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Daughter's math homework (1 Viewer)
- Thread starter MrPack
- Start date
Cool (maybe).
Willy
Footballguy
I didn't have enough time to read all of this thread, but I have enjoyed what I've read of the discussion. 
I remember a lot of people had troubles with this concept. The 2 explanations I specifically remember have been mentioned long ago. Either add 0 to each side, or think of it as -1*5^2 and then use the basic order of operations. Factoring out the -1 made the most sense to me, and that concept really helped in polynomial factorization and simplification later in algebra and calculus. While opposition points have been interesting, I'm just going to take it on faith that mathematicians have this concept right. I mean Andrew Wiles spent most of his adult life trying to prove Fermat's Last Theorem:
I remember a lot of people had troubles with this concept. The 2 explanations I specifically remember have been mentioned long ago. Either add 0 to each side, or think of it as -1*5^2 and then use the basic order of operations. Factoring out the -1 made the most sense to me, and that concept really helped in polynomial factorization and simplification later in algebra and calculus. While opposition points have been interesting, I'm just going to take it on faith that mathematicians have this concept right. I mean Andrew Wiles spent most of his adult life trying to prove Fermat's Last Theorem:That is dedication. I seriously doubt guys like that would overlook this one if there were any hint that it's not true.
Serenity Now
Footballguy
7-18
In this case, I read the - as an operation.
Starting an equation with an operation makes no sense to me. Would you write:
+5^2? Of course not, because when the 5 is written on its own the + is implied. When you put the - there, you're signifying its negativity.
jonessed
Footballguy
What a gem. Why explain or clarify your point so everyone can understand it when you know you're right and you can just jam it down their throats. Very tactical approach. Please tell me you don't teach or manage people.Sorry but when someone that supposedly has a doctoral in math begins his answer with "You really should be precise" I'm out. The question is precise to anyone that understands convention.
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tommyboy
Footballguy
lets review
^2 = yandx = -5therefore, literally replacing the x with -5 the new equation reads-5^2 = ynow it is the convention, allegedly, that -5^2= -25 because it is implied as -(5^2).however it is obvious as well that -5^2= +25 if you read it as negative five, squared, which most people will if it is written as in integer, that is -5^2. If it is written as -x^2, then it is known that x must be squared first then made negative by rule. However when it is written as an actual integer, in this case -5, then it is NOT known by rule that (-) sign in front is an operative or a value. Since it is not known by rule then it is required of the writer to make clear the question so the reader understands if -5^2 means negative five, squared or if it means five squared, negative.
^2 = yandx = -5therefore, literally replacing the x with -5 the new equation reads-5^2 = ynow it is the convention, allegedly, that -5^2= -25 because it is implied as -(5^2).however it is obvious as well that -5^2= +25 if you read it as negative five, squared, which most people will if it is written as in integer, that is -5^2. If it is written as -x^2, then it is known that x must be squared first then made negative by rule. However when it is written as an actual integer, in this case -5, then it is NOT known by rule that (-) sign in front is an operative or a value. Since it is not known by rule then it is required of the writer to make clear the question so the reader understands if -5^2 means negative five, squared or if it means five squared, negative.
Smoo
Fear the Beaver
I still refuse to accept this "-1*5^2" nonsense as an explanation.If stuff like that were permissible, then I could take something like 4^2 and rewrite it as 2*2^2. But that obviously doesn't get you the same result.I didn't have enough time to read all of this thread, but I have enjoyed what I've read of the discussion.
I remember a lot of people had troubles with this concept. The 2 explanations I specifically remember have been mentioned long ago. Either add 0 to each side, or think of it as -1*5^2 and then use the basic order of operations. Factoring out the -1 made the most sense to me, and that concept really helped in polynomial factorization and simplification later in algebra and calculus.
While opposition points have been interesting, I'm just going to take it on faith that mathematicians have this concept right. I mean Andrew Wiles spent most of his adult life trying to prove Fermat's Last Theorem:
That is dedication. I seriously doubt guys like that would overlook this one if there were any hint that it's not true.
There are ways of explaining the situation well, Maurile has accomplished it, but invoking "-1*5" is a completely incorrect way of doing it.
No, that's wrong.x is negative five. So when we square x, we have to square negative five. To square negative five, we have to write it as "(-5)^2". If you were to write it as "-5^2", you would be failing to insert x anywhere in there. The expression "-5^2" does not contain a negative five anywhere. What is negative in that expression is not five, but twenty-five (since exponentiation comes before the unary minus).lets review
No, you can't rewrite 4^2 as 2*2^2, since "4" doesn't contain an operator that means "multiply the square root of the operand by itself" (or whatever).The unary minus, on the other hand, is an operator that means "multiply the operand by negative one." So -5 can be rewritten as (-1)(5).
The "-1*5^2" explanation works perfectly well once you understand the unary minus to be an operator that negatives the operand (by multiplying it by negative one).
roadkill1292
Footballguy
s to the front of us. s to the back of us.
rolyaTy
You're Heinous
It's basic mathematical language
^2=y means that y equals the quantity that x represents, squared. That's simple. If that quantity is (-5) then the (-5) is being squared. If the quantity is (-5*2+3) then its' that entire quantity being squared. Whatever quantity x represents, it gets squared.Also, when you read:
-x^2=y , you should read "y equals the quantity that x represents, squared, times negative 1." X represents a quantity, and it will be multiplied by negative 1 and also squared. According to the OoO, you square first and multiply later. So if x equals the quantity of five, it's assumed to be written like -(5)^2=y.
