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So, if that way is wrong, enlighten us as to the correct way? of course, it's very probable that I'm getting something mixed up somewhere, as I really could not care less about math.
Right, multiplication comes before addition. That's why it's 288. Hitler was one of the smartest people, I don't get why him agreeing on a math problem could be insulting.
Right, multiplication comes before addition. That's why it's 288. Hitler was one of the smartest people, I don't get why him agreeing on a math problem could be insulting.
You are correct. The sign " ÷ " is non-standard in algebra, and is rarely if ever used, precisely because it is ambiguous. It is used only in arithmetic. In algebraic notation, the division command is always the straight line, with elements above the line to be divided unambiguously by elements below the line. Just as the " x " is never used to command multiplication. Several members expressed serially, which may or may not be parenthesized, are understood to be multiplied, and two members above and below the line are understood to be divided. That is the standard algebraic notation, and anything else does not conform.
The sumbol " ÷ " is a convenience, to be used where an above and below line is inconvenient. It means that the expression to the left of the sign is to be divided by the expression to the right of the sign. Therefore, it unambiguously means
48
2(9+3)
You can't have it any other way. If you are going to use " ÷ ", you MUST place the 48 and the 2 in parentheses, since you have abandoned the line to show division, and there is no longer an unambiguous statement about the division process.
The original problem was not stated using algebraic symbols, and therefore cannot be categorically resolved.
Let a=2, b=9, and c=3. Express is at 48 ÷ a(b+c), and you will see how clear it becomes. a(b+c) is obviously ab+ac, or 18+6, or 24. Does everybody agree that you resolve the parentheses first? That is exactly what I just did. Than, after resolving the parentheses, you proceed to your division.
No, that's simple enough. Where you go wrong is between the first and second line. You drop down the (9+3) below the 48 along with the 2.
48÷2(9+3)
48 x .5(9+3) [Remember that division is just multiplication of inverse. The inverse of 2 is 1/2 or .5]*
48 x .5(12) [Add what's in the parenthesis)
24(12) [Start multiplying left to right.]
288 [Finish]
* Since division is really just multiplication of inverse, it's on the same rank. Just like how subtraction is justs addition of a negative number.
I think that people here are thinking that multiplication is higher rank than division. But that is not the case. Multiplication comes before addition, but not division.
This confusion is precisely why infix expression should be avoided. I don't know why they still use that as the primary method of teaching algebra in school.
Multiplication comes before division, therefore 2 and 12 are multiplied before you would divide from 48.
This is 4th grade stuff, people.
edit: Nevermind, apparently there are people in this country that actually read M/D and then A/S from left to right. so I guess it depends on how you were taught and how your teacher interpretted it.
PEMDAS does NOT mean that Multiplication comes before division, nor does it mean that addition comes before subtraction.
P
Parentheses first
E
Exponents (ie Powers and Square Roots, etc.)
MD
Multiplication and Division (left-to-right)
AS
Addition and Subtraction (left-to-right)
This is Algebra I
Quote:
Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)
You will see that " ÷ " is not on the chart of Algebraic symbols. Therefore, there is no algebraic rule about how do resolve a problem using a non-standard symbol. The solver is left to guess that the symbol means.
You will see that " ÷ " is not on the chart of Algebraic symbols. Therefore, there is no algebraic rule about how do resolve a problem using a non-standard symbol. The solver is left to guess that the symbol means.
According to that list, +,-,/,* are not algebraic symbols either. Seriously, algebra includes the basic math symbols. The ones on that list are just the ones that are brought to the table by algebra.
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