, gradually coming to the unpleasant realization that they were, in fact, wrong.

Cognitive dissonance is a bitch.

 

[NeilPearson]

From searching on the internet, it looks as though there are arguments on both sides of this... and from people that really should understand the math.

Calculators don't agree either. I blame the "÷" sign. It is kind of ambiguous in this case.

For everyone I think a ÷ b X c is straight forward

a / b X c should mean the same thing
but should a / bc ?

a / bc gets a little fuzzy. Whoever wrote this could have easily meant

a
__
bc

which is how I would have wrote it to avoid confusion or

a / (bc)

I think the original statement is obviously poorly written and even people who are well versed in math seem to have different ideas about what is meant by the equation

 

[NeilPearson]

I'm enjoying a rather delicious thought: posters who could have sworn they were right, gradually coming to the unpleasant realization that they were, in fact, wrong.

Cognitive dissonance is a bitch.

So you are finally realizing you are wrong?

 

[bulldogz]

Hahahaha!


Almost. "÷2" is the same as "??½".

Thus

48 ÷ 2(9+3)
​

becomes

48 ?? ½(9+3)
48 ?? [½(9)+½(3)]
48 ?? (4.5 + 1.5)
48 ?? (6)
= 288
​

lol...you just can't change the first part of the equation from division to mulitiplcation and add brackets later on just to make it work...

If that's the case...lets just add more parenthesis and do it like this: (48÷2)(9+3) <---wrong by the way

You have to do the 2(9+3) first...no ways around this...parenthesis must be done first in math and the 2 is attched to the parenthesis...

Either by first distributing the 2 or adding what's inside the parenthesis and then mulitplying.....2(12) since the number 2 is still attached to the later part of the equation and it is still in parenthesis...the parenthensis will drop once you mulitiply the 2(12), giving you 24...

I see your logic but it does not work that way and if you have a math degree you should know this...

 

[hoyle21]

^^^^^The answer is 288. Following the rules it's the only answer you can get. I still say it is poorly written as well. One set of brackets would make this thread pointless.

 

[MyK]

 

[Marat]

I think the issue is that the people who answer "2" form a polynomial-type relationship that isn't there.

In the expression " 10/2x " or "5 ÷ 3x "there is an implied parenthesis (that might not be a real term, it probably isn't) between the variable and the number it's associated with.

I think Built touched on this, but the expression "3x" means 3 multiplied x times. It implies that there is a parenthesis around "3x", it is implied that it is read "(3x)". The variable introduces a relationship that isn't present in the original 48/2(9+3) expression.

In our original expression, there is no variable that presents an implied parenthesis. Therefore, the normal order of operations needs to be followed.

For example, f(x) = 5/2x ;;; does f(10) = 25 or 0.25?

I say that it equals 0.25 because you are implying that there are two 10's that first find themselves in the denominator, before dividing up the "5" that is in the numerator.

f(x) = 5/2x = 5/(2x)
f(10) = 5 / (2x10)
= 5/20
= 0.25

If we were ignoring that there is a variable involved, and simply going with the expression "5÷2(10)", then we would have to follow the order of operations. First, we'd dividing 5 by 2. That would be 2.5. Then would we multiply by 10. That would be 25.

However, because of the variable, we first multiply 2 x 10. That equals 20. Then we divide 5 by 20. That equals 0.25.


This analogy applies directly to our original expression.

 

[Built]

You have to do the 2(9+3) first...no ways around this...parenthesis must be done first in math and the 2 is attched to the parenthesis...

Almost.

Calculations are performed from left to right, with multiplication and division taking priority over addition and subtraction.

For example:

3 x 5 + 8 ÷ 4 - 2
Here, because there are no parentheses to tell you otherwise, when parsing from left to right, multiplication and division are performed before addition and subtraction. Here, underlines indicate these groupings:

3 x 5 + 8 ÷ 4 - 2​

and the calculation becomes

15 + 2 - 2 = 15​

Parentheses may be used to deliberately change this order. For example:

3 x 5 + 8 ÷ (4 - 2)​

I will again illustrate with underlines

3 x 5 + 8 ÷ (4 - 2)​

The (4 - 2) is calculated first, and we get

15 + 8 ÷ 2
15 + 4
19​

If that's the case...lets just add more parenthesis and do it like this: (48÷2)(9+3) <---wrong by the way

Actually this is right, because here they don't change the default order of operations. Superfluous brackets aren't wrong; they're just messy notation.

