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Daughter's math homework (1 Viewer)

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
The calculator is squaring -5 which is (-5)^2.
According to Google, -5^2 = 25.
Google does the same thing.And so does Excel.

 
Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
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.
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".

 
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
The calculator is squaring -5 which is (-5)^2.
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.
 
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".

 
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".
-5 is not an operation. -5 is an integer. Don't pretend you don't understand our POV.
 
Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
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.
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".
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=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.

 
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".
-5 is not an operation. -5 is an integer. Don't pretend you don't understand our POV.
Yes, -5 is an integer. It is also the opposite of 5.
 
This is the end all, be all answer!
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.

 
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Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
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.
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".
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=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.
Once again:When you put -5 into a calculator, Excel, etc, and then square it, you are entering this: (-5)^2.

 
Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
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.
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".
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=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.
Once again:When you put -5 into a calculator, Excel, etc, and then square it, you are entering this: (-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.
 
Clayton, the condescending schtick is already taken.
What I wrote was not read the first time. Using "the calculator says so" is a flawed argument.
I agree because the person entering in the -5 is already doing the order of operations for the calculator incorrectly.
 
Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
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.
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".
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=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.
Once again:When you put -5 into a calculator, Excel, etc, and then square it, you are entering this: (-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.
My poorly made point is that the calculator is reading it as (-5)^2.
 
I didn't read the whole thread, but I can tell you what every certified math teacher in the country will tell you...-5^2 = -25This 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.Common misunderstanding. Its a concept that I see students in college make. Not a shocker if an adult gets away with this mistake for years and thinks its a new idea.Actually, I see this mistake being brought to the forefront more often now due to technology. Graphing calculators (and many other calculators) allow you input a long expression before being evaluated. You can type "-5^2+4*3^2" all in one line in most newer calculators. It leads to a certain laziness when it comes to order of operations. Students get to rely on the calculator not messing up. Problem is that the student doesn't full understand order of operations and gets upset when they get the wrong answer. Calculator did what you told it to do, but you put in the wrong thing because you weren't sure of what the expression really meant.In closing...-5^2=-25(-5)^2=25Its 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.

 
My poorly made point is that the calculator is reading it as (-5)^2.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.
 
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.
You should really read the whole thread. There have been some interesting arguments around this idea.
 
So 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.
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)^2

I mean come on...it's the "negative" of something inside the parenthesis...anything else and you're saying "negative number squared"

It may be that way now...but I think it's a terrible way to teach...

 
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Its 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.
Hence the argument for parentheses.(-5)^2

-(5^2)

Neither of those is ambiguous.

-5^2, however, can cause five pages worth of confusion.

 
Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.
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.
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".
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=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.
Once again:When you put -5 into a calculator, Excel, etc, and then square it, you are entering this: (-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.
My poorly made point is that the calculator is reading it as (-5)^2.
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.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.
If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.
 
My poorly made point is that the calculator is reading it as (-5)^2.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.
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.
 
My poorly made point is that the calculator is reading it as (-5)^2.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.
If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.
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.

 
My poorly made point is that the calculator is reading it as (-5)^2.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.
If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.
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.
 
I wouldn't find fault in anyone for interprieting it as (-5)^2 since calculators interpreit it that way.
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.
 
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I will say this is another reason a lot of people hate math.
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.
 
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.
What make and model of calculator?
 
I wouldn't find fault in anyone for interprieting it as (-5)^2 since calculators interpreit it that way.
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.
Can we at least agree that it would be better to use parenthesis to avoid this confusion all together?
 
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".
:goodposting: 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.

 
My poorly made point is that the calculator is reading it as (-5)^2.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.
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.
I need to get one of these new calculators that is capable of choosing. Science has come a long way!
 
My poorly made point is that the calculator is reading it as (-5)^2.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.
If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.
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.
For the first time ever, Google is indeed wrong.
 
Can we at least agree that it would be better to use parenthesis to avoid this confusion all together?
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.
 
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.
What make and model of calculator?
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?
 
My poorly made point is that the calculator is reading it as (-5)^2.
That's Rooster's point as well. That the calculator is interpreting it that way, and that calculators don't get math questions wrong.
If the problem was 3*5^2 and you entered 15^2, the calculator would correctly offer 225.
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.
 
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".
:goodposting: 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.
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:

(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.

 
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I will say this is another reason a lot of people hate math.
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.
No, because it can be easy to make a mistake.
 
I wouldn't find fault in anyone for interprieting it as (-5)^2 since calculators interpreit it that way.
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.
Can we at least agree that it would be better to use parenthesis to avoid this confusion all together?
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.
 
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".
:goodposting: 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.
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:

(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.
Ok, good point:The opposite of five squared.

or

The opposite of five, squared.

The second one has a comma, which is the exact reason why we need parentheses to make it 25 instead of -25.

 

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