When writing it out and a computer / means "divide by." But that is what a fraction is anyways. 1/4 (one fourth) is just one dividing by 4 which equals .25.
The problem is that while doing operations (i have no clue if that's right in english) the parts after "/" could easily be part of the 4 there... like 1/4 and 1/(3+1)... except that in writing you wouldn't need the () because it's:
1
---
3+1
The problem is that "/" in writing is actually ____ and you can't easily tell what it encompasses... this is why this was never a math problem to begin with, but one of spelling/interpretation of signs.
The right written sign for division is ÷, and / is used instead because it's the one on a computer keyboard. It's not a shortcut for ____ (fraction), it's just a bad design decision from those who defined the keyboard standard.
the correct writting should be 48÷2(9+3), wich is less ambiguous.
Anyway, just replace the / by *, what do we get: 48*2(9+3)
that's the same as (48*2)(9+3), right?
since * and / have the same precedence, 48/2(9+3)=(48/2)(9+3)
When writing it out and a computer / means "divide by." But that is what a fraction is anyways. 1/4 (one fourth) is just one dividing by 4 which equals .25.
The problem is that while doing operations (i have no clue if that's right in english) the parts after "/" could easily be part of the 4 there... like 1/4 and 1/(3+1)... except that in writing you wouldn't need the () because it's:
1
---
3+1
The denominator and numerator are already in a parenthesis, but because of how it is written on paper they are redundant so you can just leave them out.
I am struggling a touch with your interpretations. To take your equation f=m*v and rearrange your equation so our force ends up on the right hand side, we would need to do a division of the force to both sides of the equation. so it looks like this:
(f/f)=(m*v)/f the f/f is simply 1, so your equations should look like
1=(m*v)/f
Not quite. The reason for this method is that one can consider an algebraic expression as a tree. That notation I used can be interpreted any number of ways but in this example it is what as called a "prefix expression". The equation, interpreted as a tree, can look something like this:
you'll have to paste this into notepad for it to display in a form that looks like a tree as HTML has no space tag to format it properly. The leading periods are simply for spacing purposes.
...=
../ \
..f *
.../ \
...m v
The equation can easily be manipulated by simply shifting bits of it to the left side of the tree. One can brute force solve an algebraic expression by simply doing this again and again until the proper configuration is reached. It isn't terribly clever or smart but it works and even though this is inefficient, it really doesn't matter as the number of elements in an expression are generally relatively small.
Thus, if you wanted to solve the equation for m, the result would look like:
(= m (/ v f))
or, as a tree:
...=
./ \
m /
..../ \
....v f
You'll note that precedence is handled in the most obvious way: operations at the bottom of the tree are performed before operations at the TOP of the tree.
flippedthebitch said:
Unless your computer science requires a completely different method of imput specific to your programs, which I understand it very well could be. your manipluation of that equation is flawed.
It isn't so much program specific as much as it is programmer friendly. Simply put, that sort of expression makes the task of writing a program that would say solve a system of equations for some variable with some number of unknown quantities relatively simple.
flippedthebitch said:
So would be your comment that the rules of procedence are unnessessary.
The rules of precedence are unnecessary because the structure of the equation contains any rules for precedence inside. All operations are inherently performed between an operator and a pair of operands. Having a program convert between the usual form and this list form (or vice versa) is relatively trivial and while the program must understand the rules of precedence to do the conversion any user would not. There is a less confusing form that this idea is based upon called Polish Notation [http://en.wikipedia.org/wiki/Polish_notation], better known as prefix notation. The commonly used infix notation makes things easy to read but introduces problems of precedence which prefix notation sought to resolve. The equation 48/2(9+3) would instead be written as:
* / 48 2 + 9 3.
When performing this calculation, the procedure is even a bit odd. You start with the right rather than the left. Simply take whatever symbol (it doesn't matter what) comes next from right to left and add it to a stack (thus the stack read from left to right, would be 3, then 9, 3). When you reach an operand take the next two values from the stack and perform the operation described by the operand upon them (9 + 3). Take this value and put it on top of the stack. Proceed as usual (the stack will eventually look like: 48, 2, 12) until you come to the next operand and perform it's described operation on the top two elements of the stack (48 / 2) then take the result and put it on the stack (which now is 24, 12). Then perform the last operation (24 * 12) and put IT on the stack. We have no more equation to work with and the stack only has one thing left so that is the result!
flippedthebitch said:
In fact if you want to mantain the equality of these equaltions the procedure of equation manipulation is utterly important to the whole process. The second equation has similair flaws, your manipulation loses the equality of the equation making, as far as I can interprete, the two sides of your equation no longer equal and totally useless to solving for any kind of variable.
Maintaining equality is easily done even if you follow the standard rules of algebra. Rest assured the only difference is how the information is presented (and how it is considered as a structure). All the usual rules still apply.
-edit-
Minor changes for clarity in the tree and the example of polish notation. It's far too early in the morning for this nonsense it would seem.
No, still has a problem, because you can easily put it in (48*1)/[2 * (9+3)] on paper...
The problem is that "/" in writing is actually ____ and you can't easily tell what it encompasses... this is why this was never a math problem to begin with, but one of spelling/interpretation of signs.
Like i said, that's what [] {} where invented for...
Yes, that's why [] {}, etc were invented for and that's exactly why they weren't used here.
You can't just imagine it as
Code:
48
------
2*(9+3)
because nothing points to it. Following your way of phrasing it. (48*1)/(2*1) * (9+3). It's nothing but simple a*b where a = 48/2 and b = (9+3). Even when considering that "/" is the same as "___" a/b*c makes it pretty clear that you have
Seems to be a bit of a culture break.
