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Evaluating algebraic expressions can be a simple process, but needs to follow an order of operations to get the right answer. The sequence details the order you follow to add, subtract, multiply, and divide. The order is:
P.E.M.D.A.S.
Parenthesis | Exponents | Multiplication | Division | Addition | Subtraction
Perform the operations inside a parenthesis first
Then exponents
Then multiplication and division, from left to right
Then addition and subtraction, from left to right
You can also create a little phrase to memorize the sequence:
Please Excuse My Dear Aunt Sally
multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication.*
Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently.
The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations.
Originally posted by MegaMind
reply to post by Honor93
so you believe the answer is 1/9?
what about every thing after the FIRST "/" being the denominator? That was what u said earlier.
6 / 2 (1 + 2) / 9 = ?edit on 2-5-2011 by MegaMind because: (no reason given)
Originally posted by MegaMind
Originally posted by Honor93
as a matter of fact, time's up and i gotta go ... i'll check back in a few hours ... you got your answers but i doubt you'll acquiesce ... we'll see if progress is truly measured by effort or argument.
where it is likely we'll progress in an argument, it would please me much more if the progress were measured by effort, really, you should try it sometime.edit on 2-5-2011 by Honor93 because: add text
HA! Got you!
6 / 2 (1 + 2) / 9 = ?
the answer, by the way, is 1. Given your logic I expected you to say either 1/9 or 9 depending on how you ordered it. (hint: that's why rules matter)
While I'm at it what about these?
3 / 3 / 3 = ?
3 / 3 * 3 = ?
3 * 3 / 3 = ?
6 / 2 (1 + 2) (1 + 2) = ?
3 * 3 * 3 = ?
I think your just trolling and I've been punked!
You log off and star yourself with another accountedit on 2-5-2011 by MegaMind because: (no reason given)
You log off and star yourself with another account
Originally posted by spy66
This is my reply to you Honor93
Well of course its wrong to space out the equation like you did. because you changed it totally.
Once again, 6/2(1+2) distributes to 6 divided by [(1+2)+(1+2)] or 6/[(1+2)+(1+2)]
You can't take 6/2 and do as you did. You can't take what 6 is divided by and carry it over to (1+2) and create the equation 2(1+2)
standard basic math coupled with rules of combining operations, otherwise known as 'distributive laws.'
How is that possible?
Explain to me how that is correct.
A (B + C) = AB + AC
1 / 3 (B + C) = (1/3)B + (1/3)C
is that clear? what don't u get? A = 1/3, or 6/2 or whatever the hell else you want it to be.
edit on 2-5-2011 by MegaMind because: (no reason given)
Originally posted by heavenlysouldier
reply to post by darius2025
it really depends on how you read it...
Or how it's written out..
idk..
Maybe it's a possibility of both?
We linearize simple formulas, using the rule that multiplication indicated by juxtaposition is carried out before division.*
In algebra, multiplication involving variables is often written as a juxtaposition (e.g. xy for x times y or 5x for five times x). This notation can also be used for quantities that are surrounded by parentheses (e.g. 5(2) or (5)(2) for five times two).
Originally posted by grey580
In algebra, multiplication involving variables is often written as a juxtaposition (e.g. xy for x times y or 5x for five times x). This notation can also be used for quantities that are surrounded by parentheses (e.g. 5(2) or (5)(2) for five times two).
Unless someone can find some concrete evidence about the whole juxtaposition thing. the answer is 9.
This whole equation is very ambiguous.
This is of course in contradiction to what Honor93 and others seem to be claiming, that parentheses indicate a higher order of multiplication.
If anyone can provide some hard evidence for the juxtaposition precedence thing, please do. Otherwise correct order of operations state that multiplication and division carry the same precedence and are carried out left to right, and I am still going with 9.
The sticky point here is the calculators and those who programmed them with linear functionality solely. Juxtaposition is nothing new, nothing changed and nothing confusing when you understand and play by the rules.
The notion that the expressions 6/2(1+2) and 6/2*(1+2) are different expressions because of this higher order juxtaposition seems ridiculous to me. To denote everything after the / to be in the denominator another set of parentheses must be used: 6/(2(1+2)).
Originally posted by Honor93
did it ever occur to any of you geniuses who swear your teachers taught you wrong that maybe, just maybe ... on the day the effects of juxtaposition may have been discussed at great length, perhaps, you were absent or played hookey or just skipped that day?
especially, as i know soooo many youngins' figure once they have the 'basics', they are good to go.
This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.
(And please do not send me an e-mail either asking for or else proffering a definitive verdict on this issue. As far as I know, there is no such final verdict. And telling me to do this your way will not solve the issue!)
Originally posted by GobbledokTChipeater
This also implies that if you are using a 'dumb' calculator (windows, google, various programming languages), then you will have to format the equation yourself by bracketing the juxtaposed values, else the calculator will give you a false result.
.edit on 2/5/11 by GobbledokTChipeater because: (no reason given)