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Posted: 8/29/2016 1:04:44 PM EDT
[#1]
16
EDIT again: Fixed in my lower post. |
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Posted: 8/29/2016 1:09:23 PM EDT
[#2]
1
We always did PEMDAS in school. |
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Posted: 8/29/2016 1:12:33 PM EDT
[#3]
Quoted:
8/2(2+2)= ? Please explain how you came to this conclusion. This equation tore Arfcom apart something like five years ago. |
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Posted: 8/29/2016 1:25:41 PM EDT
[#4]
I got 1 also, but there is a supposed PHD and her minions that are trying to tell me and this very bright young lady that we are wrong, that the answer is indeed 16.
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Posted: 8/29/2016 1:35:18 PM EDT
[#5]
I was under the impression that the order of operations is not strictly PEMDAS, but P and E, then M and D, then A and S, in sequential order, running left to right. multiplication and division have the same priority, so it goes left to right, as does addition and subtraction.
So the parenthesis is a 4, and 8 divided by 2 times 4 equals 16. |
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Posted: 8/29/2016 1:47:35 PM EDT
[#6]
Quote HistoryQuoted: I was under the impression that the order of operations is not strictly PEMDAS, but P and E, then M and D, then A and S, in sequential order, running left to right. multiplication and division have the same priority, so it goes left to right, as does addition and subtraction. So the parenthesis is a 4, and 8 divided by 2 times 4 equals 16. The equation in the OP and the equation that is written out in pen in the 5th post are two different equations. The equation in the OP does = 16 now that I look harder at it. The equation in post 5 which I (and I think the OP) incorrectly assumed was being written originally would have to be 8/(2(2+2)) to be equal to 1. Basically you can't just put everything else in the denominator. |
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Posted: 8/29/2016 1:52:49 PM EDT
[#7]
16
PEMDAS is a bit misleading. The actual steps are: 1. Parentheses 2. Exponents 3. Multiplication and division from left to right, whichever comes first 4. Addition and subtraction from left to right, whichever comes first So 8/2(2+2) = 8/2(4) = 4(4) = 16. EDIT: I can see how some would get 1 (it would have to be written 8/[2(2+2)]. The notation is very important. |
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Posted: 8/29/2016 1:54:54 PM EDT
[#8]
Quote HistoryQuoted:
16 PEMDAS is a bit misleading. The actual steps are: 1. Parentheses 2. Exponents 3. Multiplication and division from left to right, whichever comes first 4. Addition and subtraction from left to right, whichever comes first So 8/2(2+2) = 8/2(4) = 4(4) = 16. EDIT: I can see how some would get 1 (it would have to be written 8/[2(2+2)]. The notation is very important. Yep. |
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Posted: 8/29/2016 2:01:01 PM EDT
[#9]
So here is where I am thinking about this physically:
8 gallons divided by 2(2 gallon + 2 gallon buckets) 8 gallons divided by 2(4 gallons) 8 gallons divided by 8 gallons |
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Posted: 8/29/2016 2:10:51 PM EDT
[#10]
Quote HistoryQuoted: So here is where I am thinking about this physically: 8 gallons divided by 2(2 gallon + 2 gallon buckets) 8 gallons divided by 2(4 gallons) 8 gallons divided by 8 gallons |
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Posted: 8/29/2016 2:11:30 PM EDT
[#11]
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Posted: 8/29/2016 2:13:03 PM EDT
[#12]
Quote HistoryAre you reading any of the replies? |
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Posted: 8/29/2016 2:28:07 PM EDT
[#13]
8/2(2+2)
8/2(4) 8/2x4 4x4 16 |
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Posted: 8/29/2016 2:34:47 PM EDT
[#14]
What I'm saying is that 2(4) is one thing. To find what 2(4) is, you multiply 2*4.
Everyone is converting 2(4) to 2*4, and then starting from the beginning. If you fininsh the parentheses, 2(4) you get 8. Thend to your Aunt Sally mnuemonic. 8/8=1 2(4) means 2*4 You cant just add a * just like I cant add [ ]. You never finished the denomenator side. |
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Posted: 8/29/2016 2:34:59 PM EDT
[#15]
Yes, I am reading the replies.