Now here, it would be wrong:
48-2(9+3)
(48-2)(9+3)

 

[Built]

I think the issue is that the people who answer "2" form a polynomial-type relationship that isn't there.

In the expression " 10/2x " or "5 ÷ 3x "there is an implied parenthesis (that might not be a real term, it probably isn't) between the variable and the number it's associated with.

I think Built touched on this, but the expression "3x" means 3 multiplied x times. It implies that there is a parenthesis around "3x", it is implied that it is read "(3x)". The variable introduces a relationship that isn't present in the original 48/2(9+3) expression.

In our original expression, there is no variable that presents an implied parenthesis. Therefore, the normal order of operations needs to be followed.

For example, f(x) = 5/2x ;;; does f(10) = 25 or 0.25?

I say that it equals 0.25 because you are implying that there are two 10's that first find themselves in the denominator, before dividing up the "5" that is in the numerator.

f(x) = 5/2x = 5/(2x)
f(10) = 5 / (2x10)
= 5/20
= 0.25

If we were ignoring that there is a variable involved, and simply going with the expression "5÷2(10)", then we would have to follow the order of operations. First, we'd dividing 5 by 2. That would be 2.5. Then would we multiply by 10. That would be 25.

However, because of the variable, we first multiply 2 x 10. That equals 20. Then we divide 5 by 20. That equals 0.25.


This analogy applies directly to our original expression.

Marat, I appreciate the support, but using x just means there is no need for the multiplication operator, just like there is no need for one when using parenthesis:

3y = 3 = 3 ?? y

The function you describe,

f(x) = 5/2x​

could be written

f(x) = 2.5x​

That is to say, it is linear, with a slope of 2.5

Had it been written thus,

f(x) = 5/(2x)​

it would have been a reciprocal function with an odd asymptote at 0.

 

[Marat]

oh yea

 

[Marat]

lol i had a math epiphany so i'm going to wave the white flag now.

 

[Built]

LOL - happens to the best, my friend. You're still my go-to guy for citric acid cycling.

 

[myCATpowerlifts]

I'm enjoying a rather delicious thought: posters who could have sworn they were right, gradually coming to the unpleasant realization that they were, in fact, wrong.

Cognitive dissonance is a bitch.

Thus proving, the ages old addage, that women should stick to reading and writing, and let men take care of the math/science.

 

[bulldogz]

Yes from left to right, but when parenthesis are invloved you have to, have to do the parenthesis first (meaning get rid of or drop the parenthesis)...the only way to drop the parenthesis is to do the opertation 2(9+6) first...giving you 2(12)....

Since the parenthesis are still incorporated in the equation you must do the multiplication of 2(12)....in other words 2 x 12 to get rid of the parenthesis....then you do left to right...

I'm gonna ask my cousin who's an algebra teacher at our local high school....lol...

 

[hoyle21]

And some are confused about the distributive property.

 

[bulldogz]

And some are confused about the distributive property.

Either way works...
2(9+3)
=2(12)
=24

OR

2(9+3)
=(2*9+2*3)
=18+6 <--since we distrubited the 2 the parenthesis drop off the equation
=24

 

[maniclion]

If you guys are going to distribute you still have to work left to right so the division would come first....
48/2=24

so now the problem is 24(9+3)
(24*9)(24*3) = 216+72

216+72= 288

Huh-zah, you are welcome....

 

[myCATpowerlifts]

(2b+1d) x (2t+1p)=j


IF:
b=balls
d=dick
t=tit
p=pussy
j=?

 

[maniclion]

(2b+1d) x (2t+1p)=j


IF:
b=balls
d=dick
t=tit
p=pussy
j=?

J=mycatpowerlifts in a baby carriage....

