pushing_wins
Hall of Fame
brackets means inside the brackets
Are you sure you have a MSEE and a BSEE?please scan the page of the (engineering) book where 1/3x means 1/(3x) rather than x/3.
Because somehow it doesn't seem to sink into the heads of you 288ers.
Are you sure you have a MSEE and a BSEE?
The very first thing I searched for under electrical engineering came up with this website: http://www.bowest.com.au/library/formulae.html#17
Look under the Energy section.
This is one of the equations:
The energy W stored in a capacitance C holding voltage V with charge Q is: W = CV2 / 2 = QV / 2 = Q2 / 2C
Solve for V in the first two equations and you get W = Q^2/2C with 2C in the denominator and no parentheses around the 2C.
Um...I thought we were talking about the limitations of typing out equations with a computer keyboard? "Official textbooks" can show actual equations with the horizontal divide line and a numerator above and a denominator below that horizontal line. Not so easy to do with a computer keyboard, which is why the / sign is often used to substitute for the horizontal divide line. Do a search on the Internet. You'll find tons of examples of engineering equations using the / sign in which everything to the right of the / sign is in the denominator and with no parentheses around the denominator.First of all -- you embarrasse yourself again.
This is NOT an official book, but a web page.
Second, notice the way the equations are written -- with spaces, ASSUMING something, which is the wrong assumption (not following the strict rules).
Lastly, I will actually give you a credit for the "engineering" example as some things, just like omitting the "*" are "allowed" in engineering, and those are NOT strict to the rules.
Do not question someone with the math experience longer than Your existance about simple things like this...
It makes me laugh people taking pictures of calculators and software like they don't have a brain. Work it out yourself.
/thread
What I know is that there is no basis for believing that the (9+3) in the equation 48÷2(9+3) MUST be in the numerator and CANNOT be in the denominator. So far, no one has been able to explain this.
What is the answer?
But what's inside the parentheses is in the denominator, not the numerator.
48/2(12) = 2
(48/2)(12) or (48/2)12 = 288
Thus, the way it's written, the answer is 2.
(Note: I have scored in the Top 1% or 2% in the country in every standardized math test I have ever taken, and have engineering and MBA degrees from Ivy universities.)
Numerator? Denominator? This is all on one line. Simply replace "÷2" with (1/2), (that's what the "÷" sign tells you to do, use the reciprocal of the number immediately after it.) Now it's all about multiplying! (Because dividing is simply multiplying by reciprocals.) We have (48 )(1/2)(12) which = 288.
Now order doesn't make a difference.
(48 )(12)(1/2) = (576)(1/2) = 288
(1/2)(48 )(12) = (24)(12) = 288
(1/2)(12)(48 ) = (6)(48 ) = 288
(12)(48 )(1/2) (576)(1/2) = 288
(12)(1/2)(48 ) = (6)(48 ) = 288
The "÷" is a bad symbol IMO. When you see one, use it to convert the number in question into a factor. Now, order won't matter, and you can hardly go wrong!
Oh really? And what if the equation was written as: 48÷(9+3)2 ?There is no numerator and denominator. There are three actions: a division, a multiplication, and an addition.
Order of operations explicitly states in what order they must be performed. Explicitly.
You feel like you must do the 2*12 before 48÷2 because you feel like the notation implies a fraction where 9+3 is in the denominator.
That is simply not the case.
Oh really? And what if the equation was written as: 48÷(9+3)2 ?
Doesn't ab = ba? So 2(9+3) and (9+3)2 should be the same, right?
It would be true if the monomial consisted of "a" and "b" alone. With the addition of a third variable with a division operation, as in "c÷a*b", the variables "a" and "b" do NOT commute under multiplication.Breakpoint said:Doesn't ab = ba? So 2(9+3) and (9+3)2 should be the same, right?
That's because the programmers and engineers in those countries are willing to work for 10%-30% of the salary that American engineers demand. THAT'S why companies hire them! It's all about profits for the tech companies. If the programmers and engineers in those countries demanded $200,000 salaries, believe me, companies wouldn't hire so many of them.And this is why a MAJOR percentage of your programmers, engineers, and scientists of any kind are from Asia (India, China...etc) and Eastern Europe (Russia and Romania included).
Because you (who CLAIM to have superior education) can't even properly assess the requirements of a problem (project) and start making assumptions regarding what "the guy giving you the problem that needs solving" (a.k.a. the "customer") actually meant instead of assuming that what he gives you is what he actually wants...and he does know what he wants.
Yes...the problem is formulated ambiguosly (probably on purpose) and any proper math book will make sure to state things properly, but you quoting blogs or informal online sites to somehow support your so called arguments on why you are making ASSUMPTIONS is not going to help.
Your kind will probably start asking if (or even worse...start assuming) you have an additional tool (like a marker pen) available for making some signs on the recipients if asked the question "[FONT="]If you had an infinite supply of water and a 5 liter and 3 liter jar, how would you measure exactly 4 liter?"[/FONT] instead of putting your little gray cells to work with the tools available...and clearly stated in the problem.