I drew dots to represent the numbers, and what they say. 8 dots divided by two groups of two plus two dots 8 dots divided by two groups of four dots 8 dots divided by 8 dots |
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Posted: 8/29/2016 2:42:58 PM EDT
[#16]
Quote HistoryQuoted:
What I'm saying is that 2(4) is one thing. To find what 2(4) is, you multiply 2*4. Everyone is converting 2(4) to 2*4, and then starting from the beginning. If you fininsh the parentheses, 2(4) you get 8. Thend to your Aunt Sally mnuemonic. 8/8=1 2(4) means 2*4 You cant just add a * just like I cant add [ ]. You never finished the denomenator side. That's the thing, in PEMDAS, that division sign doesn't mean numerator and denominator. It just means divided by. So reading it as 8/2 FIRST, you get 4, and only then move onto the multiplication. Which is why the strict interpretation means 16. That said, I'm like you and read it as numerator and denominator.  I say 1.
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Posted: 8/29/2016 2:51:15 PM EDT
[#17]
Quote HistoryQuoted:
That's the thing, in PEMDAS, that division sign doesn't mean numerator and denominator. It just means divided by. So reading it as 8/2 FIRST, you get 4, and only then move onto the multiplication. Which is why the strict interpretation means 16. That said, I'm like you and read it as numerator and denominator. I say 1.Quote HistoryQuoted:
Quoted:
What I'm saying is that 2(4) is one thing. To find what 2(4) is, you multiply 2*4. Everyone is converting 2(4) to 2*4, and then starting from the beginning. If you fininsh the parentheses, 2(4) you get 8. Thend to your Aunt Sally mnuemonic. 8/8=1 2(4) means 2*4 You cant just add a * just like I cant add [ ]. You never finished the denomenator side. That's the thing, in PEMDAS, that division sign doesn't mean numerator and denominator. It just means divided by. So reading it as 8/2 FIRST, you get 4, and only then move onto the multiplication. Which is why the strict interpretation means 16. That said, I'm like you and read it as numerator and denominator. I say 1.When you use sugar cubes PEMDAS is broken. 
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Posted: 8/29/2016 2:51:45 PM EDT
[#18]
Quote HistoryQuoted: 16 PEMDAS is a bit misleading. The actual steps are: 1. Parentheses 2. Exponents 3. Multiplication and division from left to right, whichever comes first 4. Addition and subtraction from left to right, whichever comes first So 8/2(2+2) = 8/2(4) = 4(4) = 16. EDIT: I can see how some would get 1 (it would have to be written 8/[2(2+2)]. The notation is very important. Ah, I understand OP's confusion now. When we say "Parentheses", it means everything WITHIN the parentheses. So to expound on my first response - 1. everything inside the Parentheses 2. Exponents 3. Multiplication and Division from left to right, whichever comes first 4. Addition and Subtraction from left to right, whichever comes first Another way to notate the OP's equation is 8 ÷ 2 * (2 + 2) |
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Posted: 8/29/2016 2:55:06 PM EDT
[#19]
1
-or- Teacher's lazy notation is not your fault. |
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Posted: 8/29/2016 2:57:28 PM EDT
[#20]
Some asshole did it wrong, wrote a book, now everyone references his bad work and tries to tell you why your wrong.
In the real world. Bob has eight people working for him. Bob has two boxes of meals. Each box contains two Chinese meals and two Italian meals. How many meals will Bob's employees have? |
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Posted: 8/29/2016 2:57:55 PM EDT
[#21]
Quote HistoryQuoted: What I'm saying is that 2(4) is one thing. To find what 2(4) is, you multiply 2*4. Everyone is converting 2(4) to 2*4, and then starting from the beginning. If you fininsh the parentheses, 2(4) you get 8. Thend to your Aunt Sally mnuemonic. 8/8=1 2(4) means 2*4 You cant just add a * just like I cant add [ ]. You never finished the denomenator side. ETA: Plug the equation into a scientific calculator exactly as written and you will get 16 every time. |
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Posted: 8/29/2016 3:16:10 PM EDT
[#22]
Quote HistoryQuoted: What I'm saying is that 2(4) is one thing. To find what 2(4) is, you multiply 2*4. Everyone is converting 2(4) to 2*4, and then starting from the beginning. If you fininsh the parentheses, 2(4) you get 8. Thend to your Aunt Sally mnuemonic. 8/8=1 2(4) means 2*4 You cant just add a * just like I cant add [ ]. You never finished the denomenator side. 2(4) IS 2*4. 8/2(4) = 8/2*4 =/= 8/(2(4)) |
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Posted: 8/29/2016 9:19:03 PM EDT
[#23]
There are real practical reasons math is not done using typesetting conventions.
