stupid maths problem

[Libertine Seguros]

But as Hitch says, it defeats the object of using the brackets (or in this case the letter) if it's not meant to be placed as if in presumptive brackets (6)/(2(1+2)).

If you don't want us to perceive 2(1+2) as a single unit, then it shouldn't be presented as one, and presenting it without a second set of brackets (which would clear up whether the answer is 9 or 1) opens up the possibility of ambiguity.

The problem is trying to present it on a computer. To me, 6/2a clearly shows 2a to be the denominator. To you, 2 is clearly the denominator and a is modified by (6/2).

I have seen both "PEMDAS" and "PEDMAS" as method orders (some say D and M are equal, some don't), which further muddies things.

If we follow this method, the first thing we do is the brackets, giving us

6/2(3)

If we aren't to see 2(3) as one unit (and therefore 6), just as f(x) in any equation, then the use of the brackets is misleading.

As I said before, it's a poorly written equation that is designed to create ambiguity because neither reading is wrong per se. It needs to be either expressed as a fraction or with a second set of parentheses to clarify.

I guess what I'm saying is,

the way it's expressed, I don't see 6/2(1+2) as the same as 6(1+2)/2. I can see why you do read it that way, but I see 2(1+2) as one function in the form f(x).

 

[Parrulo]

i am tired of seeing this everywhere

its 9 simple as that.

why use "advanced math" to solve something a 5th grader can do?

 

[Libertine Seguros]

i am tired of seeing this everywhere

its 9 simple as that.

why use "advanced math" to solve something a 5th grader can do?

Because the point is, a 5th grader could have been taught something different. Like Hitch, the OP, and me.

The point is, it's a misleading question, and many textbooks point out that care needs to be taken to avoid confusion when using the slash symbol - and that extra brackets should be used if confusion is likely.

I think here, we have a case of confusion. Which has been deliberately left unclarified in order to provoke the kind of argument we have here. If read one way, the answer is 9. If read another way, the answer is 1.

If the problem was demonstrated in another way (fractions or additional parentheses, as shown previously), there would be no debate. And if it was simple, we wouldn't have a 55-45 split on how to interpret it.

 

[Sydney21]

na libertine my favourite person to disagree with its definitely 9 no doubt. Just like Gilbert is the best rider in the peleton.

6/2a is 3a that's not debatable really the (2a) needs to be in brackets for it to be any different.

6/2a doesn't equal 3a. It would only equal 3a if the 6/2 was in brackets.

It actually equals 3/a because one can divide 2 through the numerator and through the denomenator keeping the value of the equation the same.

The answer under the Australian school system is 1 and cadel is the best rider in the peleton.

 

[Martin318is]

While what was intended may be misleading, the answer is not.

The only way to get this to answer 9 is to insert an 'x' that isn't there. If you remove all the numbers then the equation becomes:

A/B

where:
A = 6
B = 2(1+2)


to get 9 you would have to bend the equation to create

A/BxC

where:
A=6
B=2
C = (1+2)

While it would be understood if the writer of the equation came up and said "I meant it to be this way" in the absence of such information, the first version must always be taken.

 

[Clearly Unstable]

...........................7

 

[Spare Tyre]

6/2a doesn't equal 3a. It would only equal 3a if the 6/2 was in brackets.

It actually equals 3/a because one can divide 2 through the numerator and through the denomenator keeping the value of the equation the same.

The answer under the Australian school system is 1 and cadel is the best rider in the peleton.

I was educated under the Australian school system, and I think the answer is obviously 9 and that Gilbert is the best rider in the peloton.

 

[Elagabalus]

OK, b!tches!!!

All of you who said 9 are wrong!!!

I just pulled out my Sharp™ EL-5150 "scientific calculator"from 1986. The 2032 battery maybe on life support but when I type in the original formula as written by palmerq (that is 6÷2(1+2)= ?) the answer is 1.

As it is written, so shall it be done!!!

 

[Ferminal]

My calculator says 1
I say 9

It was made in Japan
I was made in Australia

I'm sure the answer is 1, it is just confusing with the divide sign, rather than a numerator and denominator. 2(1+2) is one term

 

[mewmewmew13]

I was educated under the Australian school system, and I think the answer is obviously 9 and that Gilbert is the best rider in the peloton.

Raised in the midwest and grilled in math...I have to concur with Spare Tyre----on BOTH counts, 9 , Gilbert (and Spartacus).
(Even though the parentheses are not there they are assumed....)

 

[krebs303]

google says 9. I checked with a couple of online algebra solvers some said 9 some said 1. I have a friend who is a rocket scientist at JPL I will try to get a hold of him. he is helping to send rockets to Mars his maths is berry berry good I will go with what he says. I still say 9. But as one math teacher told me "I have never made a mistake however there have been several miscalculations"

 

[The Hitch]

google says 9.

Google doesnt say 9. It changes the equation and then says 9.

If you type it into google it gives the following answer

(6 ÷ 2) * (1 + 2) = 9

That is a different equation.

 

[Garry Allen]

I would argue 1 for the reasons everyone else has articulated. Without a multiplication sign between the 2 and the (1+2) in brackets, this takes precedence over the division operator. Using algebraic notation, 6/2a (where a is (1 + 2)) is 6/(2a). If you were wanting to say it was (6a)/2 then it would be written as 6a/2.
If the multiplication operator was there, then you would evaluate the brackets first, then work from left to right as the multiplication and divisor operators have equal precedence. Theres no multiplication operator, its now being written in algebraic notation and the 2(1+2) is evaluated first

 

[krebs303]

pretty much been already said but here from the rocket scientist Phd.

