Fixed.-5² + 4 x 2³ = 7
-6² + 2 x 3² = 18
End of discussion. I can't believe this made it to 4 pages replies.
Fixed.-5² + 4 x 2³ = 7
-6² + 2 x 3² = 18
End of discussion. I can't believe this made it to 4 pages replies.
The calculator is squaring -5 which is (-5)^2.I put these equations in a scientific calculator and still came up with 75 and 54. -5² came out as 25, not -25.
This is frigging nuts
Google does the same thing.And so does Excel.According to Google, -5^2 = 25.
He's not factoring. The analogy is that if -5 means -1 * 5 then 25 could mean 2 * 5.Nobody in this thread will ever convince me that negative numbers cannot be represented as a self-contained entity without the use of parentheses. With my dying breath, I will proclaim that -5 can be interpreted as a cohesive whole, and not some bastardized "operation".As a rule, I don't call you out. But you really need to work on your factoring, unless I just totally missed the point. I wouldn't be the first time.Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
If -5 is a number then I can square it by simply typing -5^2. The -5 doesn't stop being -5 simply because I've added an exponent.The calculator is squaring -5 which is (-5)^2.I put these equations in a scientific calculator and still came up with 75 and 54. -5² came out as 25, not -25.
This is frigging nuts
-5 is not an operation. -5 is an integer. Don't pretend you don't understand our POV.Gather around peoples....
In mathematics, another word for "negative" is "opposite". Thus, -5 should be thought of as "the oppositive of 5" which means -5^2 is "the opposite of 5^2".
The point of the article I linked is there is no standard for -5^2, there is for -x^2 though because x CAN be -5 and represent an integer, but if x = 5 and you have -x^2 that negative is clearly performing an operation on a positive 5. So we havex=5He's not factoring. The analogy is that if -5 means -1 * 5 then 25 could mean 2 * 5.Nobody in this thread will ever convince me that negative numbers cannot be represented as a self-contained entity without the use of parentheses. With my dying breath, I will proclaim that -5 can be interpreted as a cohesive whole, and not some bastardized "operation".As a rule, I don't call you out. But you really need to work on your factoring, unless I just totally missed the point. I wouldn't be the first time.Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
BINGO!!!!!!I am an actuary so I think I know my math. This is the end all, be all answer!You wouldn't treat -x^2 as (-x)^2. This is the same principal.
Yes, -5 is an integer. It is also the opposite of 5.-5 is not an operation. -5 is an integer. Don't pretend you don't understand our POV.Gather around peoples....
In mathematics, another word for "negative" is "opposite". Thus, -5 should be thought of as "the oppositive of 5" which means -5^2 is "the opposite of 5^2".
We have had end all, be all answers claimed on both sides.I'll stick to my original assertion. Nobody should write "-5^2" without parentheses because it's ambiguous. But if somebody does write it that way, and if I had to try to solve it, I'd perform the exponentiation before the multiplication (treating "-" as an operator) and get -25. But that's a last resort. My preference is to reject the expression as a syntax error.This is the end all, be all answer!
Once again:When you put -5 into a calculator, Excel, etc, and then square it, you are entering this: (-5)^2.The point of the article I linked is there is no standard for -5^2, there is for -x^2 though because x CAN be -5 and represent an integer, but if x = 5 and you have -x^2 that negative is clearly performing an operation on a positive 5. So we havex=5He's not factoring. The analogy is that if -5 means -1 * 5 then 25 could mean 2 * 5.Nobody in this thread will ever convince me that negative numbers cannot be represented as a self-contained entity without the use of parentheses. With my dying breath, I will proclaim that -5 can be interpreted as a cohesive whole, and not some bastardized "operation".As a rule, I don't call you out. But you really need to work on your factoring, unless I just totally missed the point. I wouldn't be the first time.Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
-x^2 = -25
x=-5
x^2 = 25
That's clear, I can understand and agree with the logic of the convetion. I'd argue, however, because google, excel, and all the calculators I try interpriet -5 as an integer that -5^2 should be interprieted as an integer being squared. At best it's very unclear on what -5^2 means and anyone writing it deserves the confusion that will result.