You are not forced to use a single line. |
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Posted: 8/29/2016 10:16:07 PM EDT
[#24]
Poll added
Discussed this at work with a handful of engineers and a PHD. Basically those of us over 30, treat 2(2+2) as the denominator and come up with 1 as the answer. The younger guy who is fresh out of college came up with 16. One of the engineers who said 1 called his engineer dad, who majored in mathematics, that basically said that as written the answer is 1. We were in concurrence that having the 2 directly next to the parentheses without a multiplication symbol made it 8/(2*4). It's not a question of order of operations so much as it is a question of whether or not the 2 outside of the parentheses must be taken as attached to the part inside of the parentheses. |
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Posted: 8/29/2016 10:25:27 PM EDT
[#25]
Quote HistoryQuoted: 16 PEMDAS is a bit misleading. The actual steps are: 1. Parentheses 2. Exponents 3. Multiplication and division from left to right, whichever comes first 4. Addition and subtraction from left to right, whichever comes first So 8/2(2+2) = 8/2(4) = 4(4) = 16. EDIT: I can see how some would get 1 (it would have to be written 8/[2(2+2)]. The notation is very important. |
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Posted: 8/29/2016 10:33:11 PM EDT
[#26]
Quote HistoryQuoted: it is a question of whether or not the 2 outside of the parentheses must be taken as attached to the part inside of the parentheses. Like I said several posts ago, without parenthesis around the entire denominator you perform the operations from left to right and get 16. If you just pretend that there are parenthesis that don't really exist and call everything after the / the denominator you can get the wrong answer of 1. |
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Posted: 8/29/2016 10:39:02 PM EDT
[#27]
That's the mathematical equivalent of the "Giant Reptilian Man Eating Demons" thread.
Poor syntax can lead to poor understanding. The way that is written, it is not clear. |
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Posted: 8/29/2016 10:49:05 PM EDT
[#28]
Quote HistoryQuoted:
Some asshole did it wrong, wrote a book, now everyone references his bad work and tries to tell you why your wrong. In the real world. Bob has eight people working for him. Bob has two boxes of meals. Each box contains two Chinese meals and two Italian meals. How many meals will Bob's employees have? It could just as easily be Bob had 8 employees and fired half of them. Each employee needs to eat 2 meals on Friday and 2 meals on Saturday. How many meals does Bob need to buy? |
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Posted: 8/29/2016 10:57:03 PM EDT
[#29]
Quote HistoryQuoted:
That's the mathematical equivalent of the "Giant Reptilian Man Eating Demons" thread. Poor syntax can lead to poor understanding. The way that is written, it is not clear. It's the Oxford Comma debate of the math world.
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Posted: 8/30/2016 1:02:29 AM EDT
[#30]
Quote HistoryQuoted:
It's the Oxford Comma debate of the math world. Quote HistoryQuoted:
Quoted:
That's the mathematical equivalent of the "Giant Reptilian Man Eating Demons" thread. Poor syntax can lead to poor understanding. The way that is written, it is not clear. It's the Oxford Comma debate of the math world. Yes, we are aplitting hairs here. This is not math, this is shitty syntax. |
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Posted: 8/30/2016 11:32:31 AM EDT
[#31]
It is poorly formed if there is more than one way to evaluate it.
In this case it needs more parenthesis. The 'rules' are designed to force only ONE possible answer. |
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Posted: 8/30/2016 11:54:24 AM EDT
[#32]
Quote HistoryQuoted: Yes, we are aplitting hairs here. This is not math, this is shitty syntax. |
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Posted: 8/30/2016 12:35:45 PM EDT
[#33]
Quote HistoryQuoted:
When in linear form in an equation the slash signifies division not a fraction. Quote HistoryQuoted:
Quoted:
Yes, we are aplitting hairs here. This is not math, this is shitty syntax. You making a semantic distinction, not a mathematical one. A fraction is "division." |
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Posted: 8/30/2016 1:22:46 PM EDT
[#34]
Quote HistoryQuoted: You making a semantic distinction, not a mathematical one. A fraction is "division." Quote HistoryQuoted: Quoted: Quoted: Yes, we are aplitting hairs here. This is not math, this is shitty syntax. You making a semantic distinction, not a mathematical one. A fraction is "division." Using a slash in a linear equation does not signify that everything following it is the denominator, that better? |
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Posted: 8/30/2016 4:48:17 PM EDT
[#35]
Quote HistoryQuoted:
Using a slash in a linear equation does not signify that everything following it is the denominator, that better? Quote HistoryQuoted:
Quoted:
Quoted:
Quoted:
Yes, we are aplitting hairs here. This is not math, this is shitty syntax. You making a semantic distinction, not a mathematical one. A fraction is "division." Using a slash in a linear equation does not signify that everything following it is the denominator, that better? That is what parenthesis are for. To unambiguously show the order of calculations. And there is a common convention that everything following a slash is the denominator. Many units expressions follow this convention. ETA uin/in F micro-inches per inch per degree F. Thermal expansion of metal by starting size and change in temperature. Putting multiple slashes in makes little sense (uin / in / F) and is not usually seen. As a QA thing we always did uin/(in F). And often put in 'dots' to make the multiplication clear. Problems quickly occur with many type fonts not having a good symbol set. It probably should have a deltaF for more clarity. It is taken as uin/(in F) |
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Posted: 8/30/2016 4:50:51 PM EDT
[#36]
Right. I think this underscores the importance of the use of parentheses more than anything.
