Which is the correct answer for 48÷2(9+3): 2 or 288?

[Studiot]

This is obviously the most difficult math problem ever conceived.

No that would be "How long is a piece of string?"

 

[gb7nash]

And again it's a 50/50 split. This is obviously the most difficult math problem ever conceived.

Goldbach's Conjecture, move out of the way. We have a new problem!

 

[Mirin]

U aware OP?


My vote goes to 288

 

[itsgotime]

I think it's 2! I hope I'm right :(

 

[Eldar]

My vote is on 2 as well, if it were 2*(9+3) then I'd probably be more inclined to say 288.

 

[RJS]

U aware OP?


My vote goes to 288

OP is aware, and mirin.

 

[RandomName]

288. I disagree, never have I heard that implied multiplation is of higher precedence.

 

[jhae2.718]

Implied multiplication is not a feature of the standard order of operations. Some texts may define implied multiplication as having a higher precedence than explicit multiplication it seems, however, I have not come across any to date.

 

[Mark44]

I think the problem comes down to whether or not 2(9+3) is the same as 2x(9+3)

Assuming you are using 'x' to mean multiplication, which I'm not aware is done in any books past arithmetic, 2(9+3) is exactly the same as 2 x (9 + 3). In both cases you are multiplying 12 by 2.

 

[DeadOriginal]

I created an account on the forum just for this.

I thought the answer was 2 when I first saw the equation but now that I've read some of the posts, I'm not so sure anymore.

I played around with the equation and set 2 to x like the OP said. From what I can see I think it really comes down to if x should be distributed into the parentheses or not.

If you multiplied the 2 with the (9+3) first and then divided with 48 with the 24 then your answer would become 2. If you set the 2 to x then you would first distribute the x within the parentheses which in the end would leave your x = 2 if you make your equation equal to 2.

If you divided the 48 by 2 and then multiplied by 12 you would get 288 so if you substituted your 2 with x you would first divide your 48 with x before multiplying it with 12 which if written on paper would be the same as 48 multiplied by 12 divided by x. In that case if your set your equation equal to 288 you would still get x = 2.

In other words, setting it to x doesn't really help. Now that this equation has melted my brain, can someone please clarify? Haha.

 

[jhae2.718]

If you follow the standard order of operations, the expression evaluates to 288.

 

[Perfection]

The answer is to give the maker of the statement a chewing out.

 

[Triple_D]

This topic has the potential to last longer than the DDWFTTW thread.

 

[oraclelive]

48/(9+3)*2 = 48/12*2 = 4*2 = 8

I think by using or applying the rule of BODMAS this could be better understood and solved well whelther with a calculator or not. That is; 48/(9+3)*2 = 48/(12*2) = 2.

 

[oraclelive]

I created an account on the forum just for this.

I thought the answer was 2 when I first saw the equation but now that I've read some of the posts, I'm not so sure anymore.

I played around with the equation and set 2 to x like the OP said. From what I can see I think it really comes down to if x should be distributed into the parentheses or not.

If you multiplied the 2 with the (9+3) first and then divided with 48 with the 24 then your answer would become 2. If you set the 2 to x then you would first distribute the x within the parentheses which in the end would leave your x = 2 if you make your equation equal to 2.

If you divided the 48 by 2 and then multiplied by 12 you would get 288 so if you substituted your 2 with x you would first divide your 48 with x before multiplying it with 12 which if written on paper would be the same as 48 multiplied by 12 divided by x. In that case if your set your equation equal to 288 you would still get x = 2.

In other words, setting it to x doesn't really help. Now that this equation has melted my brain, can someone please clarify? Haha.

The best and simplest way of resolving implied multiplication is by proper application of the rule of BODMAS. That is, solving in the presiding order from left to right-Bracket Of Division Multiplication Addition and Subtraction. Thanks.

 

[D H]

I think by using or applying the rule of BODMAS this could be better understood and solved well whelther with a calculator or not. That is; 48/(9+3)*2 = 48/(12*2) = 2.

You are misinterpreting the rule. Division does not have precedence over multiplication.

