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I thought $10+10\times 0$ equals $0$ because: $$10+10 = 20$$

And $$20\times 0 = 0$$

I know about BEDMAS and came up with conclusion it should be $$0$$ not $$10$$

But as per this, answer is $10$, are they right?

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    http://en.wikipedia.org/wiki/Order_of_operations2012-07-03
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    In mathematics, they are right. In some computer languages or calculators, computations may be done in some other order, and of course $(10+10)\times 0 = 0$.2012-07-03
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    If you know that the order of operation has multiplication before addition (that's the "M" and the "A" in "BEDMAS" [boy, do I hate dumb acronyms that don't teach anything]), then why are you doing the `A`ddition of $10+10$ **before** the `M`ultiplication $10\times 0$? You say you know "about BEDMAS"; do you understand what it is trying to tell you?2012-07-03
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    yes sorry guys, i got confused, first expression would be 10x0 (multiplcation has higher precedence than addition) and then plus 10 resulting in 102012-07-03
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    anything is right. There is no such rule which one has to be done first . If u want to say that something has to be done first then you have to use signs like () {}, [] etc .2012-07-03
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    @ArturoMagidin BEDMAS does NOT say that it has precedence over logical rules, like the rule of replacement. He might have some sort of experience where he can replace things mechanically without altering meaning. If he thinks x+y=z is meaningful enough such that he can replace z with "x+y" in any formula, then I don't see how it's hard at all that he came to his conclusion. Why would you place BEDMAS above sound logical rules?2012-07-03
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    @Theorem: There are standard conventions, and in this case the standard conventions are precisely those that allow polynomials can be written in their usual manner without using parentheses. Deviations from the standard conventions are of course valid, but they must be signaled.2012-07-03
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    @DougSpoonwood: I've asked you before not to address me; you've downvoted me, essentially because I don't subscribe or agree with your idiosyncratic take on math and the world; I hope that brings you joy. But don't put words or actions into my mouth: you may assume they are born of your misunderstandings and misstatements, as always. I never said anything about "placing BEDMAS above sound logical rules", nor did I imply anything like that. As is clear to anyone without a personal agenda, I was talking about standing conventions. So, kindly, keep your misrepresentation and comments to yourself.2012-07-03
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    @ArturoMagidin You always seem to like to shut off discussion. You asked "If you know that the order of operation has multiplication before addition (that's the "M" and the "A" in "BEDMAS" [boy, do I hate dumb acronyms that don't teach anything]), then why are you doing the Addition of 10+10 before the Multiplication 10×0?" The answer could lie in that you derived longer formulas like 10+10x0 from shorter ones like the above using the rule of replacement. BEDMAS says to ignore such derivations when analyzing such formulas, hence BEDMAS *can* take priority over the rule of replacement.2012-07-04
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    @ArturoMagidin And what exactly is idiosyncratic about my view of math and the world here?2012-07-04
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    @DougSpoonwood: I want to shut down you addressing me. You can post whatever you want, and you can continue to downvote my answers based on your misconceptions and misstatements to your heart's content, but I don't want to get notifications with messages from you; don't address me, that's what I want. I find you both tiresome and willfully ignorant, as well as dishonest. It is patently idiosyncratic to ignore longstanding conventions, as you continue to do. It is idiosyncratic to insist that the world should follow *your* preferences. Continue to be as ignorant as you want but don't involve me2012-07-04
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    @DougSpoonwood: I didn't ask *you* anything, and you often misrepresent and misunderstand what I write, whether out of willful ignorance, your personal agenday, or something else. I care not. You can take it as read that I'm **never** asking **you** anything. So don't answer me. Don't ping me. Don't direct your post-mortem equine flagelations in my direction. Discuss whatever you want with other people, not with me. "You like to shut off discussion" is another misrepresentation on your part. I just don't want to discuss antyhing with **you**. And as such, I don't want to **hear** you either.2012-07-04

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There is a "precedence of operations": some operations should be done before other operations in the absence of indications to the contrary. This is a convention used, among other things, to make writing things like polynomials simpler and to require fewer parentheses.

Multiplication has higher precedence than addition. That means that to perform $10+10\times 0$, you should first do the product, then do the sum. So first you do $10\times 0$, then you add the answer of that to $10$. The answer is $10$.

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    Realized it later on but thanks for confirmation2012-07-03
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Multiplication has a higher precedence than addition so the multiplication is performed first.

$$10+10\times0 = 10+(10\times0) = 10$$

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Remember order of basic operations: multiplication/division have precedence over sum/substraction, so

$$10+10\cdot 0= 10+0=10$$

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    I assume there is a typo: $10+0\not=0$. ;)2012-07-03
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    Yes, there was...and a rather huge one. Thanks to Peter.2012-07-03
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To elucidate what you said above in the original post, consider that $20\times0=0$, and consider also that $10+10=20$. If we have two equations like that, with one number $n$ on one side of an equation by itself with $m$ on the other side of the equation, and $n$ also appearing in the middle of a formula elsewhere, we should then have the ability to replace $n$ by $m$ in the middle of the formula elsewhere. The rule of replacement basically says this. In other words, $20\times0=10+10\times0$, since $20=10+10$, and $20\times0=0$, we replace $20$ by $10+10$ in $20\times0=0$ and obtain $10+10\times0=0$, right? But, BEDMAS says that $10+10\times0=10$. Why the difference?

The catch here lies in that the $10+10\times0$ obtained in the first instance does NOT mean the same thing as $10+10\times0$, given by fiat, in the second instance. Technically speaking, neither $20\times0=0$ and $10+10=20$ ends up as quite correct enough that you can use the rule of replacement as happened above. More precisely, $20\times0=0$ abbreviates $(20\times0)=0$, and $10+10=20$ abbreviates $(10+10)=20$. Keeping that in mind then we can see that using the rule of replacement here leads us to $((10+10)\times0)=0$ or more shortly $(10+10)\times0=0$. BEDMAS says that $10+10\times0$ means $(10+(10\times0))$ or more shortly $10+(10\times0)$, which differs from $(10+10)\times0$. So, the problem here arises, because the infix notation you've used makes it necessary to keep parentheses in formulas if you wish the rule of replacement as mechanically as you did.

If you do express all formulas with complete parenthesis in infix notation, then BEDMAS becomes unnecessary. If you wish to drop parentheses and use the rule of replacement mechanically as you did, then you'll need to write formulas in either Polish notation or Reverse Polish notation, or fully parenthesized infix notation, instead of partially parenthesized, "normal" infix notation. If you wish to keep BEDMAS and like conventions around, and write in normal infix notation, then you have to refrain from applying the rule of replacement as mechanically as you did. Conventional mathematicians and authors of our era generally appear to prefer the latter. I don't claim to understand why they appear to prefer a notation that makes such a simple logical rule, in some cases at least, harder to use than needed.