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You resolve inside the parentheses first with PEMDAS, but all thats inside the parentheses is 3. So its really 6^2 ÷ 2 × 3 + 4. 36 divided by 2 times 3 plus 4. Division and Multiplication are equal in priority, thus its 18 times 3, not 36 divided by 6.
It...seems you are correct. After checking the math (using a calculator), it looks as though 58 is, in fact, the solution.
...
Well, I've never made it a secret that I suck at math.
It looks like maybe he's being deliberately obtuse about how the multiplication of 2 and 3 isn't actually written in? But then he went off and gave an example that doesn't fit at all.
Huh. Not seeing what's the issue. Saw it, reached 58 in a few seconds. The (3) is just meant to trip you up, but you simply replace it with x 3 in your mind.
I don't even want to know what the person was smoking when they wrote that comment.
They were smoking the idea that adding functions to an equation when they're not there should never be required. It's about as valid as dropping verbs.
I do not think that division comes before multiplication. So there are two answers depending on what route you go by solving it.
It's true, there is no "=", but I believe that the problem lies in the fact that we do not know whether to youse multiplication or divisions first.
Depending on what we chose, we get either 10 or 58.
No, Division and Multiplication are equal in priority. Which means you solve them left to right. Division comes before Multiplication whenever it shows up to the left of Multiplication.
We definitely know to use division first in this instance lol, thats the whole point of the math problem, to trick you into getting 10. 58 is the only correct answer.
Megaolix already explained that above Valette. When you place a number next to a parentheses, you must multiple it with whatever is within the parentheses. That's why 2(3+5) for instance, would equal 16. And that's why 2(3) is really 2x3.
And actually, the use of X to represent values while it's already a basic mathematical symbol should stop. Q is a perfectly fine arbitrary letter. Use that instead.
X(Y) is kind of the opposite of lazy, though? X*Y takes less work to write out.
I really don't see the issue, there's no ambiguity in what it could possibly mean to have a number next to the outside of a pair of parentheses. In every case, it means you multiply the number by what's inside the parentheses.
(X*Y) would not be correct, because the whole point of this math problem is to learn not to immediately use parentheses first for everything and to divide before multiplying, while (X*Y) forces the multiplication first.
As has been said, the point of the math problem is to trip most people up, so that they can then learn from their mistake. 2(3) is a perfectly valid way to write out 2*3 and it always has been.
Here's the lesson this equation teaches, simplified: The majority of people learn PEMDAS, and immediately assume Parentheses need to be taken care of before everything else.
However, this is not true. What this equation is teaching is that the P in PEMDAS stands for "Inside Parentheses first" not "Anything Involving Parentheses First".
Inconsistent rules do not deserve to exist inside a system of logic. This lesson is entirely a result of a pointless and unneeded shorthand, and grants no benefit to mathematics.
This is a constructed language. It does not need such nonsense.
An example sits right here. There's no need for such convolution when clarity is less complex. A function does not need two symbols, and one symbol should not mean two contrary things.
And there's no need for a test to try and trip up students if the system in question is logical, an element that is core to mathematics.
I'm starting to wonder if this debate should be taken on a thread.
Anyway, gotta disagree with you Valette. Given the low difficulty of the question itself, would use it to test young teens (10-12) if they can read equations properly.
If mathematics is to be a logical language, it should use one clearly distinct symbol for a given meaning. It should not use a symbol to mean two things.
False equivalence. It's the same way to mean two things. One may prefer one way, others another. 3 + 3 + 3, 3 x 3 and 27/3 give the same results, but it's done in different ways.
What, exactly, is the difference between 3 x 3 and 3(3) in your eyes, please? Because you have told me they perform exactly the same function, but now you are telling me otherwise.
Megaolix's saying 3(3)=3*3=3+3+3=3+(3+3)=3^2
All of those equations are functionally identical and can be simplified into each other depending on what you consider "simplest"
Yes and no. 3(3) and 3 x 3 are given the same function, but 3+3+3 is more than one function, 3+(3+3) adds an extra step on top of that, and 3^2 is entirely different.
They share the same result, but that does not make them the same thing.
Given that we have now diverted from and back to the position that 3(3) and 3 x 3 are the same function, would you care to answer my question five posts up?
Math itself disagrees with you Valette. If you actually clicked on the link I tried to share with you hours ago, you should already know why this is the way it is.
The Parentheses aren't what's important. What's important is the simply fact that, "any two symbols next to each other, barring some other operator, are connected by multiplication."
Math itself doesn't have a will. It is a language directed by its users. If that is to be the basic relationship between any two numbers lacking an operator, then the multiplication symbol is entirely useless.
Justify this. Why multiplication, and not addition or subtraction? Why not inertia, a lack of any function?
I'm not trying to justify or decide anything here, so maybe that's where this disconnect between us is coming from. This is a rule of math. It has always been a rule of math.
I'm not going to try and explain it, because I didn't make it a rule of math. All I did was learn it in school, like everyone else did. Whether or not its a GOOD rule of math, doesn't matter to me.
At one point in history, multiplication did not exist. Mathematics predates multiplication. Someone decided to use the symbol x to mark their new technique at one point. Someone decided to define the relationship between any two numbers lacking an operator, and it was an arbitrary decision.
Mathematics is a constructed language. It is supposed to be entirely logical. This is not a logical component.
Dammit Valette, this is not the kind of debate any of us can conclude. I mean, square root of 9 and 9 / 3 is still the same thing. Not any of us decided what symbol means what and why there are multiple ways to say the same thing.
What you ask us to answer is something no one on QQ (Unless one of us is an expert mathematician that learned the hows and whys here) can answer.
Because you've gone from saying "Multiplication cannot be implied" to saying "Math is wrong for allowing multiplication to be implied by juxtaposition".
Because, you aren't arguing with us anymore Valette. You're literally arguing with long dead mathematicians and the entire mathematical language. They're the ones who made the rule, and the rule itself is taught across the entire world to everyone.
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