Islander
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and help to keep the site free for all
6÷2(1+2)= ?
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No it doesn't, why do you introduce brackets when they are not in the equation.
I'm certainly sure there are some people here with great mathematical skills but to my knowledge of doing 3 years of advanced mathematics for graphics I've seen equations more complex than this and always the brackets have to resolve first and that means inside the bracket and anything immediately attached in this case the 2, there is no "x" in there so the there is no reason to talk about multiplication. Simply first solve the bracket:
2(1+2) = 6
Then solve the whole equation:
6 / 6 = 1
This is how it goes. And what I've been doing for calculating light intensity in computer graphics and always got the correct results on the screen, so I believe in what I see
End
This is how I should have put it if I'm honest.
The point I was trying to make was that the multiplication symbol ois removed in this instance to indicate that the number outside of the brackets becomes a part of the bracketed calculation and is therefore treated as above.
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You resolve the contents of the parentheses first. The multiplier has nothing to do with the contents whatsoever.
Bloody hell, this debate is turning me into Arkady
That's my whole point. The removal of the multiplication symbol means that it DOES have something to do with the contents. Do you really think it's removed (or implied) because it just doesn't matter if it's there or not? Every part of a mathematical formula is important.
Islander
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Islander
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Plug it into a calculator that follows the rules of order of operations. It'll come out as 9 every time.
By convention, you don't use a multiplication symbol when the multiplicand is the result of an operation within parentheses. The order of operations doesn't change because of this.
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Well calculators don't use brackets so that isn't going to work.
I've already said many times that the multiplication symbol is removed to indicate that it is to be calculated with the contents of the brackets before other factors are considered, I can't explain it any clearer than that. This is mathematical fact and it is being ignored.
Creaxel_photo
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To be honest, you can't really trust in all calculators I've seen some mistakes in calculators when compared, but you really need to see the point of not using a x sign, it's for a reason, this is maths, logical, everything happens for a reason! So when it's not there then the bracket is solved inside out then you move as I explained in my previous post.
Creaxel_photo
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fabs said:
This is exactly correct,
Islander
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Eh? Since when?
I've got a TI calculator and a Casio both of which use parentheses, are capable of nested operations and follow the rules of order of operations
It's not a mathematical fact. The rules of order of operations is though
Islander
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No, it's not.
Islander
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It's a mathematical convention. When the multiplicand is the result of an operation within parentheses, you don't use an operator with the multiplier.
ETA
I used to have an HP calculator that used RPN. It didn't have an equals key but it made no difference to the operation of the calculator and the results it produced.
That one would have returned 9 as well
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Eh? Since when?
I've got a TI calculator and a Casio both of which use parentheses, are capable of nested operations and follow the rules of order of operations
It's not a mathematical fact. The rules of order of operations is though
Ok, I was talking about a standard calculator that most people use.
As for your 2nd paragraph, the removal of the multiplication symbol has a direct effect on the order of operations. That's why it is removed, that is the whole point.
Creaxel_photo
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Islander said:It's a mathematical convention. When the multiplicand is the result of an operation within parentheses, you don't use an operator with the multiplier.
ETA
I used to have an HP calculator that used RPN. It didn't have an equals key but it made no difference to the operation of the calculator and the results it produced.
That one would have returned 9 as well
Well I was referring to my experience of doing this sort of equations and seeing the results, but you are referring to calculators so I win
the answer is 1 and that's all.
Islander
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:bang::bang::bang:
It's a convention. You don't need the operator when parentheses are used. It makes no difference to the order of operations.
If it had been nested, i.e. (2(1 +2)) then that would have been a different matter but using an implied operator does not imply a nested operation - they're always explicit.
Islander
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Well I was referring to my experience of doing this sort of equations and seeing the results, but you are referring to calculators so I win
No, I was using an example of implied operations.
The answer is 9.
