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6
- Thread starter Vihzel
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SnakePlissken
Lurker
I guess I look at this problem from the reverse :
How would you write these 2 seperate problems in single line form without having the ability to make a fraction or similar character from a standard keyboard device ??
6
------
2(1+2)
6
--- (1+2)
2
I would say that the first one is: 6 / [2(1+2)]
And the second is: (6/2)(1+2)
In both instances, I had to include extra brackets to the original equation to remove any possible source of ambiguity that might come into play with differences of opinions. If you look at the 2 ways I wrote the equations, there is no chance of misinterpretation which therefore tells me the original question was written poorly and leaves room for error. Hence, this drawn out forum over such a simple issue.
My final stance, there is a possibility of 2 correct answers depending on clarification of the original equation for which expressions go where.
How would you write these 2 seperate problems in single line form without having the ability to make a fraction or similar character from a standard keyboard device ??
6
------
2(1+2)
6
--- (1+2)
2
I would say that the first one is: 6 / [2(1+2)]
And the second is: (6/2)(1+2)
In both instances, I had to include extra brackets to the original equation to remove any possible source of ambiguity that might come into play with differences of opinions. If you look at the 2 ways I wrote the equations, there is no chance of misinterpretation which therefore tells me the original question was written poorly and leaves room for error. Hence, this drawn out forum over such a simple issue.
My final stance, there is a possibility of 2 correct answers depending on clarification of the original equation for which expressions go where.
Russell Ng
Android Expert
Somebody brought a dead thread back to life... lol
Anyway... I think it depends on what you were taught in school. I was taught that it was 1 simply because in terms of order, multiplication trumps division. But for some, multiplication and division are in the same order and thus you go from left to right, which gives you 9.
So, the fault(s) lies in the school education system and the damn bloody lousy equation that is ambiguous.
Either answer is RIGHT depending on what you are taught.
AND WRONG because what you want is a definitive answer since you can do plenty damage with equations like those. I am a structural engineer. Getting those wrong can cause a building to collapse. Put in the parentheses and remove the ambiguity. That's the CORRECT answer.
Anyway... I think it depends on what you were taught in school. I was taught that it was 1 simply because in terms of order, multiplication trumps division. But for some, multiplication and division are in the same order and thus you go from left to right, which gives you 9.
So, the fault(s) lies in the school education system and the damn bloody lousy equation that is ambiguous.
Either answer is RIGHT depending on what you are taught.
AND WRONG because what you want is a definitive answer since you can do plenty damage with equations like those. I am a structural engineer. Getting those wrong can cause a building to collapse. Put in the parentheses and remove the ambiguity. That's the CORRECT answer.
MyTjSux
Android Enthusiast
LOL this is the fact....while we are taught the answer is 9 (which it is) the actual number nine is a representation of a value created by man which is why the answer can also be 1 or 5 or 33 all depending on how you were taught...lol
Math is man made and while nature gives us examples of formulas and representations of (proper) math, math is in fact an idea....
i thank myself
Math is like fire.
You can make it, but mother nature invented it.
You can make it, but mother nature invented it.
Someone please feel free to correct me if I'm remembering this wrong--after all, it was back in 1982 that I took College Algebra. 
There shouldn't be any ambiguity about this equation because you're supposed to solve the contents of parentheses first, hence we do the (1+2) to get 3. Then, since the remainder of the problem involves division and multiplication, we simply go from left to right to solve it.
We have:
6 / 2 * (1 + 2) or
(6 / 2) * (1+2) or
(6 / 2) * (3) or
(3) * (3) for an answer of 9.
Right...?
There shouldn't be any ambiguity about this equation because you're supposed to solve the contents of parentheses first, hence we do the (1+2) to get 3. Then, since the remainder of the problem involves division and multiplication, we simply go from left to right to solve it.
We have:
6 / 2 * (1 + 2) or
(6 / 2) * (1+2) or
(6 / 2) * (3) or
(3) * (3) for an answer of 9.
Right...?
jhawkkw
Chinchillin'
Someone please feel free to correct me if I'm remembering this wrong--after all, it was back in 1982 that I took College Algebra.
There shouldn't be any ambiguity about this equation because you're supposed to solve the contents of parentheses first, hence we do the (1+2) to get 3. Then, since the remainder of the problem involves division and multiplication, we simply go from left to right to solve it.
We have:
6 / 2 * (1 + 2) or
(6 / 2) * (1+2) or
(6 / 2) * (3) or
(3) * (3) for an answer of 9.
Right...?
Yep, you are 100 percent correct. Under standard decimal arithmetic, that is the procedure to use. Many people learn the acronym PEMDAS, or the phrase "Please Excuse My Dear Aunt Sally", and incorrectly learn or assume that multiplication has higher precedence than division. Under standard rules of arithmetic, multiplication and division have the exact same precedence and must be computed from left to right. Addition and subtraction also have the same precedence and also should be completed from left to right.
This is why when I teach this topic, I prefer to use the phrase "Please Exclude Mom or Dad As Sane". It gets a chuckle out of people and also inserts the idea that it's M or D, not M then D.
Yes, that's exactly how I do it.
I like that.
I wish my dad (actually my father-in-law) was still around. He died two years ago.
He was a college math professor and I'd LOVE to ask him about this.At any rate, when I solved it, I just pictured myself back in class taking an exam, and it seemed clear as day how to solve it. But, as I said, it was actually 1982 when I was in that particular class, so maybe I was just remembering wrong.
You know what got me? I was under the impression in PEMDAS "Multiplication or division, which ever comes first" meant what I had to use first to get rid of the parenthesis. Was never taught left to right. Maybe they meant that when they said which ever comes first. And the parenthesis as still there....so I multiplied to get rid of it.
6
6
jhawkkw
Chinchillin'
jhawkkw
Chinchillin'
I used the {} to signify a fraction, not as an extra pair of parenthesis. By mathematic definition, an operation is a function that takes 2 numbers in a specific order and yields one result. An operation can be delayed by the of parenthesis BEFORE the second number. Since the 2 is not wrapped in parenthesis, it is part of the division and since division and multiplication have equal precedence according to the order of operations, it would be done before the multiplication. there's no denying that the first operation done is the addition because of the parenthesis. Since there is no exponents, that brings us to multiplication AND division. They have EQUAL precedence, therefore it is computed from left to right. 6/2 =3, then 3*3 is 9.
jhawkkw
Chinchillin'
Another thing that might help people see that the answer is 9, is that the definition of division is the first number times the multiplicative inverse(aka reciprocal) of the second number. If using this definition, then after the parenthesis, the expression would change to 6*{1/2} * 3 or 6*.5*3.
jhawkkw
Chinchillin'
It's a common thing that I see, I even saw this question pop up in a picture on facebook with the claim that 93% get it wrong. I don't know how true that is, but I know that order of operations questions are quite popular. I personally feel that mathematics is poorly taught to students because a large number of those that are really good with math can make bigger money elsewhere, leaving numerous secondary and primary math teachers that aren't on the same level. Here in NY, you need to have a masters degree to teach, and the starting pay is horrible. I don't know many people that would be thrilled with going to college for 6 years to start with a salary of 37,500
CafeKampuchia
Android Expert
Why all the discussion? Everyone knows that the right answer is
