Listen. If you weren't taught that those aren't the same thing, then you were taught incorrectly. That is all there is to it. There is ONE grammatical syntax to math. JUST ONE. You can bend it to do all sorts of fun things, but if you write something one way, it will ALWAYS mean the same thing. It is up to the individual to understand what it's saying.mps4li3n said:
Poll: What is the answer to 48/2(9+3)?
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Joseph Webb said:
You don't seem to understand that if whatever authority is in charge of the math symbols decides to use totally different ones tomorrow then they could without changing anything about math at all.
Like when they decided that Pluto wasn't a planet, it didn't change any actual real proprieties of Pluto, just it's arbitrary designation.
It does not matter if they change the symbols. It will always mean the same thing. Why do you think that math is a universal language?mps4li3n said:
Maybe im using 'the word syntax wrong...Joseph Webb said:
But if everyone decides that - means division and / means brackets from now on the that's what they mean, and yet multiplication will still work the same...
So there's no one objectively correct way to write an equation like there is an objective way to actually solve any math problem (as in how do i divide 48 sticks to 2 people equally vs how you should interpret an A for english when i only know french).
2(9 + 3) is equivalent to 2*(9+3)Pyro Paul said:
2*9 + 2*3 = 18 + 6 = 24
2*(9+3) = 2*12 = 24
But that isn't the question.
The question is 48/2(9+3)
Which is evaluated as such
BEDMAS(or PEMDAS)
Brackets/Parentheses:
48/2(12)
Division & multiplication ( left to right)
24 * 12 = 288
Or if you prefer to distribute
48/2(9/3) = 48/2*9 + 48/2*3 = 288.
Joseph Webb said:
Precisely, so if one country uses the lack of the symbol * to mean something while another uses it just as if it's the same as using an * it in no way changes math...
The only problem would be people from the two countries not understanding what the other people are trying to say to them with the formula that uses the lack of an *.
This is what's happening here, except that we don't have any well defined borders.
Syntax is how you build a paragraph, or in this case, an equation. You're talking about variables. Variables are just that, variable. They can change and mean anything. A letter in any language is a variable. A symbol is a variable. As long as they are given meaning, they can be used in context. It doesn't matter if they switch around what +, -, =, or any other symbol means. As long as everyone knows what it means, everyone will always understand it. The problem with this equation is that people don't understand the basic rules of math. It has NOTHING to do with symbols, hell, it doesn't even have anything to do with the SYNTAX. It has EVERYTHING to do with the RULES or the language. People are not understanding that an equation like 3/2*(8+2) does not equal 3/2(8+2), because they don't understand the basic rules of math. That's all there is to it. There is indeed multiplication in both situations, but they occur at different times. Everyone is taught this in algebra. If you don't understand this basic concept, you must have done poorly in math, or somehow you managed to scrape by without seeing a problem like this (nearly impossible, but whatever). Look up the distributive property, like I've been saying this entire time.mps4li3n said:
Sorry man.Joseph Webb said:
So just to let me get this straight;
according to you (and i say this without being condescending) the sign / implies a fraction. But not everything following it is part of that fraction. In honestly didn't know that and apparantly i really don't understand mathematical notation as well as you do.
The reason why some other people who say it's 288 are correcting yet other people who say it's 2 is because it also common for people to not understand PEMDAS. As TiefBlau explained
So my intention was to introduce the following example
1/2 * 1/2 = 1
as a counterexample to your reasoning, because i assumed it would sound stupid to you as well. Which it end up doing, but unfortunately for the wrong reasons, because i wrongly assumed you didn't thought about it all that well.
I don't agree however that people who are disagreeing with you are using flawed logic as you mentioned in a couple of other posts. They simply see / sing is an operator like + and - which, to me, has little to do with logic even though it might not be according to formal mathematical notation you know.
So saying these people are "just wrong", are using flawed logic or making comments about their math skills isn't really helping you to convince them.
I have always seen / simply as an operator. This is what was okay in high school and university, didn't do math there by the way. I was actually surprised so many people thought the answer was 2, what a bunch of idiots
(In the Netherlands it also common to use : as the symbol for division which will probably give some people on this forum a headache.)
That doesn't actually mean you can't attach an extra meaning to the lack of * in relation with other symbols...Taerdin said:
And people do if this is any indication: http://www.purplemath.com/modules/orderops2.htm
The problem stems fromt eh fact that in hand writing the / symbol always had superscript and subscript, and thus you could always tell if the part in () was under the fraction or not.
Once computers couldn't do that easily thee does need to be another way to make that clear, and it seems the lack of a * is how some (perhaps the majority of scholars) decided to do it.
Well notation is not set in stone and never was... a lot of people seem to think that because math is so must mathematical notations...yeel said:
It's silly really... it's not like everyone who understood that putting 1 and 1 stick together makes 2 sticks used + in between them all of a sudden, or used the same symbol even if they where thousands of miles away, using totally different languages etc.