This question was answered on the first page. The correct answer to 48÷2(9+3) is 288. An even better answer is that this is a stupid question. When writing a mathematical expression, the number #1 rule is to leave absolutely no doubt about how the expression is to be interpreted.

Some calculators do indeed perform this incorrectly, particularly graphing calculators from the previous millennium. TI led the charge in this regard. Their TI-80, 81, 82, and 85 calculators gave implied multiplication a higher precedence than explicit multiplication. TI reversed this decision in the late 1990s. Their TI-83, 84, 89, 92, and later calculators give the same precedence to implied and explicit multiplication.

 

[tre2k3]

[URL]http://shareimage.ro/images/n10moj7k3larya94uc4o.jpg[/URL]

http://www.zazzle.com/48_2_9_3_tshirt-235882834792365529

 

[Raioneru]

the answer is two

 

[Xitami]

1 - 2 + 3 = ?
a) -4
b) +2

 

[JaredJames]

1 - 2 + 3 = ?
a) -4
b) +2

The only way to get that to -4 is to ignore the rules.

Addition and subtraction are equal weight and evaluated left to right.

Only if it was written as 1 - (2 + 3) would it equal -4.

 

[0xyg3n]

48 ÷ 2(9 + 3) Can be also written: 48 x ½(9 + 3)

48 x ½(9 + 3)

^Will not have any problems finding the right answer, 288.

 

[HallsofIvy]

It can be written that way if you assume a particular meaning- but the expression as given is ambiguous and cannot be correctly evaluated without assuming something not given.

You, basically, assumed the "correct" answer was 288 and, no surprise, arrived at that answer.

 

[micromass]

I think we should create a new option on the poll: "Ban the notation ÷" That would have my vote...

 

[Jokerhelper]

48 ÷ 2(9 + 3) Can be also written: 48 x ½(9 + 3)

48 x ½(9 + 3)

^Will not have any problems finding the right answer, 288.

that doesn't help at all, since half of the people here are arguing that 48 ÷ 2(9+3) should be interpreted as ^{48 \times\frac{1}{2(9+3)}}.

I think the best answer to this question was actually given by my professor. Some students asked this yesterday after class and he immediately answered that it was ambiguous. Which by looking at this discussion, I think is fair to say it is the case. Funny how it made it all over the interwebs though.

BTW, how were some of you able to plug this in Python or C++ ? I tried in both but failed because they both interpreted the "2(9.0+3)" as an attempt to call a function named 2. Also, my Sharp EL-W516 gives 2 for an answer.

EDIT: Maple gives 288, and MATLAB refuses to do anything with the ÷ symbol. Or with 2(9+3) without an operator after 2, for that matter.

 

[gb7nash]

I like how 2 is currently winning.

 

[EternityMech]

Matlab is not saying 288 its giving an error.

personally if you got this question in a 7th grade math test and wrote 2 you would get the answer wrong.

so its clearly 288.

 

[Hurkyl]

Grar, stop arguing over which end to crack your eggs.

The standard is that multiplication/division have same precedence, and are done left to right. Similarly for addition and subtraction.

However, some people drop parentheses around the divisor as short-hand, and others simply get it wrong.

The practical effect is that you should never write an expression like 1/2x unless you are sure it won't generate any confusion -- e.g. if you can be certain your audience will infer from context whether you mean (1/2)x or 1/(2x).

Sometimes, you will face an author/teacher who uses the standard convention. If you prefer a different convention, then you're going to have to learn to read the wrong convention, and avoid writing anything that would be different amongst the two conventions.

The same advice applies to someone who prefers the standard convention, but is faced with a book/teacher that uses a different one.


There's a general style guideline here -- if there is a reasonable chance of ambiguity, use parentheses.



For the record, on more than one occasion, I've seen a student who doesn't put parenthesis around divisors make arithmetic mistakes because he wrote an expression intending some operation to happen in the divisor, but later read the expression differently (and others make mistakes in the other direction). So I pretty much always insist on parentheses, no matter what convention the student wants to use.

 

[Greg Bernhardt]

Closing thread
https://www.physicsforums.com/showthread.php?t=494675