Poll: 6÷2(1+2)

6/2(1+2) = ?

  • 9

    Votes: 516 68.9%

  • 1

    Votes: 233 31.1%
  • Total voters
    749
Hatter The Mad said:
You are right - the notation is rubbish, but apply the universally accepted standard order of notations and you get the same, right answer - 9.

terms inside parenthesis
exponents and roots
multiplication and division
addition and subtraction

Parsed left to right.
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I've never disagreed with you on that - but then I think we were both arguing very different points all along. I guess this comes from both of us coming from two different backgrounds :)

If you wrote that down on a piece of paper and asked me to work it out I'd ask you to write it again, properly ;) For a computer though, I guess things I take for granted like associativity and commutativity aren't the be all and end all when we're talking about things like programming - which again, I don't know jack about :p
 
Killerkebab said:
So you're saying if we let:

x=6
y=2
z=1+2=3

Then we write our equation as x/yz

The answer is still 9? ;)

The notation is poor. I don't know a thing about programming but I do know a thing or two about maths and I can tell you that the notation is rubbish. Whoever wrote this might get away with it in a computer program but not everyone will understand it - which means they've written it poorly. It is not clear enough whether we should be multiplying by 3 or its reciprocal.

Now, if your programming language of choice happens to understand what you've written correctly, then so be it (which was what I meant by my post, I wasn't making fun of computer scientists :p), but from a mathematician's point of view, the problem is poorly written, and if you wrote that down on a piece of paper I'd ask you to write it again.
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I can tell you that by convention:

x/yz is exactly equal to (x/y)z

anywhere where those multiplications are defined.

The notation only doesn't make sense if you are unaware of this convention.

Of course this is only my lecturing mathematician's point of view (dick waving).

By the way any programming language should interpret it in exactly the same way as it is the unique, correct method.
 
Hatter The Mad said:
You have got to be ****ing me?

Edit: A quick Google shows it was a mistake in the AQA answer guide. Poor kids :(
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5669761418_f32ddf8027.jpg
 
As I stated before the answer is 1 because:

2(1+2) is shorthand for 2+4 or (2x1)+(2x2) which means that the 2 is part of the equation in the brackets. Thus to fully calculate the part of the equation associated with the brackets you have to do:

1+2=3
Then 3x2=6

From the original equation you then get 6÷6=1

If the original equation was 6/2(1+2) then it could be interpreted that 6/2 is a fraction which is then multiplied by the result of the addition in the brackets ie:

6(1+2) = 3(1+2) = 3x3 = 9
2

But this is not how the equation is written so the correct answer is 1.

Also anyone stating that the equation is 6÷2*(1+2) or 6/2*(1+2) is incorrect as they have changed the original equation. A bracket must always have a number to the left of it which is multipied by the result of the equation within the bracket ie (1+2) is actually 1(1+2) but for shorthand the 1 outside the brackets is dropped. As such writing the original equation as 6÷2*(1+2) or 6/2*(1+2) means that it is no longer the same as the original equation as you have infact changed it to 6÷2*1(1+2) or 6/2*1(1+2).

So the fact that there is a 2 to the left of the bracket means that the result of the bracket is multiplied by 2.
 
Someone said:
As I stated before the answer is 1 because:

2(1+2) is shorthand for 2+4 or (2x1)+(2x2) which means that the 2 is part of the equation in the brackets. Thus to fully calculate the part of the equation associated with the brackets you have to do:

1+2=3
Then 3x2=6

From the original equation you then get 6÷6=1

If the original equation was 6/2(1+2) then it could be interpreted that 6/2 is a fraction which is then multiplied by the result of the addition in the brackets ie:

6(1+2) = 3(1+2) = 3x3 = 9
2

But this is not how the equation is written so the correct answer is 1.

Also anyone stating that the equation is 6÷2*(1+2) or 6/2*(1+2) is incorrect as they have changed the original equation. A bracket must always have a number to the left of it which is multipied by the result of the equation within the bracket ie (1+2) is actually 1(1+2) but for shorthand the 1 outside the brackets is dropped. As such writing the original equation as 6÷2*(1+2) or 6/2*(1+2) means that it is no longer the same as the original equation as you have infact changed it to 6÷2*1(1+2) or 6/2*1(1+2).

So the fact that there is a 2 to the left of the bracket means that the result of the bracket is multiplied by 2.
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Exactly how i see it, p(n) is a short hand notation.

Any number before a bracket is implicitly associated with the expansion of the bracket step.
 
Someone said:
Also anyone stating that the equation is 6÷2*(1+2) or 6/2*(1+2) is incorrect as they have changed the original equation. A bracket must always have a number to the left of it which is multipied by the result of the equation within the bracket ie (1+2) is actually 1(1+2) but for shorthand the 1 outside the brackets is dropped. As such writing the original equation as 6÷2*(1+2) or 6/2*(1+2) means that it is no longer the same as the original equation as you have infact changed it to 6÷2*1(1+2) or 6/2*1(1+2).
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So, forgetting the 6 and divide sign for one second, your saying that

2*1(1+2) is not the same as 2(1+2)?
 
Someone said:
As I stated before the answer is 1 because:

2(1+2) is shorthand for 2+4 or (2x1)+(2x2) which means that the 2 is part of the equation in the brackets.
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If 2(1+2) = 2 + 4, then

a(1+2) = a + 2a therefore

let a=6/2

6/2(1+2) = 6/2 + 12/2

=9

Hurrah!

6/2 is a number as far as I'm concerned.
 
Using the ÷ symbol leads to confusion as to the order of operations, hence why you rarely use it at higher level and instead just express division as fractions. In this case, 6÷2(1+2) can mean the following:

{6/2} * {1+2} = 3 * 3 = 9

or

{6} / {2(1+2)} = 6 / 6 = 1

As result of this confusion with the usage of the ÷ symbol, we have BODMAS to help, which specifically states that you should do division before multiplication when the order of operations is ambigious, hence we have 9 as the correct answer because:

6÷2(1+2) = 6÷2*3 = 3*3 = 9

This could all have been avoided if they expressed the calculation in terms of fractions, i.e.

{6/2} * {1+2}
 
Tokenbrit said:
I can tell you that by convention:

x/yz is exactly equal to (x/y)z

anywhere where those multiplications are defined.

The notation only doesn't make sense if you are unaware of this convention.

Of course this is only my lecturing mathematician's point of view (dick waving).

By the way any programming language should interpret it in exactly the same way as it is the unique, correct method.
Click to expand...
If only I (and everyone else, clearly) were taught this convention - then arguing on the internet where I can't write my equations properly (unless there is some sort of code or a method of writing equations in VB that I am unaware of - things like fractions, superscripts, subscripts, integrals, matrices and the like would be helpful) wouldn't be so much of a chore :p
 
FoxEye said:
If 2(1+2) = 2 + 4, then

a(1+2) = a + 2a therefore

let a=6/2

6/2(1+2) = 6/2 + 12/2

=9

Hurrah!

6/2 is a number as far as I'm concerned.
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And as I stated 6/2(1+2) is not the same as 6÷2(1+2). If the original equation was written as 6/2(1+2) then the answer could well be 9 or 1 (and in this case I would lean towards 9 rather than 1 but this is not the way the original equation is written).

There is confusion because people are changing the original equation by writing it as 6/2(1+2) rather than 6÷2(1+2) which is not the same thing.
 
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