EPTThe confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2], rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:
A Simple Math Problem? - Page 58
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chonkyfire
United States451 Posts
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BluePanther
United States2776 Posts
On April 08 2011 15:55 Annoying wrote: http://www.purplemath.com/modules/orderops2.htm check example 5 and it's explanation! thread? Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. Like has been said much earlier.... it's a matter of semantics. Both are completely legitimate answers depending on the standard being used. A lot of computer programs use the technically wrong answers, which is why when you program you tend to abuse parentheticals... | ||
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Annoying
Canada34 Posts
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Cutlery
Norway565 Posts
On April 08 2011 15:55 Annoying wrote: http://www.purplemath.com/modules/orderops2.htm check example 5 and it's explanation! thread? This problem has proper brackets and isn't written ambiguously. Had the OP written 48*(9+3) ÷ 2, any ambiguety, and hence any attempt to have a little fun, would be lost. | ||
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BluePanther
United States2776 Posts
On April 08 2011 15:55 Akari Takai wrote: Exactly. 27^3 = 27*27*27 = 19,683 3^27 = 3*3*3*3*3*3*3*3.....*3*3 = 7,625,597,484,987 HUUUUUUUUUUGE difference. Yes, I've made it clear I made a mistake... sheesh. some poeple don't let that die, do they? | ||
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Brandish
United States339 Posts
288, and 2 | ||
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KobeLobster
70 Posts
48/2x12=? By convention, you do multiplication/division (since they are basically reciprocals) from left to right giving 288. You need to move left to right because without it, it will just be pure chaos. Ex: 40/5x10/2 Going left to right gives 40. Going in some random order yields some different number. So hence everyone should follow convention. | ||
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BluePanther
United States2776 Posts
On April 08 2011 15:58 Brandish wrote: clearly, there are two types of people in this world. 288, and 2 clearly, there are 10 types of people in this world. 288, and 2 | ||
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GizmoPT
Portugal3040 Posts
for me its 5 | ||
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Annoying
Canada34 Posts
On April 08 2011 15:58 Cutlery wrote: This problem has proper brackets and isn't written ambiguously. Had the OP written 48*(9+3) ÷ 2, any ambiguety, and hence any attempt to have a little fun, would be lost. The 2 problems seem very similar to me. | ||
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Kar98
Australia924 Posts
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Cutlery
Norway565 Posts
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duk3
United States807 Posts
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igotmyown
United States4291 Posts
In front of the parentheses there's implicitly a multiplication sign. However, the interpreted answer is more a question of laziness than correctness. I would read the 1/2x as 1/(2x), because I'm lazy and I don't want to write 1/(2x). I wouldn't do this for the first example, first of all because the division operator ÷ is used very clearly as a binary operator of divide object on left (subject to order of operations) by object on right. Therefore, I would assume we are using very precise operational syntax/logic on the numbers, so the parentheses would strongly suggest multiplication. In other words, ÷ means we can't be lazy. Whereas / is seen more as a fraction. Even moreso when we're using variables, since we technically we would have to write * before every variable, and it would be a huge hassle to write out 1 / ( 2 * x ). You could argue parentheses have the laziness exception, but it's nowhere near as bad as with variables. | ||
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mcc
Czech Republic4646 Posts
On April 08 2011 15:51 chonkyfire wrote: I really don't know anymore. if 2(9+3)=24 then 2 is apart of the parenthesis. If you do 18 + 6 = 24 Both answers are correct in some notation. Basically depends if you think OP expression is 48/(2*(9+3)) or (48/2)*(9+3). And contrary to what some will tell you you can choose freely as OP did not specify notation. (48/2)*(9+3) you get in standard notation , whereas 48/(2*(9+3)) in more informal notation. | ||
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chonkyfire
United States451 Posts
On April 08 2011 16:04 duk3 wrote: The problems can be interpreted in various ways, leading to all answers being essentially correct. I don't know. I think the only correct way to look at it is 2(9+3) is always 24 48/2(9+3) = 48/24 so the question is meant to trick you and should always just be 48/24 = | ||
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Tommie
China658 Posts
I am also wondering what all the people study. Studying to become a construction worker is not engineering/science. | ||
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Daozzt
United States1263 Posts
I hope people realize that 48÷2(9+3) is the same as 48 ÷ 2 * 12 No, the 2 being next to a ( does not mean it is "connected" to it. The answer's 288. It's as clear as day, no ambiguity at all. | ||
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Annoying
Canada34 Posts
http://www.purplemath.com/modules/orderops2.htm check out the nice drawing too | ||
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chonkyfire
United States451 Posts
On April 08 2011 16:07 Daozzt wrote: It's beyond me how this thread has gone on for 58 pages, but after reading the past couple pages, it's pretty laughable. I hope people realize that 48÷2(9+3) is the same as 48 ÷ 2 * 12 No, the 2 being next to a ( does not mean it is "connected" to it. The answer's 288. It's as clear as day, no ambiguity at all. edit:nvm but i was getting at what's the difference between 2(9+3) and 9+3? If there the 2 isn't involved then it's 12, but 2(9+3) is always 24. but it's not 288 | ||
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