Yes it does change math. Math works the same all over the world. They will always have some sign letting you know what operation to perform. That's how mathematicians work. They have rules, and they follow them.mps4li3n said:
I'll explain this one last time to you. In the equation 48/2(9+3), 2 is part of the parentheses. Therefore, distributing it amongst the 9 and the 3 comes before EVERYTHING else. It is the FIRST thing you do.Taerdin said:
Don't disagree when I say the people that are getting the answer wrong are using flawed logic. They are using calculators to solve the problem, which utilize flawed logic to solve problems like these. Calculators generally DO NOT distribute automatically. The 2 in the denominator of this problem is a coefficient of (9+3), meaning it belongs inside of those parentheses, but this is implied. Taking a basic algebra class should teach you something like this. Calculators do NOT imply that the 2 is included in the parentheses, and instead treats 48/2 as a fraction, instead of 48/2(9+3). The (9+3) is part of the denominator.yeel said:Sorry man.Joseph Webb said:
So just to let me get this straight;
according to you (and i say this without being condescending) the sign / implies a fraction. But not everything following it is part of that fraction. In honestly didn't know that and apparantly i really don't understand mathematical notation as well as you do.
The reason why some other people who say it's 288 are correcting yet other people who say it's 2 is because it also common for people to not understand PEMDAS. As TiefBlau explained
So my intention was to introduce the following example
1/2 * 1/2 = 1
as a counterexample to your reasoning, because i assumed it would sound stupid to you as well. Which it end up doing, but unfortunately for the wrong reasons, because i wrongly assumed you didn't thought about it all that well.
I don't agree however that people who are disagreeing with you are using flawed logic as you mentioned in a couple of other posts. They simply see / sing is an operator like + and - which, to me, has little to do with logic even though it might not be according to formal mathematical notation you know.
So saying these people are "just wrong", are using flawed logic or making comments about their math skills isn't really helping you to convince them.
I have always seen / simply as an operator. This is what was okay in high school and university, didn't do math there by the way. I was actually surprised so many people thought the answer was 2, what a bunch of idiots
(In the Netherlands it also common to use : as the symbol for division which will probably give some people on this forum a headache.)
Yeah, you're taking syntax to mean what it does in math, while i mean more of how words go together in ways that tell the same thing with different words...Joseph Webb said:
And you obviously don't understand that 2(x) and 2*(x) being different from each other is the same thing as - and + are different, but there's nothing stopping the majority from declaring
that from now on + means the same as - in maths, and just finding another way to represent addition... they're just symbols in the end...
You can teach someone math just as correctly as you know it with 2(x) being the same as 2*(x) as long as you use something else for what you know as 2(x).
Thus the meaning you derive from those symbols isn't dependent on the symbols themselves, but what you've been taught to understand from them...
I'm not trolling. The two is the coefficient of (9+3), meaning it technically is inside of the parentheses. Look up coefficients, you'll find a bunch of nonsense involving variables and stuff you won't understand. However, it won't matter, because I am not trolling. 2 is involved in the parentheses, therefore (9+3) is part of the denominator.The_AC said:
You don't get it. I've offered every example I can, but you don't understand it. You can phrase a mathematical equation any way you want, but if you write it correctly, it will still mean the same thing. 2 = 4/2 = 8/4 = 9(6+6)/9(3+3) = 2 You can get as complex as you want, it still means the same thing. The problem is that people aren't understanding the basis of math here. Coefficients are multiplicative factors, they always stay with their pairs. That's how math works. In the original equation, 2 is the coefficient of (9+3), meaning (9+3) will ALWAYS stay with the 2, meaning it will drop down into the denominator with it. The 2 wouldn't be (9+3)'s coefficient if there was a multiplication symbol between the two terms, because that's just how they work. Order of operations would kick in, and the answer would be 288.mps4li3n said:
Honostly...Taerdin said:
The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication.
Source:
http://www.purplemath.com/modules/orderops2.htm
(bottem half of page)
The fact that you where NOT taught this in basic algebra and that i have to go to 'purplemath' to prove you wrong hurts my brain...
there is a complex reason involving distribution, coeffecents and terms that are probably beyond your comperhension as to WHY you calculate numbers against brackets First... but i'll leave it at just Basic Algebra level for you...
And that's the thing, you take it as a coefficient while others do not... and if this was given to someone in 8th grade it would have to be (42/2)....Joseph Webb said:
Context is always important, which is why, unless i'm very sure of the intentions of whoever gave it to me i'd always ask about it.
And as i said before, notation can and does differ based on country... saying that because that's the notation you use for that doesn't instantly mean it's what everyone uses... or even that whoever gave you the formula isn't using the lack of * wrong (like he could be asking how much money he would make in 48 days is he's working half a shift and the full shift gave him 9+3 $ per day).
The worst part is that I've already directed them to that page, and they didn't believe me still.Pyro Paul said: