[MERIT]

Again, this adds nothing to the argument, it simply states it differently. Here is where we see to be coming to a disagreement at:

You say that multiplication and division both bear equal precedence between one another, therefore, in a complex equation involving both multiplication and division, one should simply operate from left to right.

My disagreement, which I supported with numerous and equally credible links, says that multiplication ALWAYS takes precedence over division, just as addition ALWAYS takes precedence over subtraction, per the PEMDAS method of operation that was cited in my links, and has been taught to me my entire life, with which Big3 also agreed with.

We both cited sources that are completely conflicting with one another as far as the precedence involved within the order of operations goes. One source says A, the other says B. Both are not correct, but both are not wrong either. As MoonlitSunshine has said, the equation is too ambiguous at this point to be correctly solved using either method of operation.

And I have literally NEVER heard anyone say that they bear the same precedence to one another. I was never taught that in my middle school Pre-Algebra class, Statistics, Algebra, Pre-Calculus, Trigonometry, Calculus I, Calculus II, Calculus III, or the Differential Equations courses that I have completed. I feel that my professors who hold Masters and Doctorates degrees would be a better authority than Google. Again, there seems to be a fundamental difference between the sources that really makes no sense to me.

But if asked to explain why one method of operation would be superior to the other, I would posit this:

Addition is positive, meaning that you are adding something to the number. Subtraction is negative, meaning that you are taking something away from the number. Rather than a left to right interpretation for a method of operation between the two, one should use a Positive>Negative order of operation, as a positive number > a negative number. Do the positive (Addition) first, and the negative (Subtraction) second.

Thusly, Multiplication should be considered the "positive" operation, as the exponents are positive, and Division should be considered the "negative" operation, as it is the inverse of multiplacation, meaning that the exponent is negative.

As all sources have stated, exponents takes precedence over ALL other operations. Per the transitive property, Multiplication (utilizing a positive exponent) therefore takes precedence over Division (utilizing in essence a negative exponent).

With that being said, and Multiplication being the positive operation, and Division being the negative operation, it is easy to come to the result that:

6/2*(1+2) = 6/2*(3) = 6/6 = 1

Mrd00d

I remember clearly being taught in my California high school what Burning Down said about P.E.(M./D.)(A./S.) with the left to right. And I made it to AP Calculus and I remember that being taught in a few classes.

I think, oojay, that there are a handful of teachers simply forgetting to tell some generations of students about that important piece of info, that they share precedence and go left to right.

9

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CanwllCorfe

By multiplying the 2 by 3, wouldn't that mean you're pairing it with the divisor? Even if you did multiplication first, shouldn't you be multiplying 6 by 3? And then getting 18, then dividing by 2? Thereby getting 9.



The 1 is unnecessary, but I wanted to add it so that everything would line up nicely in Photoshop.

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TheBig3

Where would you multiply 6 by 3? I got 1, and I'm not seeing your logic.

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CanwllCorfe

Well, I don't know how else to say it. 6/2 * 3. You would multiply the 6 by 3, because if you didn't, you'd be pairing it with the divisor. Which would pretty much mean you're doing 6/2 * 1/3, getting 6/6. 3, as a fraction, is 3/1. 6/2 * 3/1 = 18/2 = 9.

EDIT: Here's a picture:



You multiply the 6 by 3, getting 18. Then divide by 2.

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Burning Down

I think I get it, looking at your previous post. You're using multiplication as the main operation here, and then turning it into a simple fraction by using 6x3 as the numerator and 2x1 as the denominator. So, logically, the next step is 18/2, which of course equals 9. Right?

CanwllCorfe

Yurp!

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midnight rain

There's no lack of one, just misunderstanding in this thread. Math is hard facts, not multiple answers.

What canwll said, basically the problem wouldn't involve multiplying the denominator unless there were some sort of parenthesis to contain the 3 in the denominator and not the the numerator. Otherwise, the 3 is looked at as a whole separate number. As canwll showed, it's 3, not 1/3.

(6/2)*(1+2)=9 or (6/2)*3=9...........18/2=9.............9=9

6/(2*(1+2))=1 or (6/2)*(1/(1+2))=1.........6/(2*3)=1...........6/6=1

There's only one answer and it's 9. Without the parenthesis, at least.

MoonlitSunshine

ahahahahahahaa... Man, that's a good one.

Ever heard of Heisenberg's Uncertainy Principle? That you cannot know both the location and velocity of an atomic particle at the same time? Or what about the "Schodinger's Cat" paradox, which states that the cat is both alive and dead at the same time? It can't be both, because maths is hard facts, not multiple answers, right?

Even moving away from physics and into pure maths, x = 5 mod 6. What's x? Well, it's 5. It's also 11, and 16, and 365. In fact, it's 6n + 5, but without any information about n, you can't get a more accurate answer.

That's what's going on here. This is EXACTLY like a function with multiple possible values. Take a quadratic equation, like x^2 + 2x -3 = 0. "x" is both 3 and -1, right? You can't get one specific answer until you are given more information, like x>0. With this lovely equation, 6/2*(1+2) is both 1 and 9 unless more information about the order in which the multiplication and division should be done is given. Once the extra parentheses are added, the answer would be clear.

If anyone responds to this post with "but but but we were taught in school that you do PEMDAS" or "We were taught in school that if you have multiplication and divison in the same equation you just work from left to right", I am just going to ignore you, or assume that you're just completely incapable of reading seeing as I've explained this 5 times before.

THERE IS NO STANDARD CONVENTION FOR THE ORDER OF EVALUATION OF OPERATIONS. THEY ARE MADE UP IN ORDER TO MAKE IT EASIER TO TEACH THE SUBJECT. It just so happens that most of you tend to have been taught one of two common methods. This thread is all the evidence anyone should need to prove this is the case. If you want more, there's currently a facebook poll with about 2 MILLION votes, and about 200k difference between the two.

If anyone wants to argue this, I'm happy to do so, so long as you have an argument other than "look at these links" or "this is what my maths teacher said". I taught maths for 6 months, and the amount of white lies I had to say in order to avoid topics that were confusing the students was slightly soul-destroying. If anyone wants to disagree with me on the principle that you feel that you are right and I am wrong just because, please go and study maths - specifically Group Theory and Real Analysis - for a few years, and then get back to me.

/end rant

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midnight rain

I wasn't trying to offend you. When I said multiple answers, I didn't mean a problem can't have two solutions. I meant that you can't go about problems like the one this thread is about in two different ways and get two wildly different answers, because one is technically incorrect. What I mean is, you can't pick and choose how you solve a problem and then call it the correct answer. There are certain guidelines to follow by, otherwise it is incorrect.

Sorry for the misunderstanding, but I still stand by 9 being the only answer. Even if you do multiplication first, this thread has proven the answer is still 9. It's not a matter of how you do the order of operations, it's a matter of multiplying correctly.

And the parenthesis or lack of makes no difference, as the problem stands (and with the parenthesis it currently has), the solution reads as 9. Thats why if you copy & paste it directly into Google it'll give you 9.