199 réponses à ce sujet

[Rose of Mars]

Pacifien wrote...

*gasps at the people who answered 288*

http://www.wolframal...i=48÷2(9+3)]288

[ejoslin]

*sigh* No, nonononono. Ok, I'll get pedantic here.

the problem is 48÷2(9+3), not 48÷(2(9+3))

So it would be solved, first what is in the parentheses -- so you get

48/2*12
Next you solve left to right
24*12
=288

Substitute 2 for X and see what I mean

48÷x(9+3) = 288
48/x*12 = 288
48*12=288x
576 = 288x
2=x
x=2

Or to make it clearer
48÷2(9+3) = 288
48÷2(12) =288
48/2 = 24
24 = 24

People are looking at the problem and thinking automatically that 2(9+3) should be solved first, but that is not the case.  It is confusing the way it is written out, however.

Modifié par ejoslin, 08 avril 2011 - 04:17 .

[TheMufflon]

RainyDayLover wrote...

Jesus, people

I think the confusion lies within how it's worded (in particular, how the division sign is implied)


Is it :

48                           48
----             =          ------    =    2
2(9+3)                    24


OR


48                                 48
----  x (9+3)      =         ------ x 12         =      24 x 12   =    288 
 2                                    2

Yep, that seems to be the problem most people are having. The ÷ means that it's the second case.

[Madame November]

Madame November wrote...

288

He is right if anyone is.  He also says this is a deceptive way to write the problem and could have been meant the other way but technically it is 288.

Um, I did declare the case closed, right? Closed.<3

Modifié par Madame November, 08 avril 2011 - 04:15 .

[mousestalker]

Three out of three Flemish mathematicians agree

So there.

[RainyDayLover]

Strangely Brown wrote...

RainyDayLover wrote...

48                                 48
----  x (9+3)      =         ------ x 12         =      24 x 12   =    288 
 2                                    2

But this is not the same equation as the OP.

So you're saying multipication takes precedence over division? Since the order of operations for multipication and division doesn't matter, you can, in fact interpret it in both ways.

48÷2(9+3)  could mean 48÷(2(9+3)) OR (48÷2)(9+3)

The problem lies in the '÷' as you wouldn't normally use that when doing division in problems on paper. If you do use that symbol, you have to use brackets wherever possible....otherwise it'll only cause confusion.

Modifié par RainyDayLover, 08 avril 2011 - 04:21 .

[Madame November]

RainyDayLover wrote...

Strangely Brown wrote...

RainyDayLover wrote...

48                                 48
----  x (9+3)      =         ------ x 12         =      24 x 12   =    288 
 2                                    2

But this is not the same equation as the OP.

So you're saying multipication takes precedence over division? Since the order of operations for multipication and division doesn't matter, you can, in fact interpret it in both ways.

48÷2(9+3)  could mean 48÷(2(9+3)) OR (48÷2)(9+3)

The problem lies in the '÷' as you wouldn't normally use that when doing division in problems on paper. If you do use that symbol, you have to use brackets wherever possible....otherwise it'll only cause confusion.

He said it could be taken both ways, but that there is a technically correct answer without the implied additions.
288

Modifié par Madame November, 08 avril 2011 - 04:22 .

[Pacifien]

I suppose the confusion lies on whether you interpret 2(9+3) as 2x or 2 * x.

[ejoslin]

RainyDayLover wrote...

Strangely Brown wrote...

RainyDayLover wrote...

48                                 48
----  x (9+3)      =         ------ x 12         =      24 x 12   =    288 
 2                                    2

But this is not the same equation as the OP.

So you're saying multipication takes precedence over division? Since the order of operations for multipication and division doesn't matter, you can, in fact interpret it in both ways.

48÷2(9+3)  could mean 48÷(2(9+3)) OR (48÷2)(9+3)

The problem lies in the '÷' as you wouldn't normally use that when doing division in problems on paper. If you do use that symbol, you have to use brackets wherever possible....otherwise it'll only cause confusion.

'

Order of operations has you go left to right though.

First you solve what's in the parentheses.  
Next exponents/radicals (again, left to right)
Then muliplicaton/division (again, left to right)
Then addition/subtraction (again, left to right)

So you will be solving 48÷2(9+3) as that.  First you solve what is in the parentheses (9+3) then you solve 48/2 then multply by 12.

Modifié par ejoslin, 08 avril 2011 - 04:32 .

[Krimson_Wolf]

288, stop trying to confuse us

[mousestalker]

Don't make me consult more mathematicians. I'm sure no one wants that.

[Madame November]

Hi, maybe I didn't introduce myself. My name is M November and I am married to an award winning physics professor who works on millennium problems for fun in his spare time.

288

Math has rules.

EDIT: Sexy Rules<3

Modifié par Madame November, 08 avril 2011 - 04:46 .

[RainyDayLover]

Strangely Brown wrote...

RainyDayLover wrote...

Strangely Brown wrote...

RainyDayLover wrote...

48                                 48
----  x (9+3)      =         ------ x 12         =      24 x 12   =    288 
 2                                    2

But this is not the same equation as the OP.

So you're saying multipication takes precedence over division? Since the order of operations for multipication and division doesn't matter, you can, in fact interpret it in both ways.

48÷2(9+3)  could mean 48÷(2(9+3)) OR (48÷2)(9+3)

If you take away the parentheses and make the equation into fractions this is the OP's equation:

48       1             48        1
---  x    ---     =    ---   x   ---
2       (9+3)         2         12

NOT

48      (9+3)       48      12
---   x    ---      =   ---  x   ---
2            1            2        1

Ugh, see that's the thing...when making the equation into fractions from the current form, how would you know it's not the latter without parentheses? There's simply no way of knowing unless the parentheses are provided in the question.

