I think the difference here is that xy would be considered a single term, so 48 must be divided by xy as a whole. 2(9+3) would be considered three separate terms, and each must be dealt with individually.
Ok..lets mix it up x=2 y=9+3. It's the same thing. It has nothing to do with variable, but the fact that he grouped them together without the multiplication sign. My point is people view 1/xy differently than 1/x*y. The lack of the * symbol pretty much implies that you want them together.
I agree that people might view them differently, but that makes one group of people completely wrong. 1/xy is exactly the same thing as 1/x*y. If people dont see that, then they fail at basic mathematics. If you want to group things together, you throw in parenthesis.
sigh..woosh. over your head. It's a matter of convenience not right or wrong. again I ask this quesiton If I were to write this following equation out to you, what do you interpret my intentions were? 1/xy(1+z)+3/ac^dv 1) 1/(xy(1+z))+3/(ac^(dv)) or 2)(1+z)y/x + (3vc^d)/a The purpose of language is to convey my message. If 1/xy can be conveyed as 1/(xy), why bother going through the trouble of writing out 1/(xy)? People who do math and equations set up there equations in a certain manner. If I wanted 1/x*y I would have stated in that fashion or even more simply y/x. It's generally understood by people who deal with equations all the time what your intentions are. If I see ab/cd I'm not going to assume abd/c, because if that's what he meant, he would have typed it out that way.
That's fine. The new standard is the way you say. But please try to understand that generations of perfectly intelligent people were taught a different standard. And they certainly would not write out the equation that way if they wanted to be clear. That is ALL anyone is saying. Things change. Big deal.
And MY point is that changing 2(9+3) into xy where x = 2 and y = 9+3 is tantamount to multiplying these separate terms together before the rest of the equation is considered. That violates order of operations. You can't just say, "Oh, the writer of the equation IMPLIED he wanted them together," and then work off assumptions. There are rules that are followed, and if the equation does not explicitly state that everything beyond the / is to be considered part of the denominator, not everything beyond the / is part of the denominator.
Seriously, you are killing me Nero. Really? I see the following three numbers (or numerals as you referred to them earlier): 1, 3 and 2. I also see two subtraction operators. Now, before you read the rest of this, google the difference between numbers and operators and then come back. Okay, you see now? Nope, still talking about the same three numbers (1, 3 and 2) and two subtraction operators, only the numerals (as you referred to them before) are now in a different order. Nope, never changed any numbers from positive to negative, they are all still positive. This is highly entertaining. Please continue to teach me Nero. Sigh. You think this is a good example to illustrate the order of operations rules for addition and subtraction in an equation?
Never mind. It's clear you don't have any clue what you are talking about. Several people have already stated as well that addition/subtraction sequences do not depend on the order at ALL. And I notice you tellingly failed to answer the final question. It's as though you seriously think 2 and -2 are the same number. Anyway, this is pointless. You will figure it out some day.
I'll bite: you are asking about this question? "Do you REALLY think it matters which order you do them in? Seriously?" I think it very much matters what order you carry out operations in an equation. Now let me pose a question to you, it might sound familiar: Do you think it matters what order you do the following equation: 48/2*12 = ?
You must have missed it back earlier when I stated clearly that of COURSE the order you do more advanced equations matters. Why are you asking about that, when the ONLY point I am making is about the unimportance of the order of an ADDITION/SUBTRACTION problem? Again, you refused to answer the specific question I asked. Do you REALLY, honestly, seriously believe that the order in which you subtract your debits and add your deposits will alter the sum at the end?
Poor Nero. Oh yes, very complex indeed! But I think we are finally getting to the crux of the problem for you. You believe that order is only important in equations that have multiplication/division (aka advanced equations :grin, but the order is unimportant for addition/subtraction. I'm sorry to tell you that the same rules apply for addition/subtraction. That was your example and, as I alluded to earlier, it's a bad one. But now I will go ahead and fill you in on why it is a bad example. Usually, balancing your checkbook is not an equation with multiple operators that would cause you to call on the rules of the order of operations. You normally are just doing a summation of simple equations. Specifically, a sum of independent equations where you are either adding two numbers or subtracting two numbers (credit or debit). Having said that, you could write it out in one long equation, and in that case, yep, you guessed it, order of operations would be very important. So, if I have $50 in my account and I have the following credits and debits: $3 debit $2 credit $5 credit I could balance my checkbook using the following equation: 50 - 3 + 2 + 5 and I should get $54. But what if I had started from the right side and did the 2+5 operation first? Would I still get the same result? Please, for the love of god tell me you are starting to catch on.
I thought some of the spelling on the board was hysterical... now I see math can be just as entertaining! :grin:
This. Yes, it goes it order if you have division and multiplication together. However, the parenthesis stays even after you add "(9+3)." Therefore, the multiplying comes first in this case. 48/2(12) 48/24 2
That parentheses are dealt with first only applies to equations inside said parentheses. 48/2(12) means 48/2*12. That 12 is in parentheses instead of having a symbol for multiplication in front of it doesn't give it any precedence in the order of operations.
