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If you have a math degree you're probably not holding steadfastly on to a rule that's taught in 5th grade, which like a lot of things we're taught in 5th grade, turn out to be simplified rules that are refined when we study subjects more deeply. I think this is why the author I cited in the OP expressed that some of these rules we teach to 5th graders are in some ways doing them a disservice. If you forget everything you learned since 5th grade, you might get 288 too?
bastion
reply to post by GogoVicMorrow
Nope. I've got a degree in maths. You need to solve the brackets/parenthesis first. 2(9+3) simplifies to 2(12) not 2 x 12 - where no brackets/parenthesis are present, causing the mistake - so the denominator is 24, giving the answer 2.
Calculators can't do fuzzy logic.
I hope everyone agrees with that. I do.
Pilgrum
What's been proven here without a doubt (as if it needed any proof) is that if we leave any room for misinterpretation in our expressions, they'll be misinterpreted by man & machine alike.
It is more convenient, but if convenience leads to ambiguity that's bad. I'd like to point out if you wanted the answer to be 288, you could write the problem as 48(9+3)/2, and you don't need to add any extra parentheses, and I don't think it's ambiguous, is it? Or does someone get an answer other than 288 if it's written that way? People can avoid confusing themselves if they make the expression to the left of the slash the numerator and the expression to the right of the slash the denominator. This isn't taught universally but it can avoid some ambiguity.
jonnywhite
Here's my opinion: 3(5) = 3 * 5.
...
And this is easier to write: 3(3+5)...
Versus: 3 * (3+5).
So the convenience of writing the formula wins.
I'm not so sure about that. What's the answer?
sean
If 48÷2(3+9) is used then there is no misinterpretation for sure, but no one ever uses it. lol
From correspondence with people on the the 48/2(9+3) problem, I have learned that in many schools today, students are taught a mnemonic "PEMDAS" for order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If this is taken to mean, say, that addition should be done before subtraction, it will lead to the wrong answer for a−b+c. Presumably, teachers explain that it means "Parentheses — then Exponents — then Multiplication and Division — then Addition and Subtraction", with the proviso that in the "Addition and Subtraction" step, and likewise in the "Multiplication and Division" step, one calculates from left to right. This fits the standard convention for addition and subtraction, and would provide an unambiguous interpretation for a/bc, namely, (a/b)c. But so far as I know, it is a creation of some educator, who has taken conventions in real use, and extended them to cover cases where there is no accepted convention. So it misleads students; and moreover, if students are taught PEMDAS by rote without the proviso mentioned above, they will not even get the standard interpretation of a−b+c.
Masterjaden
reply to post by James1982
You CAN'T get to
48
-------
2(9+3)
Because that is NOT what is written...
3mperorConstantinE
I can't believe that this question even made it to the internet.
288
We really do live in that universe where the movie “Idiocracy” becomes a true story.
Still, S&F for the thread~
—Mathematical Physicist
James1982
3mperorConstantinE
I can't believe that this question even made it to the internet.
288
We really do live in that universe where the movie “Idiocracy” becomes a true story.
Still, S&F for the thread~
—Mathematical Physicist
If
F(x) = 4(x^2) + 5x + 4
G(x) = 3x+4
What is (f o g)(x)?
What is (f o f)(x)?
What is (g o f)(3)?
Could I even ask you that question if I was at an idiocracy level of education? It's incredibly easy math to me, but I can still see 2 as being correct depending on how you frame the initial problem.
3mperorConstantinE
James1982
3mperorConstantinE
I can't believe that this question even made it to the internet.
288
We really do live in that universe where the movie “Idiocracy” becomes a true story.
Still, S&F for the thread~
—Mathematical Physicist
If
F(x) = 4(x^2) + 5x + 4
G(x) = 3x+4
What is (f o g)(x)?
What is (f o f)(x)?
What is (g o f)(3)?
Could I even ask you that question if I was at an idiocracy level of education? It's incredibly easy math to me, but I can still see 2 as being correct depending on how you frame the initial problem.
Please clarify.
Am I now supposed to be impressed that you can ask me a question about … algebra?
James1982
mojo2012
what is 48/2(x+y)? i typically assume that 48 is being divided by 2(x+y). I guess it should be written like this 48/[2(x+y)].
Great way of looking at it.
That would be 48/2x+2y
x=9
y=3
Then you get 48/18+6 or 48/24 or TWO.
I can't believe some people still think it's anything other than two. Sad state of education for sure.
GogoVicMorrow
reply to post by James1982
Its 288. Any college math class you go to will give you 288. You are applying incorrect attributes and/or changing the problem.
You do the addition first always as its in the parenthesis. Then you have 48/2·12.
So you are trying to sell us that 48/2·12 = 2? You are incorrect.
48/2 (9+3)
48/2·12
24·12
= 288
You and a few other is this thread are trying to manipulate the problem. Why? I dont know, its a very simple problem.
You always know there is a multiplication sign between a number and a parenthesis. You always solve a problem with division and multiplication in order (if there is no parenthesis).
So after you solve the addition in the parenthesis you have a simple division and multiplication job.
Anyone getting something other than 288 has forgotten basic math.. maybe because they've done too much math, I dont jnow, but regardless as to the reason, 2 is wrong. 288 is correct.edit on 2-3-2014 by GogoVicMorrow because: (no reason given)
GogoVicMorrow
reply to post by James1982
And the algebra analogy is incorrect, too. 48/2x is not equivalent to 48/2(9+3) where x = (9+3). Algebra treats 2x as a single algebraic term whereas 2(9+3) are two separate elements. When this is parsed in an expression calculator and separated into terms with the operators in between, 2x is considered one term, while 2(9+3) are considered 2 separate terms.