In my previous career I was an electronics engineer and worked in design of complex audio filters and amplifiers in an R&D lab - I used paper to perform operations much harder than this including j notation (imaginary numbers - electrical and electronic engineers use j rather than i to avoid confusion).
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DemiLion
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FYI, if we are talking about conventions:
2(2+1) = [2 x (2+1)]
As for various calculators, the standard rules apply; ***** in, ***** out.
DemiLion
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Calculators aren't proof of mathematical absolutes. If you put duff data in then you'll get an equally duff result.
You need to go back to basic principles. For heavens sake, any GCSE student would get this in one, or at least they should.
You need to go back to basic principles. For heavens sake, any GCSE student would get this in one, or at least they should.
Creaxel_photo
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If we use a simple proof and substitute 1 with 'x' and try the values we get something like this
6/2(x+2)=9
6/2x+4=9
6=9(2x+4)
6=18x+36
-30=18x
x= -(30/18), which definitely isnt 1.
6/2(x+2)=1
6/2x+4=1
6=1(2x+4)
6=2x+4
2=2x
x=1
Well the proof says 1 is correct.
6/2(x+2)=9
6/2x+4=9
6=9(2x+4)
6=18x+36
-30=18x
x= -(30/18), which definitely isnt 1.
6/2(x+2)=1
6/2x+4=1
6=1(2x+4)
6=2x+4
2=2x
x=1
Well the proof says 1 is correct.
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aerobandit
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I cannot believe that this still goes on:bonk: Its a very basic maths(primary school level)
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Is that maths x the solved contents of the bracket?
Anyway, everyone has missed the solution, it's 42 obviously.
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No it isn't. It's -
parenthesis, exponents, multiplication and division, addition and subtraction.
A subtle difference but most important. Your error is the same as the one made by those who think the answer is 1.
Extract from here
Mnemonics are often used to help students remember the rules, but the rules taught by the use of acronyms can be misleading. In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If PEMDAS is followed without remembering to do multiplication and division at the same time and done instead with multplication then division students will get wrong answers. For example: 6÷2(1+2)=9, not 1. In other English speaking countries, Parentheses may be called Brackets, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, and since multiplication and division are of equal precedence, M and D are often interchanged, leading to such acronyms as BEDMAS, BIMDAS, BODMAS, BOMDAS, BERDMAS, PERDMAS, PEMDAS, and BPODMAS.
These mnemonics may be misleading, especially if the user is not aware that multiplication and division are of equal precedence, as are addition and subtraction. Using any of the above rules in the order "addition first, subtraction afterward" would also give the wrong answer.
Goodnight.
redddraggon
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Hi. I'm the world's worst at this sort of thing. I get the 'do the brackets first' bit, but then flounder about what you do with this 'product' - where does it say you multiply? Am I missing something obvious? If it was in excel there would be a *, right??
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If you put the original equation into Excel, you get an error. The whole point is the effect when you have a number followed by a calculation within brackets but without the multiplication sign in between. This indicates that it is a complete calculation in itself and needs to be resolved first.
As Excel can't deal with this, you need to use =6/(2*(1+2)) from which the answer is, of course, 1.
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It's actually 1, 7 or 9 depending on how you look at it. The problem is the way the expression has been written is ambiguous, which is why you stop using that form pretty much as soon as you leave primary school.
Punching that directly as written into my TI-89 gives 9 basically because it's evaluating 6÷2×3 which in my mind is correct - sequence takes precedence when the operators are of equal priority.
To get 7 first get rid of the brackets: 2(1+2) = 2+4 thus 6÷2+4 = 7 this is very wrong - it's just an example of how this form of expression is ambiguous.
To obtain 1 as the result then really it should be written as 6÷(2(1+2))
Punching that directly as written into my TI-89 gives 9 basically because it's evaluating 6÷2×3 which in my mind is correct - sequence takes precedence when the operators are of equal priority.