When you read:
-5^2=y, you should read "y equals the quantity 5 squared, times negative 1." It's unclear what quantity is being squared, and if it's not specified that the quantity is (-5), then you assume it's (-1)(5)^2.
I'd like to know what grade this homework was given in, as this is really one of the basic principles of math.
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Willy
Footballguy
After reading the rest of this thread,I still refuse to accept this "-1*5^2" nonsense as an explanation.If stuff like that were permissible, then I could take something like 4^2 and rewrite it as 2*2^2. But that obviously doesn't get you the same result.I didn't have enough time to read all of this thread, but I have enjoyed what I've read of the discussion.
I remember a lot of people had troubles with this concept. The 2 explanations I specifically remember have been mentioned long ago. Either add 0 to each side, or think of it as -1*5^2 and then use the basic order of operations. Factoring out the -1 made the most sense to me, and that concept really helped in polynomial factorization and simplification later in algebra and calculus.
While opposition points have been interesting, I'm just going to take it on faith that mathematicians have this concept right. I mean Andrew Wiles spent most of his adult life trying to prove Fermat's Last Theorem:
That is dedication. I seriously doubt guys like that would overlook this one if there were any hint that it's not true.
There are ways of explaining the situation well, Maurile has accomplished it, but invoking "-1*5" is a completely incorrect way of doing it.
, I shouldn't have said it was factoring out the -1. But it is still -1*5^2 as Maurile explained it a few posts up.
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Juxtatarot
Footballguy
If red indicates a negative number, compute this...
5^2
5^2
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I think many people are getting confused because the negative is being linked to a "1". -5^2 can turn into (-1)(5^2) but 4^2 can not turn into 2*2^2. The reason that the 1 appears from nowhere is because in order to factor out the negative you need to link it to a numeral. Being that 1 is the multiplicative identity, you can link it to a "1" without altering the answer to the problem.
Nathan R. Jessep
Footballguy
I'm just glad I got in on page ONE with the CORRECT answer 
oh, and :IBTL:
oh, and :IBTL:
You people still here?
Willy
Footballguy
I know a guy who once argued on a math/science message board that Einstein's E = mc^2 was wrong. He said it should actually be E = mc^3. He was not a mathematician or scientists. He was just some schmoe who thought he was really smart. Needless to say, that didn't go well for him.
Ditkaless Wonders
Footballguy
I can't believe I read the whole thing. Smoo, Maurile, Shick!, Clayton, Pony Boy, you guys are each relentless. Kudos to all.
BTW, this is exactly like stating that, according to what we have been arguing, if you replace x with -5 then 9x looks like this:9-5
which based on what we have been saying would be the same as (9-5) not 9(-5).
The answer is: uh, no, that's not what we've been saying.
It is true that 9-5 is is the same as (9-5) (i.e., it is 4). But it is not true that 9x turns into 9-5 when x is -5. You can't just substitute the characters "-5" in there wherever you see "x" and expect the result to be coherent. You would be fine, however, if you substituted "(-5)" in there.
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tommyboy
Footballguy
the expression -5^2 is not an expression. An expression would be -x^2. The figure -5^2 contains only one operation and that is the exponent of negative five. When you write a variable say X or Y or Z as a representation and put it in a formula then you practice the order of operations. When you simply write a real number that is -5, or 3 or 1/2 or 8/5 or any real number you do not apply the positive or negative after the fact, because that positive or negative is the value of the number, not an operation.
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So what is 8/5^2?
Oh my.
Harry Manback
Footballguy
In case anyone was wondering, we reserve the lowest levels of hell for those that don't grasp basic math facts.I know we had an agreement tommy, but unless you learn the order of operations correctly the deal is off.
Are we clear?
I meant 8/5^2.If there are no parentheses, you apply the operations in their proper order. Exponentiation comes first -- whether we're talking about 8/5^2 or -5^2.
Kleck
Footballguy
Well looky here now tommy. Ya see, we have these rules in math that we use to avoid confusion. We call them the order of operations. Your gut, your opinion, your feelings, well... they don't mean ####.You can go back to where ever you got a high school diploma and beat the mother living piss out of whoever was responsible for allowing you to pass, or you can just accept that you don't quite grasp what we're talking about here. Who knows, maybe you were too busy dreaming about Mary Jane Rottencrotch during math class. Whatever. I don't care much at the moment. I'm fairly drunk right now and somewhat amazed I can actually type. Thank God for all those typing classes.
In closing, if you choose to procreate, please promise me you won't help your kids in their math classes. TIA.
tommyboy
Footballguy
I love it. I have more math experience than probably 90% of this board and you're telling me I don't get it. I get it. If you fail as the writer of the question to ask the question the way you want it answered, you don't get it. If Maurile wants an answer to (8/5)^2 then ask that. If he wants an answer to 8/(5^2) then ask that. Simple really. This isn't even an argument. It just is. a real number squared, is a real number squared. In the original question that started this mess, the question was "what is the base negative 5 squared?" as it was written. It would be no different if the question had been what is x^-x and x = -5, then the expression would be -5^5. However if the question was asked without variables and instead expressed as -5^-5 then the answer would be far different.
writing
-5^2= y produces the correct answer of 25. Thanks for playing. Good night.
