There is no difference, from left to right or right to left, in the direction you do the multiplication and division...they are the same operations. The only difference with division is you invert the number and change it to multiplication...you get the same number all the time... (48)*(1/2)*(12)=(12)*(1/2)*(48)=(1/2)*(48)*(12)...etc. They're all the same number...288 If you get 2, then the expression would read (48)/(2*12) ...essentially you'd be saying (48)*(1/2)*(1/12) I see a lot of folks talking about the PMDAS...but it should really go P 1st, M&D second(any order), A&S third(any order). Anyone that has had to factor and rearrange long expressions can vouch for that.
Here is where you went wrong. Set x=9+3 You will get 48÷2(x) NOT 48÷2x 48÷2(x)=24(x)=24(9+3)=24(12)=288 Furthermore, you can still use the distributive property to get the correct answer (288): 48÷2(9+3)=48÷2(9)+48÷2(3)=24(9)+24(3)=288 Nice try but no cigar. The answer is still 288. Google/calculators have it correct lol.
Oh, wow. I didn't see how many folks voted for 2. I can see how it'd be tricky though...no one writes an expression with the dividing term in the middle...it looks really awkward like that.
The way you are writting the expression is still incorrect. If you divide something by 2 it is the same thing as multiplying it by (1/2) or (0.5). Get rid of the \2 and replace it with *(0.5), they are mathematically equivalent...the answer will be much more clearer.
People can use short hand, but in this case it is a well defined operation. You can use any calculator and type in that expression and you will get 288 unless you use rpn.
Ugh, I see people talking about distribution. You would do the math inside the paretheses first, you don't distribute unless you're working with unknown variables and trying to simplify an expression...there are none of those in this problem. Either way, distributing would still give you the same answer...as long as you are multiplying by the correct number which is (0.5) in this case, not 2. Ex: 5x+2(x+y)...distribute...=5x+2x+2y=7x+2y Besides, the '2' in the original expression is really a multiply by '1/2'
OK, the length of this thread may be curious. I came across this link: http://mathforum.org/library/drmath/view/54341.html [rquoter] Date: 05/19/99 at 17:03:49 From: Doctor Peterson Subject: Re: Algebraic expressions and order of operation Hi, Stephanie and Meghan. You are not alone in wondering about this. We have had several other questions about expressions similar to yours, from confused teachers and students who have found that different books or teachers have different answers, and even calculators disagree. As written, your expression ax/by should be evaluated left to right: a times x, divided by b, times y. The multiplication is not done before the division, but both are done in the order they appear. Your first solution is right. Some texts make a rule, as in your second solution, that multiplication without a symbol ("implied multiplication") should be done before any other operations in an expression, including "explicit multiplication" using a symbol. Following this rule, you would multiply a by x, then multiply b and y, then divide one by the other. Some (probably most) texts don't mention such a rule - but some of those may use it without saying so, which is far worse. I don't know of a general rule among mathematicians that implied multiplication should be done before explicit multiplication. As far as I'm concerned, all multiplications fit in the same place in the order of operations. It's not an unreasonable rule, though, since it does seem that implied multiplication ties the operands together more tightly, at least visually; but the idea of Order of Operations (or precedence, as it is called in the computer world) is supposed to be to ensure that everyone will interpret an otherwise ambiguous expression the same way - so if some texts change the rules, or if people do what feels natural, the purpose has been lost. ... So to answer your question, I think both answers can be considered right - which means, of course, that the question itself is wrong. I prefer the standard way (your first answer) when talking to students, unless their own text gives the "implicit multiplication first" rule; but in practice if I came across that expression, I would probably first check where it came from to see if I could tell what was intended. The main lesson to learn is not which rule to follow, but how to avoid ambiguity in what you write yourself. Don't give other people this kind of trouble. - Doctor Peterson, The Math Forum [/rquoter]
just simply say I'm wrong now that I realize MD and AS in PEMDAS are the same priority and should be evaluated from left to right. and Basic-Mathematics.com is wrong as well
This is actually a poorly written problem. There's no way of knowing if the variables are 'ax' and 'by' or a,x, b, and y. :grin: EDIT: I see in the link a, x, b, and y are given separate values. Still, I don't remember ever seeing math or engineering text write a problem as ax/by unless they intended you to follow the order of operations properly. Otherwise they would write: __ax__ by
That's where the confusion stems from. I'm guessing (myself included) most people that voted 2, have the "implied multiplication" ingrained in their minds. I see why it's 288, and coming to the conclusion of 2 has nothing to do with error in the PEMDAS [more like PE(M<->D)(A<->S) as gwatson86 put it on facebook], but more the "implied multiplication" "rule" that some teachers/text books seem to teach.
Because the answer is 2!! The ambigious math problem turned out genius if you ask me. Look at the sh1tstrom it started. It's got me wondering how many things I F'd up at work....hahahaaaa. Awesome!