No. I'm not. I'm entering it exactly -5^2 with no parenthesis at all. You are right that Google interpriets it as (-5)^2, but that's my point. If our calculators and such interpreit the ambiguous expression one way, it should be the de facto standard.Once again:When you put -5 into a calculator, Excel, etc, and then square it, you are entering this: (-5)^2.The point of the article I linked is there is no standard for -5^2, there is for -x^2 though because x CAN be -5 and represent an integer, but if x = 5 and you have -x^2 that negative is clearly performing an operation on a positive 5. So we havex=5He's not factoring. The analogy is that if -5 means -1 * 5 then 25 could mean 2 * 5.Nobody in this thread will ever convince me that negative numbers cannot be represented as a self-contained entity without the use of parentheses. With my dying breath, I will proclaim that -5 can be interpreted as a cohesive whole, and not some bastardized "operation".As a rule, I don't call you out. But you really need to work on your factoring, unless I just totally missed the point. I wouldn't be the first time.Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
-x^2 = -25
x=-5
x^2 = 25
That's clear, I can understand and agree with the logic of the convetion. I'd argue, however, because google, excel, and all the calculators I try interpriet -5 as an integer that -5^2 should be interprieted as an integer being squared. At best it's very unclear on what -5^2 means and anyone writing it deserves the confusion that will result.
What I wrote was not read the first time. Using "the calculator says so" is a flawed argument.Clayton, the condescending schtick is already taken.
I agree because the person entering in the -5 is already doing the order of operations for the calculator incorrectly.What I wrote was not read the first time. Using "the calculator says so" is a flawed argument.Clayton, the condescending schtick is already taken.
My poorly made point is that the calculator is reading it as (-5)^2.No. I'm not. I'm entering it exactly -5^2 with no parenthesis at all. You are right that Google interpriets it as (-5)^2, but that's my point. If our calculators and such interpreit the ambiguous expression one way, it should be the de facto standard.Once again:When you put -5 into a calculator, Excel, etc, and then square it, you are entering this: (-5)^2.The point of the article I linked is there is no standard for -5^2, there is for -x^2 though because x CAN be -5 and represent an integer, but if x = 5 and you have -x^2 that negative is clearly performing an operation on a positive 5. So we havex=5He's not factoring. The analogy is that if -5 means -1 * 5 then 25 could mean 2 * 5.Nobody in this thread will ever convince me that negative numbers cannot be represented as a self-contained entity without the use of parentheses. With my dying breath, I will proclaim that -5 can be interpreted as a cohesive whole, and not some bastardized "operation".As a rule, I don't call you out. But you really need to work on your factoring, unless I just totally missed the point. I wouldn't be the first time.Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
-x^2 = -25
x=-5
x^2 = 25
That's clear, I can understand and agree with the logic of the convetion. I'd argue, however, because google, excel, and all the calculators I try interpriet -5 as an integer that -5^2 should be interprieted as an integer being squared. At best it's very unclear on what -5^2 means and anyone writing it deserves the confusion that will result.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.My poorly made point is that the calculator is reading it as (-5)^2.
poor guyBINGO!!!!!!I am an actuary so I think I know my math. This is the end all, be all answer!You wouldn't treat -x^2 as (-x)^2. This is the same principal.
You should really read the whole thread. There have been some interesting arguments around this idea.This isn't new. This is thousands of years old. The negative sign you see in front of the 5 is equivalent to multiplying by a -1. Exponents take predence. The 5 is to be squared before multiplying before the -1. Again, nothing new.
I absolutely was taught the same way as well...and this was early to mid 80's...in Virginia...-5^2 does not mean "the negative of 5 squared"...how on Earth do they expect people to think that way? It makes absolute clear and concise sense to say that "the negative of 5 squared" should and only be written as: -(5^2) or -(5)^2So MrPack, Bewdude and I were all taught the same way, and we're decidedly not from the same geographic area. So I don't know where roly went to school, but he's either much younger, or his district was way ahead of its time.
Hence the argument for parentheses.(-5)^2Its not about being right or wrong. Its about agreeing on a proper syntax so that we can clearly communicate mathematical ideas to each other without confusion.