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Posted: 8/31/2016 2:16:30 PM EDT
[#37]
Quote HistoryQuoted:
I was under the impression that the order of operations is not strictly PEMDAS, but P and E, then M and D, then A and S, in sequential order, running left to right. multiplication and division have the same priority, so it goes left to right, as does addition and subtraction. So the parenthesis is a 4, and 8 divided by 2 times 4 equals 16. This is correct. |
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Posted: 8/31/2016 7:25:16 PM EDT
[#38]
Quote HistoryQuoted:
This is correct. Quote HistoryQuoted:
Quoted:
I was under the impression that the order of operations is not strictly PEMDAS, but P and E, then M and D, then A and S, in sequential order, running left to right. multiplication and division have the same priority, so it goes left to right, as does addition and subtraction. So the parenthesis is a 4, and 8 divided by 2 times 4 equals 16. This is correct. Is is poorly formed and thus WRONG from the start. |
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Posted: 8/31/2016 9:10:25 PM EDT
[#39]
Quote HistoryQuoted:
Is is poorly formed and thus WRONG from the start. Quote HistoryQuoted:
Quoted:
Quoted:
I was under the impression that the order of operations is not strictly PEMDAS, but P and E, then M and D, then A and S, in sequential order, running left to right. multiplication and division have the same priority, so it goes left to right, as does addition and subtraction. So the parenthesis is a 4, and 8 divided by 2 times 4 equals 16. This is correct. Is is poorly formed and thus WRONG from the start. We have rules, Smokey. Everyone knows the rules. The equation, if observing the rules, is very simple and not open to interpretation. |
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Posted: 9/1/2016 7:28:06 PM EDT
[#40]
Quote HistoryQuoted:
We have rules, Smokey. Everyone knows the rules. The equation, if observing the rules, is very simple and not open to interpretation. Quote HistoryQuoted:
Quoted:
Quoted:
Quoted:
I was under the impression that the order of operations is not strictly PEMDAS, but P and E, then M and D, then A and S, in sequential order, running left to right. multiplication and division have the same priority, so it goes left to right, as does addition and subtraction. So the parenthesis is a 4, and 8 divided by 2 times 4 equals 16. This is correct. Is is poorly formed and thus WRONG from the start. We have rules, Smokey. Everyone knows the rules. The equation, if observing the rules, is very simple and not open to interpretation. PEMDAS is NOT a "rule." It is a gross simplification and a mnemonic to remind users who do not work every day in mathematics. This whole thread is why it does NOT WORK. |
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Posted: 9/1/2016 8:52:14 PM EDT
[#41]
Quote HistoryQuoted:
PEMDAS is NOT a "rule." It is a gross simplification and a mnemonic to remind users who do not work every day in mathematics. This whole thread is why it does NOT WORK. This is my take also Quote HistoryQuoted:
Quoted:
Quoted:
Quoted:
Quoted:
I was under the impression that the order of operations is not strictly PEMDAS, but P and E, then M and D, then A and S, in sequential order, running left to right. multiplication and division have the same priority, so it goes left to right, as does addition and subtraction. So the parenthesis is a 4, and 8 divided by 2 times 4 equals 16. This is correct. Is is poorly formed and thus WRONG from the start. We have rules, Smokey. Everyone knows the rules. The equation, if observing the rules, is very simple and not open to interpretation. PEMDAS is NOT a "rule." It is a gross simplification and a mnemonic to remind users who do not work every day in mathematics. This whole thread is why it does NOT WORK. This is my take also By simply changing how you write something down (ie linear) is supposed to change the result? Eight divided by two-X: 
ETA: If the third one looks wrong to you, I've got no idea what photobucket is doing. I corrected the image before posting. |
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Posted: 9/1/2016 10:06:41 PM EDT
[#42]
Quote HistoryQuoted:
PEMDAS is NOT a "rule." It is a gross simplification and a mnemonic to remind users who do not work every day in mathematics. This whole thread is why it does NOT WORK. Quote HistoryQuoted:
Quoted:
Quoted:
Quoted:
Quoted:
I was under the impression that the order of operations is not strictly PEMDAS, but P and E, then M and D, then A and S, in sequential order, running left to right. multiplication and division have the same priority, so it goes left to right, as does addition and subtraction. So the parenthesis is a 4, and 8 divided by 2 times 4 equals 16. This is correct. Is is poorly formed and thus WRONG from the start. We have rules, Smokey. Everyone knows the rules. The equation, if observing the rules, is very simple and not open to interpretation. PEMDAS is NOT a "rule." It is a gross simplification and a mnemonic to remind users who do not work every day in mathematics. This whole thread is why it does NOT WORK. Something I've noticed since the "common core math" threads started, is that for some people mathematics is not a means to an end, or representation of something else, but an end in itself. They're more like advanced puzzle players who get upset if another puzzle is introduced which they aren't as familiar with. |
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Posted: 9/1/2016 10:22:24 PM EDT
[#43]
Of course the plane takes off !!!
