[leftnose]

Quote:

Originally Posted by Duggeh /img/forum/go_quote.gif PEMDAS? I was taught BODMAS (brackets, order, division, multiplication, addition, subtraction). Whats PEMDAS? (parenthesis, exponentials, multiply, divide, add, subtract)?

PEMDAS? That sounds dirty.

I learned Pretty Please Make Difficult Algebra Simple

or, Parenthesis, Powers, Multiplication, Division, Addition, Subtraction

 

[scompton]

Quote:

Originally Posted by K2Grey /img/forum/go_quote.gif I thought negation was used for like, boolean operations. Granted in that case it's unclear to me how it would interact with multiplications and divisions and so on. Ahh, math, you can get ridiculously complicated.

It makes a big difference on exponents and roots.

I was never taught any mnemonics, were were just expected to know it. Of course, I'm old enough that college was the first exposure most people got to computers.

Then again, I've never been a fan of mnemonics. For me it's easier just to remember what the mnemonic stand for and forget the mnemonic. So I guess the may have taught us one, but it went right out of my head.

 

[JerryG20]

I think the OP knows about PEMDAS or whatever. The question is WHY PEMDAS? Why was it decided that 8*2+3 should equal 19 instead of 40? Is it because multiplication and division are designed/drawn together (so it looks like (8)(2) + 3)?

 

[rsaavedra]

Quote:

Originally Posted by JerryG20 /img/forum/go_quote.gif Is it because multiplication and division are designed/drawn together (so it looks like (8)(2) + 3)?

I think that's a reasonable explanation, and possibly not just derived from handwriting.

Even with this font you are reading, the expression 8x2+3 most likely shows 8 and 2 more strongly clustered than 2 and 3. If no parentheses are indicated, 8x2+3 seems to more naturally suggest (8x2)+3 instead of 8x(2+3) to our visual system. So the shape and spacing introduced by the binary operators involved might be the underlying reason for this established convention with operator priorities.

 

[nikongod]

Quote:

Originally Posted by DNT /img/forum/go_quote.gif So PEMDAS and BODMAS are two different systems? One says division first and the other says multiplication. So which one is conventionally correct?

I personally multiply by fractions before i divide by wholes. hows that. its the same thing done differently. you get the same results with both systems.

i also add negatives to whatever before i subtract positives.
Quote:

Originally Posted by JerryG20 /img/forum/go_quote.gif I think the OP knows about PEMDAS or whatever. The question is WHY PEMDAS? Why was it decided that 8*2+3 should equal 19 instead of 40? Is it because multiplication and division are designed/drawn together (so it looks like (8)(2) + 3)?

the WHY comes from a long long time ago. people got pissed at eachother when they would get different answers to the same problem. as wiggy said, rather than writing parenthesis everywhere they just agreed to a convention.

to make the point in english:
in a couple languages the order of words is not important (with few exceptions) it can get confusing.

the order of words is not important, it can get confusing (with few exceptions) in a couple of languages.

it can get confusing, the order of words is not important (with a few exceptions) in a couple of languages.

theres probably a few more things to say with the same words.

 

[Arainach]

Quote:

Originally Posted by goldenratiophi /img/forum/go_quote.gif huh? Negation is just multiplication by -1. If negation is to be read first then you'd have -5^2 = 25. However we write -5^2 = -25 and (-5)^2 = 25. Unless I'm misinterpreting what you mean by negation...

I've always known -5^2 to be 25 and -(5^2) to be -25. Also, Having 5^-2 = -25 makes no sense; it's 0.2 because we process the - first.

 

[pez]

Quote:

Originally Posted by Febs /img/forum/go_quote.gif Multiplication is cummutative. In other words, the order may be changed without changing the result. Division is the same as multiplication by a reciprocal. X/Y = X * 1/Y Thus, the order does not matter.

He's right

. I don't think there's a really explanation of the order they chose, but it's probably a deep answer that they came to with a reasonable conclusion. When you start getting into exponents, you start getting into imaginary numbers, too, and that's kind of a whole new thing considering what the OP is talking about.

