Nope. The math people say it's not ambiguous because they know how the precedence rule applies to evaluating expressions.Math has a strict set of rules, and getting it right is simply a question of knowing the rules, and applying them.
the letter why wrote:
No, the math people are saying it is ambiguous. The only people taking a firm stance have no idea what they are talking about.
sugarcookies from Mom wrote:
sajdfhhsbg wrote:well
48÷2(9+3)=?
I vote two gross
This whole thread grosses me out. No wonder the Hubble needed glasses!
Next thing we'll have Carol Lewis telling us the second leg is the longest in a 4x100meter relay.
As a math person, it isn't really ambiguous, but it is rather poorly written. As someone previously mentioned, nobody who studies math would ever write it that way. Just as we wouldn't write 7x/2y if we meant it to be (7x/2)*y.
Math Guy #288 wrote:
I don't agree that the answer is 288. When you have an equation like this you should write the question out properly. A division sign is the same thing as a fraction line. Anything under the fraction line needs to be solved first.
48÷2(9+3)should be written as:
=48
------
2(9+3)
=48
-----
2(12)
=48
----
24
= 2
Hopefully this comes out looking when I hit post.
You're changing the meaning of the division sign. It doesn't mean that you automatically apply brackets around everything that follows, as that would be unclear. Matlab, TI calculators, google, and whatever other program you want to use will return the same result because the order of operations is programmed into them. I don't think you're actually a math guy.
lllll wrote:
Math Guy #288 wrote:I don't agree that the answer is 288. When you have an equation like this you should write the question out properly. A division sign is the same thing as a fraction line. Anything under the fraction line needs to be solved first.
48÷2(9+3)should be written as:
=48
------
2(9+3)
=48
-----
2(12)
=48
----
24
= 2
Hopefully this comes out looking when I hit post.
You're changing the meaning of the division sign. It doesn't mean that you automatically apply brackets around everything that follows, as that would be unclear. Matlab, TI calculators, google, and whatever other program you want to use will return the same result because the order of operations is programmed into them. I don't think you're actually a math guy.
Not disagreeing with the order of operations, but the logic that because computer methods read input a certain way implies that things are always a certain way is not really an argument at all.
Speaking up wrote:
Not disagreeing with the order of operations, but the logic that because computer methods read input a certain way implies that things are always a certain way is not really an argument at all.
You're misconstruing his argument. His argument rests upon his claim that the programs listed are programed to use the standard order of operations. He's not saying that we should do things a certain way because computers are programed to do things that way. He's saying that the computer programs are programed to do things correctly, so the results that they give are the results that one would obtain from following the proper order of operations.
jeez wrote:
[quote]mplatt wrote:
48÷2X=288
Solve it.
X = 12. This has been made abundantly clear. 48 divided by 2, THEN multiplied by X equals 288. X must therefore equal 12.
The "then" is important. Left to right. No matter how many times you try to pretend otherwise, "2X" still means "2 * X" Always. If you want parentheses, you must add them.
You are just plain wrong. The brackets are implied when you write a problem 2X or 2(x+Y).
This morning I brought this question to a person who is/was a director and judge in the New England Math League, RI math league, Math Olympiad and has 35 years and the highest credentials regarding these types of math problems in competition. He agrees with me, and actually laughed.
He says the spreadsheets and calculators are limited by the input of the user.
Final verdict: 48÷2(9+3)=2
mplatt wrote:
jeez wrote:[quote]mplatt wrote:
48÷2X=288
Solve it.
X = 12. This has been made abundantly clear. 48 divided by 2, THEN multiplied by X equals 288. X must therefore equal 12.
The "then" is important. Left to right. No matter how many times you try to pretend otherwise, "2X" still means "2 * X" Always. If you want parentheses, you must add them.
You are just plain wrong. The brackets are implied when you write a problem 2X or 2(x+Y).
This morning I brought this question to a person who is/was a director and judge in the New England Math League, RI math league, Math Olympiad and has 35 years and the highest credentials regarding these types of math problems in competition. He agrees with me, and actually laughed.
He says the spreadsheets and calculators are limited by the input of the user.
Final verdict: 48÷2(9+3)=2
lol your friend is a moron
mplatt wrote:
You are just plain wrong. The brackets are implied when you write a problem 2X or 2(x+Y).
This morning I brought this question to a person who is/was a director and judge in the New England Math League, RI math league, Math Olympiad and has 35 years and the highest credentials regarding these types of math problems in competition. He agrees with me, and actually laughed.
He says the spreadsheets and calculators are limited by the input of the user.
Final verdict: 48÷2(9+3)=2
Congratulations to your friend for his mathematical achievements. Unfortunately, for all of that, he would not even pass programming 101. Not even if he waived all of his credentials at the screen. You see, not only do the spreadsheets and calculators disagree with him. So do the programming languages.
Order of operations and operator precedence are not suggestions or conventions or vague ideas open to interpretation. They are rules. Precise and clear ones. One either follows them, or one gets the wrong answer. If you want the "2x" multiplication to occur before anything, you must surround it with parentheses.
Sorry. You still fail. So does your friend.
48/2(9+3) = 48/(2x9)+(2x3) = 48/24 = 2
Matlock wrote:
48/2(9+3) = 48/(2x9)+(2x3) = 48/24 = 2
I'm not sure what's worse. Your logic or your explanation. What you have written here is not true, EVEN IF your incorrect interpretation of the parentheses rule were true.
Look, people, enter the entire expression in any decent graphing calculator. Hit enter. Voila. The graphing calculator is programmed according to the proper order of operations.
For the person who said you would never see -x^2 ... a simple application of the Pythagorean Theorem could get you there.
