argue this for me please!

[annewandering]

‎5 + 5 + 5 - 5 + 5 + 5 - 5 + 5 x 0 = ?

my facebook friends are arguing it and I need a good math person to explain it. thanks!

[LittleWyvern]

This puzzle and the almost infinite variations of them are all about operator precedence. Since multiplication has precedence over addition and subtraction, we can rewrite the equation as:

‎5 + 5 + 5 - 5 + 5 + 5 - 5 + (5 x 0)

...which resolves to:

‎5 + 5 + 5 - 5 + 5 + 5 - 5 + (0)

10 + 5 - 5 + 5 + 5 - 5 + (0)

15 - 5 + 5 + 5 - 5 + (0)

10 + 5 + 5 - 5 + (0)

15 + 5 - 5 + (0)

20 - 5 + (0)

15 + (0)

15

Since addition and subtraction have the same precedence it doesn't matter what order we do them in, so I just did them left to right for simplicity.

EDIT: to be technically correct, we can do them in any order as long as we don't assume the subtraction operator is associative.

Edited November 11, 2011 by LittleWyvern

[beefche]

According to a google search:

Since there are no brackets, the answer is 15, applying the rule that you multiply first, then add and subtract.

The x 0 only applies to the last 5 making it equal 0

It is 15 - 5 + 10 - 5 + 0 = 15

The multiplication MUST be done first, so it is NOT zero.

[annewandering]

so do you know why the multiplying must be done first? the reason behind the rule is what i am looking for.

[beefche]

I think "because" is rule enough.

[estradling75]

Its called order of Operations

Order of operations - Wikipedia, the free encyclopedia

[annewandering]

Thanks all! Much appreciated. :)

[LittleWyvern]

so do you know why the multiplying must be done first? the reason behind the rule is what i am looking for.

Somebody already linked to Order of Operations, but in general when you define any formal language (this form of math being one of them) you have to specify what operations mean. Establishing precedence is one way that a formal language has meaning. Perhaps the choice was a bit arbitrary but it's for good reason. If you want to delve deeper into how formal languages have meaning and how you define meaning, I'd look up formal grammars. They're fun: it's like grammar, but for math.

[Ardell89104]

Its called order of Operations

Order of operations - Wikipedia, the free encyclopedia

+1 godzilllion

[Dravin]

Somebody already linked to Order of Operations, but in general when you define any formal language (this form of math being one of them) you have to specify what operations mean. Establishing precedence is one way that a formal language has meaning. Perhaps the choice was a bit arbitrary but it's for good reason. If you want to delve deeper into how formal languages have meaning and how you define meaning, I'd look up formal grammars. They're fun: it's like grammar, but for math.

To use English as an example think of how written words have precedence from left to right. Why? Because that's how we've set the language up , they (meaning the folks using the language) could make the order of operations anything they wanted just as Arabic works right to left and everything would be okay. Giving no order of operations though would be like having people pick words randomly out of a sentence.

Edited November 11, 2011 by Dravin

[NeuroTypical]

Huh - I got 20.5.

Just call me Mr. Precise but not Accurate.

[slamjet]

Argue, ok...

You are WRONG! You are ALL WRONG!!!

The answer is 42. Everyone knows that.

[pam]

I still say it's 0. haha But then again math was not my strong area.

[RMGuy]

We follow order of operations to be obediant. Of course there are blessings (getting the right answer being one of them), some of us have a testimony of the order of operations, but if you don't and you continue to be obedient to the rule eventually you too can have a testimony that it works and that it is good and proper.

Sorry couldn't resist. :-)

-RM

[pam]

We follow order of operations to be obediant. Of course there are blessings (getting the right answer being one of them), some of us have a testimony of the order of operations, but if you don't and you continue to be obedient to the rule eventually you too can have a testimony that it works and that it is good and proper.

Sorry couldn't resist. :-)

-RM

:p:p