48÷2(9+3)=?

Another Option wrote:

=48/2(12)

=24*12

=288

so, 1/2x = x/2?

Timmy Jenkins wrote:so, 1/2x = x/2?

The way you have written it, yes. Otherwise it would have been written as 1/(2x) or 1/2/x if you prefer the non-parentheses version.

Best thread ever. Well done OP

I see this everywhere... and this is certifiably the best way to troll ever. On one forum these 8 characters spawned 94 pages of bitching.

Ok bitches, here's how it's done:

48÷2(9+3)

48÷(2x9)+(2x3)

48÷(18)+(6)

2.6666¯+6

Answer is 8.6666¯

Some more "final" thoughts...

Here is some practical guidelines how to avoid misunderstandings, when you must post equations in a text only environment, without access to advanced rich text formats, unicode symbols, and equation editors:

http://www.purplemath.com/modules/mathtext.htm

Here is a concise "negative" opinion about orders of precedence and the evils of implied multiplication:

http://library.thinkquest.org/20991/gather/main/messages/15460.html

1. "/" is the accepted symbol for division

2. Multiplication and division have equal precedence.

3. Parentheses have a higher precedence than any arithmetic operator, so expressions in parentheses are always evaluated first.

4. SOME TEXTS (and some calculators) adopt their own rule that binds ab together more tightly than a*b, in effect treating ab as being equivalent to (a*b).

5. By CONVENTION (not by "law") the associativity of multiplication, division, addition and subtraction is left to right. Therefore, in the absence of parentheses, BY CONVENTION, these operations are simply evaluated sequentially from left to right. There is no "mathematical law" that requires this; it is simply a convention that is (nearly?) universally accepted. Without this convention, expressions like 105 / 3 * 5 would simply be ambiguous. There would be no way for people to agree as to how to evaluate such expressions in the absence of parentheses.

6. There is NO SUCH CONVENTION concerning "implied multiplication". SOME PEOPLE choose to say ab => (a*b). Most people would say ab => a*b.

IN MY OPINION, those who take it upon themselves to adopt a "new convention" (which is not a convention because it is not generally agreed upon) do us all a disservice by introducing ambiguity where there was none before. Perhaps a better convention is this: don't use implied multiplication because it is ambiguous.

But unfortunately, that's not a convention either. It's just my opinion.

Finally, it seems that this exact question has been bombarded on many forums at the same time. I wonder how the population of runners, who I thought were supposed to be good at math, stacks up against bodybuilders, tennis players, etc....

lil wayne's offspring wrote:

Ok bitches, here's how it's done:

48÷2(9+3)

48÷(2x9)+(2x3)

48÷(18)+(6)

2.6666¯+6

Answer is 8.6666¯

At least your answer is humorous. Well done.

rekrunner wrote:

5. By CONVENTION (not by "law") the associativity of multiplication, division, addition and subtraction is left to right. Therefore, in the absence of parentheses, BY CONVENTION, these operations are simply evaluated sequentially from left to right. There is no "mathematical law" that requires this; it is simply a convention that is (nearly?) universally accepted. Without this convention, expressions like 105 / 3 * 5 would simply be ambiguous. There would be no way for people to agree as to how to evaluate such expressions in the absence of parentheses.

Luckily, we all know that 105/3*5 equals 7.

Let's "simplify" PEMDAS a little. Let's just make it PEMA. Any place that normally would have been division can instead by written as multiplying the reciprocal. Any place that normally would have been subtraction can instead be written as adding the negative. This way our terms are not stuck in place, we can move them all around.

So 5-6+7 is changed to 5+(-6)+7, and now we can put those terms wherever we want. (-6)+7+5, for example.

Likewise 10/5*6/4 = 10*(1/5)*6*(1/4), and that can be rearranged to anything, such as 6*10*(1/4)*(1/6).

Also 20/10/5 becomes 20*(1/10)*(1/5) and those terms can be rearranged however we sit fit.

BACK TO THE PROBLEM - we all agree that the parenthesis happens first, right? So now the problem is 48/2*12. Since we are only using PEMA now, this can be written as 48*(1/2)*12, and it can be rearranged any way we want, like (1/2)*48*12 or 12*(1/2)*48. The answer is always 288.

almost 200 posts and nobody mentioned Teg don't run no 10K.

BUT if he did Teg would tell you the answer is 288.

smoozer wrote:

mileageGuy wrote:

The one that gets a lot of people is simply -3^2

This is either 7th or 8th grade level math. I teach 7th grade math. The reason it "gets a lot of people" is because it's rarely used outside of the math courses you take in middle school and high school. I could probably count on one hand the number of times I've had to find the opposite of a square in my daily life outside of teaching.

Is that not because the only time you do math is when you're at work? Take an engineering class, f-tard.

Math Guy #288 wrote:

PS: The argument that since I put the equation into excel or my calculator and got 288 and there that is the correct answer is absolute nonsense. Calculators/excel do not understand the rules of mathematics. When entering something like this into a calculator/excel, you must introduce some extra brackets to help the calculator understand the way the equation was written. Otherwise it will just solve left to right which is not always correct:

48÷[2(9+3)]=

Ahahahahahahah!

remember Polish Notation and RPN?

malmo wrote:

I have no idea how this thread got to be this long, but it is surely proof why Asia is kicking our asses in math and is evidence that Letsrun has many law school graduates.

There is no ambiguity except to those who have been trained to fabricate ambiguity in everything.

Fukushima is proof of why Asia is kicking its own ass with fuzzy math, if Asians don't know the answer is 2, what hope do they have of not nuking their own countries.

Another math guy wrote:

rekrunner wrote:

5. By CONVENTION (not by "law") the associativity of multiplication, division, addition and subtraction is left to right. Therefore, in the absence of parentheses, BY CONVENTION, these operations are simply evaluated sequentially from left to right. There is no "mathematical law" that requires this; it is simply a convention that is (nearly?) universally accepted. Without this convention, expressions like 105 / 3 * 5 would simply be ambiguous. There would be no way for people to agree as to how to evaluate such expressions in the absence of parentheses.

Luckily, we all know that 105/3*5 equals 7.

Based on what? Why do you keep wanting to work left to right? What rule says you multiply before you divide in this situation? None.

The answer is 175.

I know that Wikipedia is not authoritative, but if you read the entry on order of operations (http://en.wikipedia.org/wiki/Order_of_operations) you'll find the quote below. It does have a couple of references that you can check. I'll reiterate that there are different conventions on how to carry out order of operations and as others have pointed out, it is important to make clear either the convention you are using or use unambiguous means to make order clear (such as parentheses).

Also, remembering order of operations and basically all arithmetic, is really irrelevant to performance in math and science. I know plenty of skilled mathematicians and scientists who are absolutely atrocious in arithmetic.

[quote]

Some mathematicians hold that multiplication by juxtaposition (omitting the x sign, ex. 2(4+3) ) is a symbol of grouping. No fixed convention exists.

[quote]

It comes down to this, do you think the problem is:

48

----- = 2

2(9+3)

OR

48

----- x (9+3) = 288

2

If you think it is the first one, you are making stuff up. There is no reason (9+3) belongs in the denominator based on the original problem.

except for the fact that, as noted by several links, there at least is SOME (if slight) debate as to whether there is implied parentheses given the lack of an * after the 2

Implied parenthesis? I've never heard of such a thing. I'd like for those people to show me where they learned that.