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# Windows 7: 48÷2(9+3) = ?

 View Poll Results: Which answer do you prefer? 2 35 58.33% 288 25 41.67% Voters: 60. You may not vote on this poll

 13 May 2011 #61 Hopalong X Windows7 Pro 64bit SP-1; Windows XP Pro 32bit 6,472 posts Grafton,IL There is no left to right "thing". You typed in the wrong equation. Remove the outside parentheses. (48 =xx) My System Specs
 13 May 2011 #62 fseal Windows 7 x64 Ultimate 2,554 posts San Diego Heh the equation is ambiguous. It specifically exploits ambiguous math rules. Both answers are correct. What is /wrong/ is that the equation was improperly written for anything more than personal consumption. Any attempt to publish such a thing would have to have had the ambiguity removed. Comp Sci is full of such things, and even though the rules are strictly defined, if you want a chance in heck that anyone is going to understand you, you explicitly disambiguate the equations. (This is how space station parts mishaps happen, no good engineer would allow such an equation to escape his notebook) My System Specs
 13 May 2011 #63 ignatzatsonic Windows 7 Home Premium SP1, 64-bit 12,050 posts I did well at algebra and math, but cannot recall the exact order of operations as I learned them, but am not sure they are the problem here. 48÷2(9+3) = is ambiguous as written and the first consideration of communication is to not confuse the reader. I don’t know the intent of the author, but I was taught 50 years ago to say “the quantity” in such situations. When using “the quantity”, the equation could mean: 1: The quantity (48 divided by 2) times the quantity (9 plus 3), which is clearly 288, but I would have written it this way to avoid ambiguity: (48÷2)(9+3) = 288 Or it could mean: 2: The quantity 48 divided by the quantity two times (9 plus 3), which is clearly 2, but I would have written it this way to avoid ambiguity: (48)÷(2(9+3)) = 2 So---as written, I’m not sure there is a correct answer and I would fault the equation writer for not being explicit and leaving unnecessary doubt. Who knows what the intent was? Of course, maybe the correct notation has changed over the years and there is no ambiguity by current standards? Or maybe I’m all wet, not for the first time. My System Specs
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 13 May 2011 #64 Hopalong X Windows7 Pro 64bit SP-1; Windows XP Pro 32bit 6,472 posts Grafton,IL There is no ambiguity. If the answer were 288 the equation would be (48÷2)(9+3) = 288 That is the only way the equation can be written that the 48 is divided by 2. No wonder we have dropped to 25th in Math in the U.S. U.S. Teens Lag as China Soars on International Test - Bloomberg My System Specs
 13 May 2011 #65 fseal Windows 7 x64 Ultimate 2,554 posts San Diego Clearly it is ambiguous, the mere existance of this "problem" is that this equation was formulated specifically to exploit an ambiguity in mathmatical conventions. If there was none, the problem would not exist. But finally, even if it weren't ambiguous, as both Ignatz and I just pointed out, it's bad form to publish even /potentially/ ambiguous code or equations. Things like "PEMDAS" are merely conventions for writing equations. Both parties have to agree on the convention. PEMDAS actually restricts true mathmatics since it places an operator precidence where none mathmatically exists. It merely lays out a ruleset for writing equations which, if both parties agree, leads to unambiguous communication. But unless both parties DO agree and know that they are adhering to the PEMDAS convention, then there is in fact ambiguity which could and should have been taken care of by more generally understood mechansims (more explicit use of parens) My System Specs
 13 May 2011 #66 Everlong Windows 8.1 Pro x64 3,378 posts Morecambe, Lancashire, England Quote: Originally Posted by Hopalong X There is no left to right "thing". You typed in the wrong equation. Remove the outside parentheses. (48 =xx) Yes there is a "left to right" thing. I stated before, and it's the order of operations.    Quote: Originally Posted by fseal Clearly it is ambiguous, the mere existance of this "problem" is that this equation was formulated specifically to exploit an ambiguity in mathmatical conventions. If there was none, the problem would not exist. That's what it boils down to. The whole thing uses bad notation and without proper use of parenthesis will remain ambiguous. PEMDAS (as well as BODMAS) has M and D at the same precedence, same as A and S are the same precedence. To force the multiplication before division, you'd have to write it has 48/(2((9+3)). Creating a program to work it out, C, Python and MATLAB result in 288. You can easily see how different calculators give different answers too. Open Windows calculator in standard view and do 2+2*2, then do the same sum in scientific view and you'll get a different answer. My System Specs
 13 May 2011 #67 arkhi Windows 2000 5.0 Build 2195 782 posts Quote: Originally Posted by Hopalong X There is no left to right "thing". You typed in the wrong equation. Remove the outside parentheses. (48 =xx) The outside parenthesis are merely programmatic to comply with MS Math's code; they are added and formatted automatically when a standard equation is added i.e. solve(equation+sqrt(solve(equation))) My System Specs
 13 May 2011 #68 Hopalong X Windows7 Pro 64bit SP-1; Windows XP Pro 32bit 6,472 posts Grafton,IL The ambiguity if one exists is an algebraic equation has been written in basic math format. The algebraic equation should be: __48__ = x ......Which results in x= 2 2(9+3) Sorry I do not have software to write algebra formulas. So I did the best I could. _48_ (9+3) = x Which results in 288. Which would be (48÷2)(9+3)= x or 288 2 Complex algebra formulas are written as fractions not using ÷ __48__ = 48÷2(9+3) 2(9+3) I changed to forward slash / for fraction or to denote division below. a/b = c a÷b= c when converted to algebraic expression is a/b= c a=48 b= 2(9+3) c= unknown Division or the fraction in these equations is the primary action of the equation. All secondary actions must be completed first. My System Specs
 13 May 2011 #69 Everlong Windows 8.1 Pro x64 3,378 posts Morecambe, Lancashire, England Quote: Originally Posted by Hopalong X The ambiguity if one exists is an algebraic equation has been written in basic math format. The algebraic equation should be: __48__ = x ......Which results in x= 2 2(9+3) Sorry I do not have software to write algebra formulas. So I did the best I could. _48_ (9+3) = x Which results in 288. 2 Complex algebra formulas are written as fractions not using ÷ Doing the method you just did, you're giving division precedence over multiplication, which it doesn't have. You perform division and multiplication left to right. It should be __48__ = 48÷2(9+3) 2(9+3) I changed to forward slash / for fraction or to denote division below. a/b = c a÷b= c when converted to algebraic expression is a/b= c a=48 b= 2(9+3) c= unknown Division or the fraction in these equations is the primary action of the equation. All secondary actions must be completed first. Doing what you did, you're giving division precedence over multiplication which it doesn't have. It should be What you did would be written as 48/(2(9+3)). My System Specs
 13 May 2011 #70 Win7User512 Windows 7 x64 / Same 1,520 posts In Your Basement. Quote: Originally Posted by Bill2 2. For the answer to be 288, the problem should have been (48÷2)(9+3) +1. Remember: PEMDAS. My System Specs