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What is the answer?

30 ÷ 2(2+3)÷ 5

I said 15 but then some argued it to be 0.6. Which is which? Please explain.

30 ÷ 2(2+3)÷ 5

I said 15 but then some argued it to be 0.6. Which is which? Please explain.

then is 2*5 = 10

Then go left to right.

30/10=3

3/5=.6

http://www.google.com.sg/search?sourceid=chrome&ie=UTF-8&q=30+%C3%B7+2(2%2B3)%C3%B7+5

WolframAlpha gives 15

http://www.wolframalpha.com/input/?i=30+%C3%B7+2%282%2B3%29%C3%B7+5

Multiplication, addition, division, subtraction

Brackets are your means of modifying the order.

30 ÷ 2 * (2+3) ÷ 5

First order

2 + 3 = 5

Second

2 * (5) = 10

Final

30 / 10 / 5 = 0.6

Ok ...I see what's going on here.

It is 15.

Parentheses multiplication comes LAST.

Since 2 is appended to the parentheses the division would actually come first.

Therefore...

(2+3) / 5 = 1

2 * 1 = 2

30 / 2 = 15

@xuserx2000: I agree with you. However, if the BODMAS rule for operations are used, then that limits the debate...;-)

But, in any case, it's an interesting discussion!

The second equation you posted, is what is inferred by the order of operations, because multiplication with a parenthesed value comes last. The ((parentheses arithmetic) / value) is inferred as the same operation in the absence of parentheses.

PEMDAS is the correct way to solve this problem

Parenthesis

Exponents

Multiplacation

Division

Addition

Subtraction

30 ÷ 2(2+3)÷ 5

Parenthesis first leaves you with

30 ÷ 2(5) ÷5

Simplified to

30 ÷ 10 ÷ 5

Then it is division in the order it appears

30 ÷ 10 = 3

3÷ 5 = .6

2 * (5) - cannot be the second step unless it was presented as (2 * (2 + 3))

((2 + 3) / 5) is the second step for this reason.

Calculators can even be wrong if you check out this YouTube video.

Note the order of operation, where you Multiply a value by a parenthesed evaluation. - it comes LAST, not first, therefore the division of the parenthesed evaluation would come FIRST

>> Source: every calculator on earth.

You cannot rely on calculators on earth (but maybe on another planet).

Paste this into your Windows XP PC calculator:

2 + 5*2 =

Windows PC says to do 2+5, which is 7

Then it sees the *, so it gets ready to multiply the 7 by whatever follows, a 2, and 7*2 = 14

However, according to the Rules of Order of Operation, this answer is wrong.

http://en.wikibooks.org/wiki/Algebra/Order_of_Operations

And these are the rules that were taught in the U.S. in public schools as well as in College math/science courses (unless using RPN). I don't know what is taught in private schools.

The correct answer by the standard, most-accepted rules is:

2 + 5*2 = 2 + (5*2) = 2 + 10 = 12

because in the expression 2 + 5 * 2, you can see that the 5 is being vied for by two different binary operators, the + and the *. But according to the rules, in absence of parenthesis, the * attracts the vied for term stronger than the +. This means that the * binds with the 5 leaving the + temporarily stranded. Tough luck, plus.

So, Windows PC calculator does not follow the rules of Algebra. These rules for Order of Operation, although arbitrary and capricious, do provide a systematic and consistent way of communicating with other mathematicians, thereby helping to reduce potential chaos and bitter publications that would ensue with some consensus.

Seems multiplying a value by a parenthesed equation would come second to the division thereof, in every calculating hardware and software i've tested it on, unless a second set of parentheses are wrapped around it.

I'm not sure why, but it seems to apply only when this is set between two division operations. It may have something to do with a potential divide by zero.

It's an excellent brain teaser either way... I would be interested to see how many professional mathematicians would get this wrong.

30 ÷ 2(2+3)÷ 5

30 ÷ 2*(2+3)÷ 5 // show explicitly the implied * binary operator

30 ÷ 2 * (5) ÷ 5 //

Now, there is a potential conflict with

So the potential conflict is resolved:

The ÷ will bind to the 2, not because it is stronger than the * (they have equal binding strength), but because it is to the

Now the expression can be written as:

(30 ÷ 2) * (5) ÷ 5 = (15) * (5) ÷ 5

Here again we have a * and a ÷ trying to bind to the middle term (5). Again, they have equal binding strength, so the

Now the expression can be written as:

(15) * (5) ÷ 5 = (15 * 5) ÷ 5 = (3) ÷ 5 = 15

(1) Inner most parenthesis

(2) Functions

(3) x and ÷

(4) + and -

Given 2 entities of the same order of operation then proceed left to right. ( eg 16/4*2 = 4*2 = 8 )

So

30 ÷ 2*(2+3)÷ 5 (inner most parenthesis)

30 ÷ 2*5 ÷ 5 (all same order proceed left to right)

15*5÷5

75 ÷ 5

15

because ÷ and ÷ are both vying for the middle term, 36, to avoid any ambiguity, the

Then the implied parenthesis in the expression, 81/36/4, is (81/36)/4 does not equal 9.

Likewise, 81*36*4 becomes (81*36)*4. If you thought that the answer was 81*(36*4), well, you would be right, but maybe for the wrong reason.

In fact, there is more than one arithmetic rule to remember. It turns out that a*(b*c) = (a*b)*c.

But, as you can see a/(b/c) != (a/b)/c all of the time - they are the same, sometimes; one example, if a = b = c = 1.

http://mathforum.org/library/drmath/view/57021.html

and writing it as

30 ÷ 2(2+3)÷ 5

rather than as

30 / 2 * (2+3) / 5

could suggest that we need not limit ourselves to standards used by programming languages.

Apparently, in Quebec (Canada) this is no longer the case! But I can't remember the new order...

That'll be why the economy is in such a mess if economists are using two different ways to calculate!

I was taught to resolve everything to do with the parentheses first (i.e. 2(2+3) = 10 ) & when left with multiplication and division there was no specific priority so read from left to right. My electronic Casio friend seems to do the same (damn those Japanese programmers :)).

It's certainly a good job my career doesn't involve any high level math (or does it ....?)

Thanks for the debate.

If you were trying to show the sum a÷b where a=3 and b=3÷2, the result is 3÷(3÷2), if you write 3÷3÷2 there may be a rule to tell you how to interpret it, but you need to be very sure that everybody reading your work has the same interpretation.

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B Brackets first

O Orders (ie Powers and Square Roots, etc.)

DM Division and Multiplication (left-to-right)

AS Addition and Subtraction (left-to-right)

Step by step:

B Brackets first

30 ÷ 2

(2+3)÷ 5 ->DM Division and Multiplication (

left-to-right)30 ÷ 2x 5 ÷ 5 ->15 x 5÷ 5 ->75 ÷ 5

15