6÷2(1+2)= ?

[Blood]

6÷2(1+2)= ?

Is the answer 1 or 9 ?

[skywalk]

I'd say 9, using left to right order of operations...
http://www.google.com/search?cx=c&sourc ... B72(1%2B2)

[gnasen]

The term is mathematically:
6 / 2 * 3 = 6 * 2^(-1) * 3 = 9
because the sign "/" is nothing else then the inverse of the following number and multiplication is associativ.
Further there is still a "*" between 2 and 3, otherwise you have to use brackets. If there should be no "*" and no brackets, its just undefined.

[blueznl]

6÷2(1+2) =
6 / 2 * ( 1 + 2 ) =
6 / 2 * ( 3 ) =
6 / 2 * 3 =
3 * 3 =
9

Why:

- there's no operator between 2 and (1+2) so it's a multiplication
- first get the value of anything between the brackets
- substitute brackets + expression within with result
- do the rest

[graph100]

my calculator said 1.
I believe that it prioritize the use of the parenthesis like a higher priority then if it was written like : 6 / 2 * 3
And I would have said 1 too, since the "2" is near the parenthesis without operator : it is implicit.

(as you can easily guess the calculator I use is a casio Graph100+ , that is if you want too test it)

[gnasen]

And I would have said 1 too, since the "2" is near the parenthesis without operator : it is implicit.

Thats the problem. There are common standards which should be used. And one of them is, that you can omit a dot (for mutliplication) but never ever a paranthesis if it is not absolutly obvious how the term should be calculated.
Calculators (including mine) seem to bind a term in the way you observated it. However thats just arbitrariness. In a term like this you should use paranthesis right or avoid the division operator.

[spikey]

The order of precedence is denoted by the mnemonic BODMAS.

Brackets (parenthesis)
Orders (powers/roots)
Divide/Multiply
Add/Subtract

Where operators have equal precedence, overiding precedence is given to the left most operator.

So the calculation order is:-
1) 6 ÷ 2 ( 1 + 2 )
2) Brackets - gives 6 ÷ 2 x 3
3) Divide is leftmost - gives 3 x 3
4) Implicit multiply gives 3 x 3 = 9

So the answer is 9, as blueznl states.

[kenmo]

This was the topic of a big debate between some classmates recently (not the exact same numbers, of course), and the conclusion was:

Without explicit parentheses, the division should occur first (left-to-right, resulting in 9 in this case). It is misleading to write the division sign and not the implied multiplication sign. Furthermore, division should have equal priority to multiplication since it is really multiplication by the inverse (as gnasen said).

Some calculators may multiply the 2 before dividing (for convenience?) but really that is non-standard.

[graph100]

the moral is : when you take exam, type all the operator to obtain a sure answer