But what makes you think that both b and c are not both in the denominator? There's no requirement that denominators (what's below the horizontal divide line) must have parentheses around it. I've seen millions of fractions in my lifetime in which denominators with more than one variable did not have parentheses around it.Then it would be different. ab = ba but a÷b*c != a÷(b*c).
I'd expect someone who graduated from an Ivy League college would know that.
But what makes you so sure that in the equation c÷ab that ab is not the denominator?It would be true if the monomial consisted of "a" and "b" alone. With the addition of a third variable with a division operation, as in "c÷a*b", the variables "a" and "b" do NOT commute under multiplication.
Isn't the / symbol in the equation 48/2(9+3) a substitute for and the same as a horizontal divide line? That's makes the denominator 2(9+3). I've never seen a rule that states you must put everything that's below the horizontal divide line in parentheses. Again, we're not talking about programming a computer nor a calculator. We're talking about interpreting and solving this equation by hand.Division is an operation. There is a dividend and a divisor. The divisor is 2 because the rules of math say so. For the divisior to be 2(9+3) you would need to put the entire expression in parentheses or write it as an explicit fraction with 2(9+3) in the denominator.
This expression is not in fractional notation. It's an explicit series of arithmetic operations, and they must be done in the proper order.
How is 48÷2(9+3)=X not an equation?It's an expression.
It's not an equation.
One more piece of elementary math your Ivy League education missed.
Oh really? And what if the equation was written as: 48÷(9+3)2 ?
Doesn't ab = ba? So 2(9+3) and (9+3)2 should be the same, right?
Even when the denominator is 2(9+3)?Plain and simple BreakPoint is incorrect. The rule is to go left to right if everything else is equal. So you have to divide 48/2 first and than multiply by (9+3).
/Thread
That explains EVERYTHING!! No need for you to post in this thread any more. You've just lost all credibility.Wooohoooo...this just killed the mood totally...
Adios amigo.
Even those expensive schools are not what they used to be...
I am so glad I got my basics from the Russian books FOR FREE rather than paying big bucks to get embarrassed with the elementary math at a tennis forum...
That explains EVERYTHING!! No need for you to post in this thread any more. You've just lost all credibility.
Oh, and those nuclear engineers that worked at Chernobyl and the automotive engineers that designed the Lada probably also learned their basics from Russian books for free.
We need to put a break point and debug the problem.
What makes me absolutely sure that ab is NOT in the denominator, is that there are no parentheses around them. In c÷(ab), you can say that ab is in the denominator. In c÷ab, you cannot say that.Breakpoint said:But what makes you so sure that in the equation c÷ab that ab is not the denominator?
Wooohoooo...this just killed the mood totally...
Adios amigo.
Even those expensive schools are not what they used to be...
I am so glad I got my basics from the Russian books FOR FREE rather than paying big bucks to get embarrassed with the elementary math at a tennis forum...
BTW, I assumed what the intention of the originator of the equation was because he or she specifically wrote it as 48÷2(9+3) and NOT 48(9+3)÷2. There's a reason for that. Those two equations are not the same.
Even when the denominator is 2(9+3)?
Does the fraction a/b have a left to right? No? Then why does the fraction a/bc have a left to right?Plain and simple BreakPoint is incorrect. The rule is to go left to right if everything else is equal. So you have to divide 48/2 first and than multiply by (9+3).
/Thread
And most of you are assuming that (9+3) is NOT in the denominator, which is wrong.We don't know if the denominator is 2(9+3) or not! You're just assuming it is, which is wrong.
The problem is if this were an SAT/ACT type question they would expect you to know the order of operations and rules without the parentheses to clarify. It's tricky no doubt.
Why not? There's no rule that says you have to put the denominator in parentheses, is there? When you see fractions in textbooks, where they use the standard horizontal divide line, how often do you see the entire denominator in parentheses?What makes me absolutely sure that ab is NOT in the denominator, is that there are no parentheses around them. In c÷(ab), you can say that ab is in the denominator. In c÷ab, you cannot say that.
originator of the equation was because he or she specifically wrote it as 48÷2(9+3) and NOT 48(9+3)÷2. There's a reason for that. Those two equations are not the same.
Nope.well using Bedmas again, the result is the same
48÷2(9+3) = 48÷2x12
= 24x12
=288
48(9+3)÷2 =48x12÷2
=576÷2
=288
that's the whole point.
you are assuming the intention, that is your whole argument.
what most of us on the 288 camp is arguing is that:
- when there are no other context (defined parameters, additional text, etc...), you can't just assume the intention.
because different ppl with different backgrounds can come to different "obvious" assumptions.
Except for lots of people repeating that the "defined" or "standard" or "obvious" rules for the notation are such-and-such, I have seen NO definitive source establishing what those standards are. However, given that advanced publications in mathematics and engineering do sometimes use one notation or the other, you probably do need to figure out what the text or paper actually meant, and how others in the community take the expression probably does matter.- in cases like this, you must use the defined set of rules (order of operations without assumptions). Not what you are used it, or the "general" practice of a specific community.
