This thread is one giant facepalm but I can't help but post in it!
Everyone's said it already but to reiterate:
RobPaulson wrote:theres no such thing as dividing, there is only multiplying by a reciprocal, you're using imaginary algebraic operators, y0.
Uh, kind of. Division indeed exists, it is the inverse of multiplication. The division sign (÷) simply tends to fade away after elemetary arithmatic. In digital computation, the forward slash (/) is used to denote right division.
The product of c and b is equal to a; c times b equals a.
c x b = a
Therefore, a divided by b is equal to c.
a/b = c
48 ÷ 2 = 48/2 = 48 x (1/2) = 48 x 0.5 = 24
Everyone wrote:...P.E.M.D.A.S...
Misleading acronyms are misleading.
While acronyms are a helpful memory aid, they're of no use if you don't know what you're trying to remember.
Order of operations, or precedence, clarifies which operations are to be preformed first in a given mathematical equation consisting of multiple operators. The standard order of operations is as follows:
1. Calculate all terms insde brackets or parentheses; parentheses can be used to group terms and operations to, quote/unquote defy, the order of operations.
2. Carry out all exponents and roots.
3. Multiplication and division are interchangable; remember division is the inverse of multiplication.
4. Addition and subtraction are again interchangable; think of subtraction as the addition of the opposite.
Just to further reinforce the interchangeability of multiplication and division (which seems to be the issue of our particular equation), why P.E.M.D.A.S. can be misleading, and the associative and communitive properties...
While P.E.M.D.A.S. may be the common acronym of choice taught in the U.S., many other countries use the acronym B.E.D.M.A.S. (Brackets, Exponents, Division, Multiplication, Addition, Subtraction). Ignoring the interchangability of multiplication and division, and addition and subtraction would result in conflicting answers depending on the acronym you chose to religiously and inappropriately abide by. In basic mathematics, as we have here, conflicting answers do not exist.
Onto our given equation (as originally written) is:
48÷2(9+3)
For the sake of digital computation, we will switch out the division symbol, for the forward slash rewriting the equation as follows:
48/2(9+3)
Following standard order of operations we calculate all terms inside the parentheses:
48/2(12)
And just to be clear, we will once again rewrite as follows:
48/2 x (12)
This is obviously where some of us are getting confused. Lets start by cleary defining each term by asigning parentheses:
(48)/(2) x (12)
Assigning variables:
(a)/(b) x (c)
Where (b), and (b) alone, is the only interger in the denominator. In order for c to be considered as part of the divisor (denominator) it would need to be placed within the same parentheses as (b). Allowing us to "defy" the order of operations and carry out all operations inside the parentheses (b x c). However, in this particular equation, this is not the case.
Rewrite equation as text:
the product of of (a) divided by (b), and (c)
or
(a) divided by (b) times (c) (not to be confused with (a) divided by the product of (b) and (c)
or
(a) times the reciprocol of (b) times (c) (not to be confused with (a) divided by the product of the reciprocol of (b) and (c)
Evaluate division as the multiplication of the recipricol:
(a) x (1/(b)) x (c)
Evaulate at a=48, b=2, c=12; Remember to follow order of operations:
(48) x (1/(2)) x (12)
288
CLIFF NOTES: The correct, and only correct, answer for the given equation is 288. Way to much time and effort spent explaining how and why. I have no life.
PROOF: Basic mathematics.