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Of course, if you had 1 apple, and picked up another apple, you would have two apples. But, you need to think abstractly here. 1 cat plus 1 dog may equal 2 animals, but if you change the unit, it only equals 1 pair (of animals). It also depends on the base. In binary, 1 + 1 = 10 (which, of course is the decimal base 2)
It also depends on the unit value of 1:
1 small jug of water plus 1 small jug of water = 1 big jug of water.
Or,
1 pair of shoes plus 1 pair of shoes = 4 shoes.
There are two things here; yes, in basic arithmetic, you simply go from left to right. So, some people are reading the problem as 48 divided by 2, then times the sum of 9 plus 3. Which is not wrong.
Or, you can read it as 48 divided by product of 2 times the sum of 9 + 3, which I, and many other people do. In higher levels of math, the tendency is to treat everything to the left of the ÷ / : sign as one term. Then again, it really depends on the problem itself.
Anyways, here is another way to show how I "calculated" the problem:
If you had 48 ÷ 2x, the tendency would be to multiply 2 by x, then divide (which is how I read the equation).
But, it could also be written as 48 ÷ 2 * x, which, is a completely different equation, but right none-the-less.
x = (9+3)
This is one of those Are you smarter than a 5th grader social memes used to "prove" how smart the OP is.
The answer is both, as I have shown, depending on how you read the equation.
All you have shown is that you get 288 if you follow pemdas, and 2 if you do it the way that looks right visually. That doesn't make the latter correct.
In your example of 48 ÷ 2x, that's 48/2x, which translates to 48 halves times x. Just how 1/2x = 0.5x.
Your entire unit/base/qty thing of 1+1=3 is not related to this at all. That's just examples of someone who doesn't understand math at all. Atleast here, people who are getting 2, have a general understanding of math, but are making a simple mistake.
Math is a language. Math is reasoning. Math is philosophy. It can be proofed that 48÷2(9+3) is both 2 and 288, even if you follow the left to right rule of Order of Operations. However, even if you follow the left to right rule, the universal Order of Operations states that you use PEMDAS (parentheses, exponents, multiplication, division, addition, then subtraction). So, if you use PEMDAS, the answer is 2. Or 0.5 depending on your calculator.
Then again, it can be proofed that 1+1 does not equal 2.
Who cares. That proof is not widely accepted and only pompous nerdlings really care for that "truth".
So, for those who believe that 48÷2(9+3) = 288, let's see your proofs.
you dont know what you are talking about..
the only exact science is numbers.. math will always be exact... this is science 101.
PEMDAS rules say that Multiplication and division are in the same level, and you should go left to right... go and luck it up...
Please go and read first about before posting...
If you set the 2 to equal X, and set the equation equal to 288, x then = 1/72. Thus proving 2 is the correct answer.
Most people think it is 288 because they do not see the multiplication sign.
And some people will argue, even with PEMDAS, that multiplication does not take precedence over division....to which they are wrong.
you are wrong, where show me any webpage that say that multiplication goes first...
You completely forgot algebra...
lets see: soruce: Order of operations - Wikipedia, the free encyclopedia
"In the United States the acronym PEMDAS is common. It stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. If PEMDAS is followed without remembering that multiplication and division have the same weight, and addition and subtraction have the same weight, the wrong answer may be calculated."
Want more, no problem:
Source:Order of Operations
"Rule 1: First perform any calculations inside parentheses.Rule 2: Next perform all multiplications and divisions, working from left to right.Rule 3: Lastly, perform all additions and subtractions, working from left to right."
Source:The Order of Operations: PEMDAS
"It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". This tells you the ranks of the operations: Parentheses outrank exponents, which outrank multiplication and division (but multiplication and division are at the same rank), and these two outrank addition and subtraction (which are together on the bottom rank). When you have a bunch of operations of the same rank, you just operate from left to right."
source:Order of Operations - PEMDAS
"[CENTER]P[/CENTER] Parentheses first[CENTER]E[/CENTER] Exponents (ie Powers and Square Roots, etc.)[CENTER]MD[/CENTER] Multiplication and Division (left-to-right)[CENTER]AS[/CENTER] Addition and Subtraction (left-to-right)[CENTER]P[/CENTER] Parentheses first[CENTER]E[/CENTER] Exponents (ie Powers and Square Roots, etc.)[CENTER]MD[/CENTER] Multiplication and Division (left-to-right)[CENTER]AS[/CENTER] Addition and Subtraction (left-to-right)
[CENTER][CENTER]Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right) "[/CENTER]
[SIZE=-1]First do all operations that lie inside parentheses.[/SIZE]
[SIZE=-1]Next, do any work with exponents or radicals.[/SIZE]
[SIZE=-1]Working from left to right, do all multiplication and division.[/SIZE]
[SIZE=-1]Finally, working from left to right, do all addition and subtraction.[/SIZE]"
But hey, if you can find me a place that say something different I woudl be happy to read it,, but it is interesting that all webpages say the samething...
Of course, if you had 1 apple, and picked up another apple, you would have two apples. But, you need to think abstractly here. 1 cat plus 1 dog may equal 2 animals, but if you change the unit, it only equals 1 pair (of animals). It also depends on the base. In binary, 1 + 1 = 10 (which, of course is the decimal base 2)
It also depends on the unit value of 1:
1 small jug of water plus 1 small jug of water = 1 big jug of water.