Nope.
48÷2(9+3) has the (9+3) in the denominator, while 48(9+3)÷2 has the (9+3) in the numerator. It makes a difference being on the left or the right of the ÷ sign. The left side is the dividend (numerator) while the right side is the divisor (denominator).
And none of you 288ers have been able to explain why, if the (9+3) is in the numerator, the original equation wasn't 48(9+3)÷2.
And you guys also haven't explained why the (9+3) CAN ONLY be in the numerator and CANNOT possibly be in the denominator.
If the originator of this equation had wanted the (9+3) to be in the numerator, he or she would have written it: 48(9+3)÷2.
The fact that he or she specifically DID NOT write it 48(9+3)÷2, but specifically chose to write it 48÷2(9+3), is proof enough that he or she wanted the (9+3) in the denominator!
What I know is that there is no basis for believing that the (9+3) in the equation 48÷2(9+3) MUST be in the numerator and CANNOT be in the denominator. So far, no one has been able to explain this.
Um...I thought we were talking about the limitations of typing out equations with a computer keyboard? "Official textbooks" can show actual equations with the horizontal divide line and a numerator above and a denominator below that horizontal line. Not so easy to do with a computer keyboard, which is why the / sign is often used to substitute for the horizontal divide line. Do a search on the Internet. You'll find tons of examples of engineering equations using the / sign in which everything to the right of the / sign is in the denominator and with no parentheses around the denominator.
Oh, and your "math experience" can't possibly be that long if you've never seen denominators with more than one variable with no parentheses around them.
If you want to use the isolated sources argument, I think you are going to find it also a moot point. Counter examples can be shown, and it wil just end up in the situation that no one will end up being swayed. Implying that / is a substitute for a horizontal divide is FINE, and CORRECT, but the argument is over what it is going to divide over, and assuming (as you mention in the second paragraph quoted) anything in a mathematical equation is a mistake.I cited a website because people use computer keyboards to type out equations on websites. So much so that using the / symbol as a substitute for a horizontal divide line is now the accepted convention.
BTW, I assumed what the intention of the originator of the equation was because he or she specifically wrote it as 48÷2(9+3) and NOT 48(9+3)÷2. There's a reason for that. Those two equations are not the same.
I have also seen a lot of equations in the fashion you mentioned. The difference to the ones you mentioned was that they were more clearly defined.But what makes you think that both b and c are not both in the denominator? There's no requirement that denominators (what's below the horizontal divide line) must have parentheses around it. I've seen millions of fractions in my lifetime in which denominators with more than one variable did not have parentheses around it.
Again, we're not talking about programming a computer nor a calculator. We're talking about interpreting and solving this equation by hand.
Yes, they taught us what's below the horizontal divide line is called the denominator. :???:
You are injecting your interpretation here again. Why AREN'T we talking about programming computers? Math is a set of established, defined conventions that should be able to be systematically followed by a non-human object. There isn't a need for so-called "interpretations". What's the difference? If we were solving this by hand, it would be in a situation whewre this isn't a problem, IMHO. THe problem is contrived for a reason.Isn't the / symbol in the equation 48/2(9+3) a substitute for and the same as a horizontal divide line? That's makes the denominator 2(9+3). I've never seen a rule that states you must put everything that's below the horizontal divide line in parentheses. Again, we're not talking about programming a computer nor a calculator. We're talking about interpreting and solving this equation by hand.
I guess kids today have no idea how to interpret nor solve math problems without the aid of a calculator or computer (or Google).
that's the whole point.
you are assuming the intention, that is your whole argument.
what most of us on the 288 camp is arguing is that:
- when there are no other context (defined parameters, additional text, etc...), you can't just assume the intention.
because different ppl with different backgrounds can come to different "obvious" assumptions.
- in cases like this, you must use the defined set of rules (order of operations without assumptions). Not what you are used it, or the "general" practice of a specific community.
I think the intent of the originator is to make the equation ambiguous on purpose, to demonstrate that you need to use parenthesis, and that in case of an ambiguous equation you should follow the order of operations without assuming anything.
And most of you are assuming that (9+3) is NOT in the denominator, which is wrong.
Nope.
48÷2(9+3) has the (9+3) in the denominator, while 48(9+3)÷2 has the (9+3) in the numerator. It makes a difference being on the left or the right of the ÷ sign. The left side is the dividend (numerator) while the right side is the divisor (denominator).
WolframAlpha is a computer. I think the point to writing this equation this way is to prove that using a computer to solve equations is not always going to give you the same answer as solving the equation by hand. Computers have limitations. They interpret notations (or lack thereof) differently. Apparently, most computers can't tell what's in the denominator unless you put parentheses around the entire denominator. Real people don't have that problem. People are smarter than computers. Computers can only output exactly what you put in. That's why if you mis-type just one letter or symbol in a long URL, the computer can't find that web page, even though it's obvious what web page you were looking for.Here's the output from WolframAlpha, scientists use this the world over, you can trust it.
http://www.wolframalpha.com/input/?i=48÷2(9+3)