 

[ManInBlack]

 

[Curt James]

http://forum.grasscity.com/members/170697-agalloch.html^ lulz

"Let's put it this way

48÷2(9+3) written this way = 48÷[2(9+3)]

48÷2(9+3) does not = (48÷2)*(9+3)

48÷2(9+3)

The 2 and the (9+3) are adjacent, implying multiplication. Whoever wrote this equation did it to FUCK with people lol."

Agalloch @ 48÷2(9+3) = ???? - Page 41 - Grasscity.com Forums

 

[Curt James]

Agalloch's thread was closed, btw. lol

I believe the bb.com thread was closed, too.

Quitters.

"Well a lot of the confusion has arisen because there was no context behind the question. Some people have assumed that everything after the "/" sign was intended to be a denominator, while it seems that is generally not a safe conclusion to draw when you're strictly following the order of operations.

The primary argument as to why it was "2" is that the 2 next to the (9+3) was somehow "attached" to the (9+3). My argument is that the "48/" is equally attached to the (9+3) since there is no +, -, or () to separate it, and that you cannot distribute the 2 through the (9+3) without distributing it as (48/2)*(9+3).

Your answer makes sense to me, and I can see why it may be confusing. But I think if you strictly follow what the order of operations dictate, then 288 would be correct."
sanchito9999 @ Free Math Help.com - Homework Help! • View topic - Order of Operations - Need Help! Huge Debate!

And:

"I get 288. In the acronym PEMDAS, the M and D operations are at the same priority and the A and S are at the same priority. Arithmetic operations at the same priority are evaluated left to right. So for example, 2 + 5 - 3 is the same as (2 + 5) - 3 = 7 - 3 = 4, while 2 - 5 + 3 is the same as (2 - 5) + 3 = -3 + 3 = 0.

I can't say that I remember my algebra teacher in ninth grade going into quite such detail (in fact, all I remember her telling us was the acronym MDAS, with a mnemonic device of My Dear Aunt Sally), but programming languages such as C, C++, C#, Fortran, Pascal, and others are very specific about operator precedence.

For this reason, 48÷2*(12) should be evaluated as if it were written (48÷2)*12 = 24 * 12 = 288.

If you really meant

it should be written as 48/(2(9 + 3)). That forces the multiplication to be performed before the division."
Mark44 @ 48÷2(9+3)

 

[Curt James]

 

[maniclion]

I have been looking at the diversity of forums tackling this issue...bodybuilding, physics, rap, gamers, baseball fans, etc... Fascinating indeed!

 

[B-Cubed]

My very good friend, Built, brought this thread to my attention. It's had me in stitches for over an hour now!

My I present my qualifications for answering this question definitively:
A B.S. in Applied Mathematics
A M.S. in Applied Mathematics
A Ph.D. in Applied Mathematics
A 2-year post doctoral fellowship in Mathematics and Earth and Atmospheric Sciences.
My position as an Assistant Professor of Mathematics for nearly 4 years now.

If you will accept my qualifications for answering this question, I'm ready to end the discussion once and for all and put an end to your misery.

Any takers?

 

[Curt James]

^ Shoot. But it seems like it's a semantic riddle more than a math problem. And it's obviously been designed to drive us all insane.

 

[B-Cubed]

^ Shoot. But it seems like it's a semantic riddle more than a math problem. And it's obviously been designed to drive us all insane.

There is no riddle. One of the beauties of mathematics is that there is no room for interpretation; there is one, and only one correct interpretation. Therefore, only answer is correct. Period. This isn't a political science paper where you score points for arguing your point well. You are either right or wrong. I find absolutely nothing ambiguous in the statement of the problem.

Despite what the math major (who shouldn't be getting a degree any time soon) said earlier, problems are, in fact, worked from left to right - the same way we read.

As for all of you relying on calculators, let me say this - computers are STUPID. Technology gets it wrong all too OFTEN - for a myriad of reasons, not the least of which consists of poor programming and the fact that they operate on a subset of the real number line having measure zero, but mostly due to USER ERROR. Computers are only as smart as the people using them.

Once and for all: 48/2(9+3) = 24(12) = 288.

 

[Built]

God bless you.