I think both parties are tight, it just depends on the way there instructors wrote stuff out. In my experience the 2(9+3) is in the denominator, as it is written without a multiplication sign which implies it is (2(9+3)). This is just badly written, as it should be clarified as the following: (48/2)(9+3), 48/(2(9+30)), or 48/2*(9+3)
All different short hand for the same problem will all equal the same answer. But leaving out the "( )" around the 2(9+3) isn't short hand it is a complete mistake. 48/2(9+3) is completely different than 48/(2(9+3))
Different places have different symbols, which is why to me (2(9+3)) looks odd, because it should be [2(9+3)]...
And "/" is usually interpreted as ____ , which leads to problems...
Never assume that just because your country is using one system of symbols everyone else is too, you might as well assume every language is read left to right.
No, still has a problem, because you can easily put it in (48*1)/[2 * (9+3)] on paper...
The problem is that "/" in writing is actually ____ and you can't easily tell what it encompasses... this is why this was never a math problem to begin with, but one of spelling/interpretation of signs.
Like i said, that's what [] {} where invented for...
Yes, that's why [] {}, etc were invented for and that's exactly why they weren't used here.
You can't just imagine it as
Code:
48
------
2*(9+3)
because nothing points to it. Following your way of phrasing it. (48*1)/(2*1) * (9+3). It's nothing but simple a*b where a = 48/2 and b = (9+3). Even when considering that "/" is the same as "___" a/b*c makes it pretty clear that you have
When writing it out on a computer / means "divide by." But that is what a fraction is anyways. 1/4 (one fourth) is just one dividing by 4 which equals .25.
So you agree with me? I think the person who said the answer changes depending on whether you're a computer programmer or a mathematician was right. In every math class I ever took, from the sixth grade through college algebra, the / was read as shorthand for a fraction bar. This means that, as written in the problem, the answer would be 2, because the numerator would be 48, while the denominator would be 2(9+3). If the expression were expected to parse as "the fraction 'fourty-eight over two,' multiplied by the sum of nine and three," as opposed to "the fraction fourty eight over the product of two and the sum of nine and three" it should have been written as (48/2)(9+3).
To put it in less ambiguous terms
48
---- (9+3) = 24(12) = 288
2
is what the computer sees, while
You wouldn't need to because that IS a math problem, because it's
5+(-3)+2...
While the problem with the thing in the OP is that "/" is interpreted differently because of how one has been taught or understood what they've been taught.
IT'S NOT A MATH PROBLEM!
Left to right itself is not a math rule, it's an interpretation rule... in real life terms you'd already know if you break something in half and then multiply it or if you're breaking it in 2(x+y) parts...
Different places have different symbols, which is why to me (2(9+3)) looks odd, because it should be [2(9+3)]...
And "/" is usually interpreted as ____ , which leads to problems...
Never assume that just because your country is using one system of symbols everyone else is too, you might as well assume every language is read left to right.
You stop using [] after you get a hang of PEMDAS because they are the same as () but they just make easier to read it with you dont have as much experience. How else would you write (5+6(4+3(6+8(7+9(11+1(48+2)))))).
"/" is the same thing as "____", they both mean "divided by."
So I thought it was 2, voted, saw the majority voted 244. So I look it up on wikipedia and it seems they changed the bloody rules. On the other hand, since i've been handling my divisions as fractions and subtractions as additions of a negative number i've been doing it right for most of the time. It's just damn depressing they thought me the old mnemonic in elementary and forgot to tell me it's outdated in the subsequent schools (all the way up to university where i got a lot of math classes).
According to my 8th grade education, the problem is 288. Add the 9 and 3, divide the 48 and 2, multiply the 24 and 12. Of course, there could be some fancy college learnin' that I have yet to get through, rendering this a trick question.
Aaahhh the little hidden exceptions of maths that makes me despise it so. Im pretty sure its 2.
Reason being, it works out that way algebraically. Algebra fills me with much disdain but it has its purpose in identifying the patterns of how such bastard problems are delt with.
If you replace the numbers with letters a/b(c+d) you get a/bc+bd or 48/((2x9)+(2x3)) which turns out 48/(18+6), Which is the same as 48/(2x12), which turns out to be 48/24 & is therefor = 2.
I think the reason for the confusion is that in most cases the fraction symbol (/) functions the same as the division symbol (not on my keyboard) but it still has to be treated differently. Calculators play by this rule too & its ever so frustrating to get two different answers for the same problem using either button.
Not exactly. I agree you can treat 1/4 as a fraction just like you can treat 1 divided by 4 as one (mostly because they are the exact same thing).
But your mistake is thinking everything after the "/" is automatically part of the denominator, which just isn't true. That is exactly why we have PEMDAS.
Different places have different symbols, which is why to me (2(9+3)) looks odd, because it should be [2(9+3)]...
And "/" is usually interpreted as ____ , which leads to problems...
Never assume that just because your country is using one system of symbols everyone else is too, you might as well assume every language is read left to right.
You stop using [] after you get a hang of PEMDAS because they are the same as () but they just make easier to read it with you dont have as much experience. How else would you write (5+6(4+3(6+8(7+9(11+1(48+2)))))).
"/" is the same thing as "____", they both mean "divided by."
When i learned math ":" and "____" where used in different circumstances, with "____" to simplify the way a division is used...
So when interpreting "/" as "___" one tends to assume things AFTER "/" are the same as things UNDER "____"...
Frankly i don't even know if we have any rules here about "/" because i haven't seen it used in school myself for math, only in relation to computers... and as per that picture someone posted some versions of official programs interpret it in different ways...
If someone over here wrote it 48:2(x) i'd have no confusion, but using "/" would make me question it.
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