And my point is since there is no standard (read the Dr. Math article, people argue both ways) that it shouldn't be used. In the event that it IS used, I wouldn't find fault in anyone for interprieting it as (-5)^2 since calculators interpreit it that way. Because of that, it's almost a de facto standard I would argue (I can understand people disagreeing with this point, but no need to be condescending). You're making an assumption either way, at best it's unclear and best to use parenthesis to avoid the confusion.My poorly made point is that the calculator is reading it as (-5)^2.No. I'm not. I'm entering it exactly -5^2 with no parenthesis at all. You are right that Google interpriets it as (-5)^2, but that's my point. If our calculators and such interpreit the ambiguous expression one way, it should be the de facto standard.Once again:When you put -5 into a calculator, Excel, etc, and then square it, you are entering this: (-5)^2.The point of the article I linked is there is no standard for -5^2, there is for -x^2 though because x CAN be -5 and represent an integer, but if x = 5 and you have -x^2 that negative is clearly performing an operation on a positive 5. So we havex=5He's not factoring. The analogy is that if -5 means -1 * 5 then 25 could mean 2 * 5.Nobody in this thread will ever convince me that negative numbers cannot be represented as a self-contained entity without the use of parentheses. With my dying breath, I will proclaim that -5 can be interpreted as a cohesive whole, and not some bastardized "operation".As a rule, I don't call you out. But you really need to work on your factoring, unless I just totally missed the point. I wouldn't be the first time.Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
-x^2 = -25
x=-5
x^2 = 25
That's clear, I can understand and agree with the logic of the convetion. I'd argue, however, because google, excel, and all the calculators I try interpriet -5 as an integer that -5^2 should be interprieted as an integer being squared. At best it's very unclear on what -5^2 means and anyone writing it deserves the confusion that will result.
If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.My poorly made point is that the calculator is reading it as (-5)^2.
Just for clarity's sake, it's not about calculators never being wrong. I just don't think the calculators are making a mistake, they're forced to interpreit that string of characters one way or another and they're choosing the integer explanation instead of the operator one.That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.My poorly made point is that the calculator is reading it as (-5)^2.
But typing 15^2 isn't typing 3*5^2 into Google exactly as it was written. If you type 3*5^2 into Google exactly as it is written, you get 75. Rooster was typing -5^2 into Google exactly as it was written, and he got 25.If our interpretation of -5^2 is right, Google is wrong. I can live with Google being wrong, but it's somewhat odd. When Google returned 25 instead of -25, I started to second-guess my initial way of thinking.If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.My poorly made point is that the calculator is reading it as (-5)^2.
bad analogy. I'm putting it in exactly as it was presented in the problem, nobody is modifying it before entering it into the calculator.If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.My poorly made point is that the calculator is reading it as (-5)^2.
This is just not true. The standard at nearly all levels of teaching mathematics beyond sixth grade right now is the TI graphing calculator. Every one of them interprets -5^2 as -25 without exception.If you have another calculator that does otherwise, that doesn't make it correct. I'm not going to argue with you, I'm just telling you how it is in the profession. You're not going to find one degreed and certified mathematics teacher that works with exponents that will tell you different.I wouldn't find fault in anyone for interprieting it as (-5)^2 since calculators interpreit it that way.
Due to their own lack of knowledge? Perhaps not their fault entirely, but I can see how that frustration could lead to the "I hate math" feelings.I will say this is another reason a lot of people hate math.
What make and model of calculator?bad analogy. I'm putting it in exactly as it was presented in the problem, nobody is modifying it before entering it into the calculator.
Can we at least agree that it would be better to use parenthesis to avoid this confusion all together?This is just not true. The standard at nearly all levels of teaching mathematics beyond sixth grade right now is the TI graphing calculator. Every one of them interprets -5^2 as -25 without exception.If you have another that calculator that does otherwise, that doesn't make it correct. I'm not going to argue with you, I'm just telling you how it is in the profession. You're not going to find one degreed and certified mathematics teacher that works with exponents that will tell you different.I wouldn't find fault in anyone for interprieting it as (-5)^2 since calculators interpreit it that way.
Gather around peoples....
In mathematics, another word for "negative" is "opposite". Thus, -5 should be thought of as "the oppositive of 5" which means -5^2 is "the opposite of 5^2".