Let's convert the question to (I've simply added an asterik to indicate multipication):

48÷2*(9+3)

Now following the rules of simple grade school math, how would you know whether to do division or multipication first?

[ejoslin]

RainyDayLover wrote...

Strangely Brown wrote...

RainyDayLover wrote...

Strangely Brown wrote...

RainyDayLover wrote...

48                                 48
----  x (9+3)      =         ------ x 12         =      24 x 12   =    288 
 2                                    2

But this is not the same equation as the OP.

So you're saying multipication takes precedence over division? Since the order of operations for multipication and division doesn't matter, you can, in fact interpret it in both ways.

48÷2(9+3)  could mean 48÷(2(9+3)) OR (48÷2)(9+3)

If you take away the parentheses and make the equation into fractions this is the OP's equation:

48       1             48        1
---  x    ---     =    ---   x   ---
2       (9+3)         2         12

NOT

48      (9+3)       48      12
---   x    ---      =   ---  x   ---
2            1            2        1

Ugh, see that's the thing...when making the equation into fractions from the current form, how would you know it's not the latter without parentheses? There's simply no way of knowing unless the parentheses are provided in the question.

Let's convert the question to (I've simply added an asterik to indicate multipication):

48÷2*(9+3)

Now following the rules of simple grade school math, how would you know whether to do division or multipication first?

Easily.  I posted the order of operations above.  You first solve what is in the parentheses and then go left to right :/

First is solving what is in the parentheses which is (9+3)
Next is exponents/radicals -- there are none in this problem
Next multiplication/division -- you do the division first because order of operations says you go from left to right
Next is addition/subtraction -- the only one of these is in parentheses so it's solved already.

So FIRST, according to order of operations you solve (9+3) so your problem now looks like 
=48÷2(12)

Order of operations says you go left to right, so next part of the problem you solve like this:
=24(12)

Now multiply.

=288

[RainyDayLover]

ejoslin wrote...

RainyDayLover wrote...

Strangely Brown wrote...

RainyDayLover wrote...

48                                 48
----  x (9+3)      =         ------ x 12         =      24 x 12   =    288 
 2                                    2

But this is not the same equation as the OP.

So you're saying multipication takes precedence over division? Since the order of operations for multipication and division doesn't matter, you can, in fact interpret it in both ways.

48÷2(9+3)  could mean 48÷(2(9+3)) OR (48÷2)(9+3)

The problem lies in the '÷' as you wouldn't normally use that when doing division in problems on paper. If you do use that symbol, you have to use brackets wherever possible....otherwise it'll only cause confusion.

'

Order of operations has you go left to right though.

First you solve what's in the parentheses.  
Next exponents/radicals (again, left to right)
Then muliplicaton/division (again, left to right)
Then addition/subtraction (again, left to right)

So you will be solving 48÷2(9+3) as that.  First you solve what is in the parentheses (9+3) then you solve 48/2 then multply by 12.

On paper, you wouldn't really have to use this 'left to right' rule because you'd normally use fractions to indicate division so you wouldn't really encounter an ambiguous situation such as this but yeah, you're right. Multipication does in fact take precedent over division if we're taking that rule into consideration. Hence the answer is 288.

/thread.

[KenKenpachi]

Hmm....Math, I see the devils work is being done.

[ejoslin]

RainyDayLover wrote...

ejoslin wrote...

RainyDayLover wrote...

Strangely Brown wrote...

RainyDayLover wrote...

48                                 48
----  x (9+3)      =         ------ x 12         =      24 x 12   =    288 
 2                                    2

But this is not the same equation as the OP.

So you're saying multipication takes precedence over division? Since the order of operations for multipication and division doesn't matter, you can, in fact interpret it in both ways.

48÷2(9+3)  could mean 48÷(2(9+3)) OR (48÷2)(9+3)

The problem lies in the '÷' as you wouldn't normally use that when doing division in problems on paper. If you do use that symbol, you have to use brackets wherever possible....otherwise it'll only cause confusion.

'

Order of operations has you go left to right though.

First you solve what's in the parentheses.  
Next exponents/radicals (again, left to right)
Then muliplicaton/division (again, left to right)
Then addition/subtraction (again, left to right)

So you will be solving 48÷2(9+3) as that.  First you solve what is in the parentheses (9+3) then you solve 48/2 then multply by 12.

On paper, you wouldn't really have to use this 'left to right' rule because you'd normally use fractions to indicate division so you wouldn't really encounter an ambiguous situation such as this but yeah, you're right. Multipication does in fact take precedent over division if we're taking that rule into consideration. Hence the answer is 288.

/thread.

Multiplication does not precedence over division -- I think you had a typo there.  What makes the division take precedence over the multiplication is that it's to the left -- nothing more, nothing less.

The problem, if written out in fractions, would look like this

48/1 *1/2 *(9+3)/1 and while it would be simpler having it viewed like this, I think the problem is trying to see if people understand order of operations.

Obviously many people do not understand this rule.  The equation IS confusing to a certain extent, and I understand why many people do get it wrong, but the equation itself is not ambiguous. 

Modifié par ejoslin, 08 avril 2011 - 04:46 .

[RainyDayLover]

Yeah, sorry...I meant division comes first (since we're evaluating left-to-right)

[Maria Caliban]

288.

I love you all, but whaaa?

Modifié par Maria Caliban, 08 avril 2011 - 04:48 .