If you're solving for an unknown length of one of the legs, you could easily have:
3^2 + x^2 = 5^2
This would give you:
x^2 = 5^2 - 3^2
If you're hung up on the difference between subtraction and a negative sign, remember subtraction means adding the opposite. Therefor, that expression is the same as:
x^2 = 5^2 + -3^2
I just had a seance with Lukasiewics and he said 288.
rekrunner wrote:
Nope. The math people say it's not ambiguous because they know how the precedence rule applies to evaluating expressions.
Math has a strict set of rules, and getting it right is simply a question of knowing the rules, and applying them.
I have no idea how this thread got to be this long, but it is surely proof why Asia is kicking our asses in math and is evidence that Letsrun has many law school graduates.
There is no ambiguity except to those who have been trained to fabricate ambiguity in everything.
Math Guy #288 wrote:
You must do the 2(9+3) first. The 2 is a part of the brackets, you can't just ignore it and separate it out. This becomes 2x9+2x3=24. 48/24 is 2. Would you like some further help?
Yes. Please direct me to the textbook where you learned about the rule of implied parentheses. I'm not familiar with it.
Thanks.
rekrunner wrote:
The 2 is outside the brackets. In fact "48÷2" is outside the brackets, and therefore outside the scope of its influence, in spite of the direct contact of the 2 with the parenthesis. There is no direct contact rule. Associativity, commutativity, distributivity, and whatever other rules or properties you might think of, do not alter the rules of precedence. You can not ignore the preceding terms. Once you perform the calculation inside the brackets, there are no more brackets, and therefore nothing forces the 2 to be resolved with the new non-bracketed expression prematurely. The 2 is connected by multiplication after, and division before. You can not ignore either, but must follow a centuries old convention that binds all mathematicians above the age of 10, worth their salt, to evaluate such infixed expressions from left to right:
Special note: Unary operators, e.g. negative signs, factorials, form part of the number, and must be treated as an integrated number.
48÷2(9+3)=?
Step 1: Perform all groupings, e.g. brackets, parentheses, roots, from left to right
48÷2*12=?
Step 2: Perform all powers (exponents), from left to right (with stacked powers top down)
48÷2*12=?
Step 3: Perform all multiplication and division from left to right
Step 3.1: 24*12=?
Step 3.2: 288=?
Step 4: Perform all addition subtraction from left to right
288=?
Would you like some further help?
The potential problems arising from any "ambiguity" issue was discovered by mathematicians centuries ago, if not longer, and the orders of precedence were agreed by universal convention, and defined by the precedence rule, at the time of creation of the symbolic infix notation for equations. These rules are very precise, leading to only one single interpretation of every equation that gives predictable and repeatable results every time. Mathematics could not have progressed with this kind of basic ambiguity.
Parentheses are not required when it just makes explicit, that which is implicit by universal convention, although it can aid in human understanding.
You are wrong. The question is not written: 48÷2*(9+3)
It is clearly written: 48÷2(9+3)
You must multiply out the 2 first. Either 2x9+2x3 or 2x(12). Either way, the answer is 2.
lllll wrote:
As an engineer I multiply stuff out all the time and thus have a pretty good grasp on order of operations. The only way to get 2 is to add an extra set of parentheses around the 2*(9+3) term, but the problem doesn't indicate we should do that.
The tipoff that you guys are wrong is that people who actually know math are all telling you that you're wrong. Meanwhile, the other side is arguing based on a middle school mnemonic device.
In fact, I just typed this problem exactly as written into my TI-89. Answer: 288.
I feel sorry for any engineering firm that hires you or allows you to do any meaningful work. The question is not written: 2*(9+3). It is is written: 2(9+3). You must multiply out the 2 before moving on to the left to right convention. Jezzuz. Calculators do not understand this, you must enter the extra set of brackets when inputting this into a calculator. Please start a new thread when you graduate telling us which projects you have worked on so we can avoid them.
miscontruation wrote:
Speaking up wrote:Not disagreeing with the order of operations, but the logic that because computer methods read input a certain way implies that things are always a certain way is not really an argument at all.
You're misconstruing his argument. His argument rests upon his claim that the programs listed are programed to use the standard order of operations. He's not saying that we should do things a certain way because computers are programed to do things that way. He's saying that the computer programs are programed to do things correctly, so the results that they give are the results that one would obtain from following the proper order of operations.
No, you are misconstruing my argument. Any math person worth their salt would not reach for a calculator to solve this and would know that you can't just enter into the calculator as written. Read the fecking instruction booklet that comes with your calculator, it will spell this out for you morons!
Math Guy #288 wrote:
No, you are misconstruing my argument. Any math person worth their salt would not reach for a calculator to solve this and would know that you can't just enter into the calculator as written. Read the fecking instruction booklet that comes with your calculator, it will spell this out for you morons!
Are you the same person I was responding to before? Your post implies that you are, but the name change makes it hard to tell. If so, no, I did not misconstrue your argument. Your argument was that "the logic that because computer methods read input a certain way implies that things are always a certain way is not really an argument at all." That is exactly what I said your argument was.
Math Guy has clinched the title of most inappropriately named on letsrun. Once again, please point us to the Rule of Implied Parentheses.
It boggles my mind to hear you argue that, paraphrasing here, you must change the way it is written if you want to come up with the correct answer to what is written.
Order of operations clearly states do what is INSIDE the parentheses first. Not what is NEAR parentheses.
Are you really implying that:
48÷2(12)
is different from
48÷2*12 ?
Another look at this tells me, the problem is with the ÷ v. a /. If the problem was written with the /, I would agree the answer is 288. The right to left ordering is appropriate. However, by using the ÷ the 2(9+3)should be solved for first, then divided into 48 thus giving an answer of 2.