PleaseExcuse1) 57
2) 54
Parentheses
Exponents
Multiplication
Division
Addition
Subdtraction
you're done
I need to get one of these new calculators that is capable of choosing. Science has come a long way!Just for clarity's sake, it's not about calculators never being wrong. I just don't think the calculators are making a mistake, they're forced to interpreit that string of characters one way or another and they're choosing the integer explanation instead of the operator one.That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.My poorly made point is that the calculator is reading it as (-5)^2.
For the first time ever, Google is indeed wrong.But typing 15^2 isn't typing 3*5^2 into Google exactly as it was written. If you type 3*5^2 into Google exactly as it is written, you get 75. Rooster was typing -5^2 into Google exactly as it was written, and he got 25.If our interpretation of -5^2 is right, Google is wrong. I can live with Google being wrong, but it's somewhat odd. When Google returned 25 instead of -25, I started to second-guess my initial way of thinking.If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.My poorly made point is that the calculator is reading it as (-5)^2.
Sure. That would be best, but we need to have an established rule for when there are no parenthesis. It happens. It will continue to happen. This way we don't have confusion. That rule states that -5^2 is the same as (-1) * (5)^2.Can we at least agree that it would be better to use parenthesis to avoid this confusion all together?
the Windows Calculator, Google, and Excel so far. I did just confirm my TI-85 says -5^2 = -25. At the very least, since multiple sources that would normally be trusted interpreit it differently, wouldn't you agree that parenthesis are practically require to clearly communicate the intent?What make and model of calculator?bad analogy. I'm putting it in exactly as it was presented in the problem, nobody is modifying it before entering it into the calculator.
Yes it is being modified. When you put -5 into the calculator, you are putting parenthesis around the -5 just as sure as I was putting parenthesis around the 3*5.bad analogy. I'm putting it in exactly as it was presented in the problem, nobody is modifying it before entering it into the calculator.If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.My poorly made point is that the calculator is reading it as (-5)^2.
I'm on Clayton's side, but I don't think that explanation resolves the ambiguity.The opposite of five squared can be read as:Gather around peoples....
In mathematics, another word for "negative" is "opposite". Thus, -5 should be thought of as "the oppositive of 5" which means -5^2 is "the opposite of 5^2".This is the best explanation...I am a math teacher and need to put this through the heads of kids every year. The TI calculator series does it the same way (ie. -5^2=-25). I go through this with kids and ask them what negative 5 squared is and they tell me 25...then I have them type it in and they say their calculator is broken. The easiest way to explain it is just the way Clayton explained it.
No, because it can be easy to make a mistake.Due to their own lack of knowledge? Perhaps not their fault entirely, but I can see how that frustration could lead to the "I hate math" feelings.I will say this is another reason a lot of people hate math.
Obviously, more parenthesis would make problems less confusing, but the mathematician would argue that parenthesis are needed in -(5^2) as much as they are needed in (3*4)+2.Can we at least agree that it would be better to use parenthesis to avoid this confusion all together?This is just not true. The standard at nearly all levels of teaching mathematics beyond sixth grade right now is the TI graphing calculator. Every one of them interprets -5^2 as -25 without exception.If you have another that calculator that does otherwise, that doesn't make it correct. I'm not going to argue with you, I'm just telling you how it is in the profession. You're not going to find one degreed and certified mathematics teacher that works with exponents that will tell you different.I wouldn't find fault in anyone for interprieting it as (-5)^2 since calculators interpreit it that way.
Ok, good point:The opposite of five squared.I'm on Clayton's side, but I don't think that explanation resolves the ambiguity.The opposite of five squared can be read as:Gather around peoples....
In mathematics, another word for "negative" is "opposite". Thus, -5 should be thought of as "the oppositive of 5" which means -5^2 is "the opposite of 5^2".This is the best explanation...I am a math teacher and need to put this through the heads of kids every year. The TI calculator series does it the same way (ie. -5^2=-25). I go through this with kids and ask them what negative 5 squared is and they tell me 25...then I have them type it in and they say their calculator is broken. The easiest way to explain it is just the way Clayton explained it.
(The opposite of five) squared
or
The opposite of (five squared).
Just writing it out as a sentence doesn't solve the problem of where the implied parentheses should go.
Yes, I would - as any person who knows math would do.You wouldn't treat -x^2 as (-x)^2. This is the same principal.