Or,
1 pair of shoes plus 1 pair of shoes = 4 shoes.
There are two things here; yes, in basic arithmetic, you simply go from left to right. So, some people are reading the problem as 48 divided by 2, then times the sum of 9 plus 3. Which is not wrong.
Or, you can read it as 48 divided by product of 2 times the sum of 9 + 3, which I, and many other people do. In higher levels of math, the tendency is to treat everything to the left of the ÷ / : sign as one term. Then again, it really depends on the problem itself.
Anyways, here is another way to show how I "calculated" the problem:
If you had 48 ÷ 2x, the tendency would be to multiply 2 by x, then divide (which is how I read the equation).
But, it could also be written as 48 ÷ 2 * x, which, is a completely different equation, but right none-the-less depending on the particular issue the equation is attempting to solve.
x = (9+3)
This is one of those Are you smarter than a 5th grader social memes used to "prove" how smart some people are.
The answer is both, as I have shown, depending on how the equation is laid out to solve the issue.
As for PEMDAS, I've always did the multiplication first. Perhaps it was just the way the equations were written (perhaps in such a manner as to place multiplication operations first before division?), but I generally got the right answer, including on a GRE practice test I took a few months ago.
Are you serious?
48 ÷ 2 * x is the same as 48/2x nothing different... If you dont know PEMDAS and that left to right law about MD and AS then you are lost..
go and pick up any math book, if you have any, or do a search, which I already did for you.. and please come back...
Or at least prove your point with a link or something to support your understandin of arbegla. I mean, at least i post sources and try to prove my point...
In higher levels of math, the tendency is to treat everything to the left of the ÷ / : sign as one term.
This is simply not the case. Show any higher-level math textbook or college course materials that prove it. Higher-level math still uses the basic building blocks of algebra (P,then E, then M/D, then A/S).
I've asked Math PhDs, Math Masters, and dozens of engineers.
Only three people said 288 (my 6th grade daughter, her teacher, and this chick at work with a masters in math). All the engineers, the math PhD said 2. (I said 2 myself.)
Think about that. Think about sitting around a conference room table at a technical meeting and a bunch of America's best and brightest immediately think the answer is 2. Think about potentially bad designs based on this very common yet simple error. Mind Boggling.
Almost everyone sees the division sign as separating a numerator of 48 and a denominator of the product of 2 and 12. But that's not what that equation translates to.
Google, Matlab, and Excel will all provide 288.
Order of operation is important in matlab, so its more about how you define where the paranthesis are than someone being unable to carry out simple arethmatic. As someone who has programmed exhaustivly in C/C++/mathlab/mathcad etc, I can tell you that you have to be scrupulous when writing functions and solving them. Heck, calling an integer, than dividing by something that rounds to zero will give you a seg fault which sucks when you look at the equation and think it should divide nicely.
(48 ÷ 2) *(9+3)
or
48 ÷ (2 (9+3))
both will obviously give different results. As sun zu said, if people get the question wrong, one must question how clear the directions were. your directions were, frankly, awful. State the question correctly and maybe people will get it.
State the question correctly and maybe people will get it.
(I have a masters in engineering)
The question was stated correctly. I don't see where you were going. It wasn't stated as clearly as possible to the math-limited individual, but it was absolutely correct. Math has no ambiguity.
(I studied computer science Princeton University; I don't know why we're signing with our education level now for 5th grade math problems)
The question was stated correctly. I don't see where you were going. It wasn't stated as clearly as possible to the math-limited individual, but it was absolutely correct. Math has no ambiguity.
(I studied computer science Princeton University; I don't know why we're signing with our education level now for 5th grade math problems)
Because he listed that engineers got it wrong, I had to defend my brethren.
He mentioned matlab, and depending on where you place parenthesis, you will get different answers. Plain and simple. You need operators. You should know this more than I.
As for mathematical ambiguity, isn’t that the premise of quantum physics? What about constants and fudge factors? What about simplification of non-linear or higher order diff EQs? There is plenty of ambiguity in mathematics to go around.
Order of operation is important in matlab, so its more about how you define where the paranthesis are than someone being unable to carry out simple arethmatic. As someone who has programmed exhaustivly in C/C++/mathlab/mathcad etc, I can tell you that you have to be scrupulous when writing functions and solving them. Heck, calling an integer, than dividing by something that rounds to zero will give you a seg fault which sucks when you look at the equation and think it should divide nicely.
(48 ÷ 2) *(9+3)
or
48 ÷ (2 (9+3))
both will obviously give different results. As sun zu said, if people get the question wrong, one must question how clear the directions were. your directions were, frankly, awful. State the question correctly and maybe people will get it.
(I have a masters in engineering)
48÷2(9+3) is not an incorrect question..
If an equation like no other...
there is only one answer the correct one,,,
Because he listed that engineers got it wrong, I had to defend my brethren.
He mentioned matlab, and depending on where you place parenthesis, you will get different answers. Plain and simple. You need operators. You should know this more than I.
As for mathematical ambiguity, isn’t that the premise of quantum physics? What about constants and fuge factors? What about simplification of non-linear diff EQs? There is plenty of ambiguity in mathematics to go around.
I stand corrected regarding ambiguity. Even x<2 is ambiguous, lol.
I understand that computer input takes it one way or another. It's similar to what I touched on how calculators take it in a previous post. Even different versions of Excel interpret it differently.
But the order of operations is pretty straight forward. 1/2x = .5x
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