"The question is which has higher operator precedence, multiplication or division...and they are the same.

Then the order is left to right: 6 / 2 = 3 time 3 = 9. However, it is ambiguous as it is written and should have been clarified with additional parenthesis. So the real answer is that neither of you is right. (Or you both are!)

(6/2)(1+2) = 9
6/(2(1+2))= 1
You evaluate the terms in parens first, starting with the inmost one and working out."

Ok everybody wins or loses.

So I will now change my answer to "No Comment"

 

[Ferminal]

However, it is ambiguous as it is written and should have been clarified with additional parenthesis.

Yes, the question is stupid.

No proper maths question would be written like that.

 

[Buffalo Soldier]

6/2a doesn't equal 3a. It would only equal 3a if the 6/2 was in brackets.

this seems logical to me

 

[auscyclefan94]

6÷2(1+2)= ?


Brackets come before multiplication in BODMAS therefore you would add 1 to 2 (which is the brackets) then divide 6 by 2 then multiply the number outside the bracket with the number inside the bracket.

Therefore it = 9.

I can't beleive there is so much debate about this.

Don't trust your calculator as it doesn't understand order of operations.

If you multiply the 2 first you are breaking the bond the two has with the ÷ symbol. To get 1 you would have to multiply before you looked at the brackets or the division. Can Libertine explain to me what system he/she learnt?

The bond the 2 has with the bracket is multiplication.

We could write the equation like this

6÷2x3 =?

In the case of knowing what takes most importance between Division and multiplication, you always go left to right which in this case 9 would be your answer.
This way it makes it more clear how it should be done.

 

[slowingfast]

Bodmas order of operations shows the following:


B Brackets first
O Orders (ie Powers and Square Roots, etc.)
DM Division and Multiplication (left-to-right)
AS Addition and Subtraction (left-to-right)

i.e.,

Multiply or Divide before you Add or Subtract. Example:

2 + 5 × 3 = 2 + 15 = 17
2 + 5 × 3 = 7 × 3 = 21 (wrong)

Otherwise just go left to right. Example:

30 ÷ 5 × 3 = 6 × 3 = 18
30 ÷ 5 × 3 = 30 ÷ 15 = 2 (wrong)

Answer is 9

 

[Buffalo Soldier]

Easiest way: NEVER use ÷
use fractions (with 2(1+2) below the line -> it would make 1)

don't know if the terms i use are correct, not familiar with the english math terms...

 

[Captain_Cavman]

BEDMAS, BIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, PEMDAS, and BPODMAS are not exhaustive.

There are occasions where the way numbers are grouped indicate which calculations should be done first...

1 + 2
2 + 2

indicates that the addition of 2+2 should be worked out before the division

The same applies to square roots only I can't be bothered to work out how to display it here. And the same thing applies to 2(1+2) too.

 

[El Imbatido]

It is 9.

The way ACF explained it is right. Now everyone bow down and obey the Australian way to do maths

That is all

 

[theswordsman]

For me, there are 2 main parts to the equation separated by a divided by sign, s it can be written as a fraction.

6 divided by makes that the denominator, as it will be six divided by whatever.

The rest is the numerator, which turns out to also total 6 no matter which way you calculate it.

6/6=1

Imagine it was presented as an Algebra problem, with letters replacing the 1 and the 2.

6÷2(a+b)=X

The first thing you would do is move the 6 to the other side of the equation, making it

2(a+b) = 6X

divide both sides by 2

a+b = 3X

substitute the numbers back in, since we knew them all along

1+2=3, so X=1

 

[Garry Allen]

Sorry. ACF is wrong.. the 2(1+2) is written as an algebraic operator rather than an arithmetic operator. The multiplication should be done before the division.
Otherwise i would be ******ed doing the laplace transforms for filter theory.....
(me making the claim after completing an engineering degree at an Australian university with 3rd year university maths)

 

[ChrisE]

I agree with ACF.

 

[auscyclefan94]

Sorry. ACF is wrong.. the 2(1+2) is written as an algebraic operator rather than an arithmetic operator. The multiplication should be done before the division.
Otherwise i would be ******ed doing the laplace transforms for filter theory.....
(me making the claim after completing an engineering degree at an Australian university with 3rd year university maths)

One thing I never lose is deabtes about mathematics. I can also do high level mathematics quite well. and my degree also involves that.

You are wrong. The multiplication and division are interchangable in order. Order of operations can be BOMDAS or BODMAS. That means that it can be changed around. Multiplication and division are reverse operations. You can't say that multiplication always comes first. When there is both multiplication and division that could be done then you always solve it from left to right. How does multiplication take precedence over division when they are reverse operations? Divsion takes precedence over addition because they are completely different operations.

theswordsman, you can't use an algerbraic proof to show how order of operations works as there aren't variables involved in it as you are solve the equation not solving for x or y, etc.

Buffalo Soldier

If it were to be and to not use the ÷ sign. You are suggesting that the sum would be like so.

____6______
2(1+2)

then the equation would have to be written as 6÷(2(1+2) which is not what it is. Oddly enough, I used two different calculators and one said 9 was the answer and the other said one.

http://www.mathsisfun.com/operation-order-bodmas.html

The linked article teaches order of operations in a simplistic manner which justifies how to do the equation.