To get 7 first get rid of the brackets: 2(1+2) = 2+4 thus 6÷2+4 = 7 this is very wrong - it's just an example of how this form of expression is ambiguous.
To obtain 1 as the result then really it should be written as 6÷(2(1+2))
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O Rly?
6 / 2(x+2) = 1
6 / 2 = 1/(x+2)
Oh dear...
6 / 2(x+2) = 9
6 / 2 = 9/(x+2)
Aha!
Critical I
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The answer is 9.
When you write a(b+c) you are simply writing a shorthand for a*(b+c)
If I write "ab" I imply "a*b"
When you evaluate brackets first, this only applies to the numbers INSIDE the brackets, not any operators outside the brackets.
To get 1 you would have to write the above as 6/(2(1+2))
As written its the same as 6/2*(1+2)
6/2(1+2) = 6/2(3) = 3(3) = 9.
There is no ambiguity here at all. I can't believe anyone is arguing about this.
When you write a(b+c) you are simply writing a shorthand for a*(b+c)
If I write "ab" I imply "a*b"
When you evaluate brackets first, this only applies to the numbers INSIDE the brackets, not any operators outside the brackets.
To get 1 you would have to write the above as 6/(2(1+2))
As written its the same as 6/2*(1+2)
6/2(1+2) = 6/2(3) = 3(3) = 9.
There is no ambiguity here at all. I can't believe anyone is arguing about this.
Critical I
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Nope. Evaluating brackets first ONLY applies to those numbers IN the brackets.
ab is a convention for writing a*b, hence a(b+c) is the same as a*(b+c). Missing out the operator does not change the order.
a/b(c+d) is simply a/b*(c+d) in shorthand. Missing out the * does not imply it becomes a/(b*(c+d))
And yes I used to teach maths.
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Look guys this is really really simple.
the expression has 3 distinct numerical terms. the 6 the 2 and the (1+2).
So if we put in all the operators we get 6÷2×(1+2). The 2 and (1+2) are separate individual terms. Just because it's written 2(1+2) doesn't make it a singular numerical term in itself, and you can't just arbitrarily decide to keep it as one term.
Fact of the matter is that 6÷2×(1+2) = 6÷2×3 = 9.
Those of you that are getting the answer 1 are treating the 2(1+2) as a singular term. In this example it is incorrect to do so.
http://www.wolframalpha.com/ evaluates this to 9 and if given the algebraic form x/y(z+y) also gives a form of this equation that when you plug the numbers in the result is 9. Wolfram alpha is backed by mathematica, probably the leading CAS (Computer Algebra System) solution in the world. I very much doubt it's screwed up on something that's as simple as this.
the expression has 3 distinct numerical terms. the 6 the 2 and the (1+2).
So if we put in all the operators we get 6÷2×(1+2). The 2 and (1+2) are separate individual terms. Just because it's written 2(1+2) doesn't make it a singular numerical term in itself, and you can't just arbitrarily decide to keep it as one term.
Fact of the matter is that 6÷2×(1+2) = 6÷2×3 = 9.
Those of you that are getting the answer 1 are treating the 2(1+2) as a singular term. In this example it is incorrect to do so.
http://www.wolframalpha.com/ evaluates this to 9 and if given the algebraic form x/y(z+y) also gives a form of this equation that when you plug the numbers in the result is 9. Wolfram alpha is backed by mathematica, probably the leading CAS (Computer Algebra System) solution in the world. I very much doubt it's screwed up on something that's as simple as this.
Creaxel_photo
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O Rly?
6 / 2(x+2) = 1
6 / 2 = 1/(x+2)
Oh dear...
6 / 2(x+2) = 9
6 / 2 = 9/(x+2)
Aha!
This certainly is not the way to expand a bracket, if you have a(b+c) you get ab+ac and not what you getting at.
You cannot separate the 2 from the bracket when expanding.
The proof i used is a simple equation, to solve for x.
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