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Posted: 9/2/2016 10:24:53 PM EDT
[#44]
Quote HistoryQuoted:
Poll added Discussed this at work with a handful of engineers and a PHD. Basically those of us over 30, treat 2(2+2) as the denominator and come up with 1 as the answer. The younger guy who is fresh out of college came up with 16. One of the engineers who said 1 called his engineer dad, who majored in mathematics, that basically said that as written the answer is 1. We were in concurrence that having the 2 directly next to the parentheses without a multiplication symbol made it 8/(2*4). It's not a question of order of operations so much as it is a question of whether or not the 2 outside of the parentheses must be taken as attached to the part inside of the parentheses. That is incorrect. 2(x) is the same as 2*x and 2x. The paren only signifies multiplication. It's not a magic operator that gets evaluated differently than any other multiplication -- it's shorthand. |
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Posted: 9/2/2016 10:25:20 PM EDT
[#45]
Quote HistoryQuoted:
That's the mathematical equivalent of the "Giant Reptilian Man Eating Demons" thread. Poor syntax can lead to poor understanding. The way that is written, it is not clear. The way it's written is perfectly clear. |
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Posted: 9/5/2016 11:17:35 PM EDT
[#46]
Quote HistoryQuoted:
This, which is why I refuse slashy fraction bars as a teacher. It makes the denominator ambiguous Quote HistoryQuoted:
Quoted:
16 PEMDAS is a bit misleading. The actual steps are: 1. Parentheses 2. Exponents 3. Multiplication and division from left to right, whichever comes first 4. Addition and subtraction from left to right, whichever comes first So 8/2(2+2) = 8/2(4) = 4(4) = 16. EDIT: I can see how some would get 1 (it would have to be written 8/[2(2+2)]. The notation is very important. This! 
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Posted: 9/5/2016 11:21:58 PM EDT
[#47]
Quote HistoryQuoted:
The way it's written is perfectly clear. Quote HistoryQuoted:
Quoted:
That's the mathematical equivalent of the "Giant Reptilian Man Eating Demons" thread. Poor syntax can lead to poor understanding. The way that is written, it is not clear. The way it's written is perfectly clear. No. As stated, the denominator is ambiguous. Pantheses should be put around the "8/2" in order to make it clear that that's what is being done. |
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Posted: 9/6/2016 5:12:46 AM EDT
[#48]
Quote HistoryQuoted:
No. As stated, the denominator is ambiguous. Pantheses should be put around the "8/2" in order to make it clear that that's what is being done. Quote HistoryQuoted:
Quoted:
Quoted:
That's the mathematical equivalent of the "Giant Reptilian Man Eating Demons" thread. Poor syntax can lead to poor understanding. The way that is written, it is not clear. The way it's written is perfectly clear. No. As stated, the denominator is ambiguous. Pantheses should be put around the "8/2" in order to make it clear that that's what is being done. not required. |
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Posted: 9/6/2016 6:56:12 AM EDT
[#49]
Quote HistoryQuoted:
The way it's written is perfectly clear. Quote HistoryQuoted:
Quoted:
That's the mathematical equivalent of the "Giant Reptilian Man Eating Demons" thread. Poor syntax can lead to poor understanding. The way that is written, it is not clear. The way it's written is perfectly clear. An assertion readily refuted by the fact this thread even exists. |
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Posted: 9/6/2016 9:29:54 AM EDT
[#50]
Quote HistoryQuoted:
An assertion readily refuted by the fact this thread even exists. Quote HistoryQuoted:
Quoted:
Quoted:
That's the mathematical equivalent of the "Giant Reptilian Man Eating Demons" thread. Poor syntax can lead to poor understanding. The way that is written, it is not clear. The way it's written is perfectly clear. An assertion readily refuted by the fact this thread even exists. That really only proves that people are no longer taught math. |
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