 

[aaron313]

The expression y=5+x is equivalent to y=5+1*x, and if it weren't the case that multiplication comes first, then y=5+x would also be y=(5+1)*x = 6x, which makes no sense since we always omit the "1" multiplying x.

 

[manofmathematics]

You have to be careful.

-5^2 is actually -25. This is because, in this case, -5 is actually -1*5, and the order of operations tell us that (-1)5^2 should have the exponent evaluated first, followed by the multiplicative negation.

It is wise to group the "-" appropriately. say, (-5)^2, which would indeed equate to -25 since the multiplication is completed first, once again due to the order of operations.

aaron313, has a very good point above. Indeed it holds true for all numbers. "1" is considered one of those "special numbers" and can throw a few curveballs, especially when diving into a little Number Theory.

Also remember that 1 is not a prime. I've seen many people argue over this one, but 1 is indeed not prime due to the Fundamental Theorem of Arithmetic, which I really don't feel like explaining, but look it up, it's not a difficult matter really.

 

[d-cee]

Quote:

Originally Posted by manofmathematics /img/forum/go_quote.gif It is wise to group the "-" appropriately. say, (-5)^2, which would indeed equate to -25 since the multiplication is completed first, once again due to the order of operations.

don't you mean that equals 25?

come on, with a name like manofmathematics i expect better

 

[manaox2]

Quote:

Originally Posted by leftnose /img/forum/go_quote.gif PEMDAS? That sounds dirty. I learned Pretty Please Make Difficult Algebra Simple or, Parenthesis, Powers, Multiplication, Division, Addition, Subtraction

"Please Excuse My Dear Aunt Sally"

Works for me.

 

[JSTpt1022]

Quote:

Originally Posted by manofmathematics /img/forum/go_quote.gif You have to be careful. -5^2 is actually -25. This is because, in this case, -5 is actually -1*5, and the order of operations tell us that (-1)5^2 should have the exponent evaluated first, followed by the multiplicative negation. It is wise to group the "-" appropriately. say, (-5)^2, which would indeed equate to -25 since the multiplication is completed first, once again due to the order of operations.

Your reasoning is, of course, correct. But, it has been my experience that if someone writes -5^2, they mean 25. And also, how do you reconcile this with the fact that 5^-2 = 0.04?

Wait, never mind.
5^-2
Apply order on base: go to exponent
Apply order to exponent: (-1)*2
Complete operation: 5^(-2) = 0.04

 

[Arainach]

Quote:

Originally Posted by manofmathematics /img/forum/go_quote.gif You have to be careful. -5^2 is actually -25. This is because, in this case, -5 is actually -1*5, and the order of operations tell us that (-1)5^2 should have the exponent evaluated first, followed by the multiplicative negation. It is wise to group the "-" appropriately. say, (-5)^2, which would indeed equate to -25 since the multiplication is completed first, once again due to the order of operations. aaron313, has a very good point above. Indeed it holds true for all numbers. "1" is considered one of those "special numbers" and can throw a few curveballs, especially when diving into a little Number Theory. Also remember that 1 is not a prime. I've seen many people argue over this one, but 1 is indeed not prime due to the Fundamental Theorem of Arithmetic, which I really don't feel like explaining, but look it up, it's not a difficult matter really.

Except that the unary operator is an operator itself - it's not multiplication by -1. That's only the case in the sense of the Field of (+, *). In Number Theory, the additive inverse is in a class of itself and the unary operator refers to that concept, not to multiplication.

 

[goldenratiophi]

Quote:

Originally Posted by Arainach /img/forum/go_quote.gif Having 5^-2 = -25 makes no sense; it's 0.2 because we process the - first.

The - is processed first because it's in the exponent. And when all else fails:

ps: I don't argue that -x doesn't always equal -1*x in some algebraic structures, but I think it's safe to assume that we're talking about a field here

 

[Chrisboff]

Well in my school we learned:

B brackets
I indices
D division
M multiplication
A addition
S subtraction