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When it comes to a calculator, it really depends on how well it is programmed. Poor calculators will calculate: 3 + 2 * 7 as 35 instead of 17. A lot of other calculators will force you to enter the -5^2 by entering 5 then pressing the +/- key to make it -5 and then do the ^2 which tells the machine that you entered the integer (negative 5). So while it may appear that it interpreted the equation as (-5)^2, really you gave it the rule by using the +/- key which explicitly tells the calculator that you are using a negative integer (and thus not an operator) and takes all of the interpretation out of the equation.I think the standard way to write it would be to use parentheses no matter which interpretation you favored.If I were a calculator, I might reject "-5^2" as a syntax error. But if I were a calculator I'd probably be a real *******.I think if you're counting on a nonstandard interpreitation (and based on Google, Excel, and Scientific Calculators it seems nonstandard) that it's your responsibility to make it clear through the use of parenthesis.
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.
That's fine if they are taught that way, but it should be understood that the -1*5 is done PRIOR to the squaring if it isn't explicitly written out. -5 is assumed to be -5, not a mathmatical operation. It's one thing to understood the methodology of why -5 is what it is, but it's another thing to not be able to see -5 for what it is - a negative number.I'm sure the teacher taught them specifically to treat -5 as -1*5 for the sake of questions like these, and therefore, is not in the wrong to give no credit for treating it otherwise. At least, that's how I was taught way back in the day. Following directions, that's what school is all about. It's not about learning. Jeez, people.
It has nothing to do with knowing math. It has to do with following the conventions used in a given class. I can't imagine the teacher would give them that problem and expect them to do it the above way unless she had previously explained it to them.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.
What if X = -1?You wouldn't treat -x^2 as (-x)^2. This is the same principal.
I understand if a student taught that way would think it was right, but the bottom line is that it isn't. Credit should be given, but you can't go around teaching kids the wrong way to do things and have them grow up thinking it's right.It has nothing to do with knowing math. It has to do with following the conventions used in a given class. I can't imagine the teacher would give them that problem and expect them to do it the above way unless she had previously explained it to them.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.
Or sometimes kids are just stupid. I'm just saying.I think you guys are missing the real issue here:
If your daughter can't explain to you why she got this problem wrong, then either (1) you teacher did a horrible job of explaining this, or (2) you daughter was not paying attention that day and didn't do the homework. I don't see any other options.
I can agree with this.That's fine if they are taught that way, but it should be understood that the -1*5 is done PRIOR to the squaring if it isn't explicitly written out. -5 is assumed to be -5, not a mathmatical operation. It's one thing to understood the methodology of why -5 is what it is, but it's another thing to not be able to see -5 for what it is - a negative number.I'm sure the teacher taught them specifically to treat -5 as -1*5 for the sake of questions like these, and therefore, is not in the wrong to give no credit for treating it otherwise. At least, that's how I was taught way back in the day. Following directions, that's what school is all about. It's not about learning. Jeez, people.
Yes, well this is only going to happen to kids that aren't good at math to begin with. There are plenty of kids like this out there, who just plug and chug without ever actually grasping the underlying principals. Once these kids hit calculus and beyond, when knowledge of what the equations are actually saying matters, they begin to struggle. And that's when they'll realize that a future in something math related just isn't for them.It's not really a big deal. Like I said, school isn't about learning, it's about following directions. Right or wrong, that's the truth.I understand if a student taught that way would think it was right, but the bottom line is that it isn't. Credit should be given, but you can't go around teaching kids the wrong way to do things and have them grow up thinking it's right.It has nothing to do with knowing math. It has to do with following the conventions used in a given class. I can't imagine the teacher would give them that problem and expect them to do it the above way unless she had previously explained it to them.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.
Don't know. I'm old. This is math. Does that = old math? I seem to remember that this was along about the 6th grade for me which would have made it 1962. I remember having a very good math teacher in the 5th grade and a very bad one in the 6th, so whether I am right or wrong may depend on which one taught me. I am so old that it is all a bit fuzzy; GB Old Timers disease! As a software designer/programmer I would fully parenthesize this so there is no ambiguity at all as to what I was trying to accomplish, to do otherwise is just asking for someone to misinterpret it and make really large mistakes.This is weird. Is this old math then?I would have learned this in the early '80s (what grade do they do this in? 5? 6?) and I was taught that -5^2 == +25.IIRC, I was taught this stuff in the early to mid 60s. The way I was taught was that -5^2 == -25
No, because under the view that the "-" is an operator, "-5" is not a good analogue of "6". It would be a good analogue for "3*2", and "3*2^2" is indeed 3*4.I think that by taking -5^2 and making it -1(5^2) you're violating the distributive property of exponents. You need to square the -1 if you're going to factor the number. Otherwise you're condoning the following logic, which is obviously wrong:
6^2
3(2^2)
3(4)
12 = 6^2
Assumed by whom? That's the whole crux of the matter.-5 is assumed to be -5, not a mathmatical operation.
That may be, but it's unfortunate and I think our state of our educational systems show how effective that kind of teaching has been.Yes, well this is only going to happen to kids that aren't good at math to begin with. There are plenty of kids like this out there, who just plug and chug without ever actually grasping the underlying principals. Once these kids hit calculus and beyond, when knowledge of what the equations are actually saying matters, they begin to struggle. And that's when they'll realize that a future in something math related just isn't for them.It's not really a big deal. Like I said, school isn't about learning, it's about following directions. Right or wrong, that's the truth.I understand if a student taught that way would think it was right, but the bottom line is that it isn't. Credit should be given, but you can't go around teaching kids the wrong way to do things and have them grow up thinking it's right.It has nothing to do with knowing math. It has to do with following the conventions used in a given class. I can't imagine the teacher would give them that problem and expect them to do it the above way unless she had previously explained it to them.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.
For me, THAT part didn't come until the late 60s!\/\/o\/\/Math in the sixties must have been psychadelic with all those double equals signs.IIRC, I was taught this stuff in the early to mid 60s. The way I was taught was that -5^2 == -25
Oh, I agree. Whatcha gonna do?That may be, but it's unfortunate and I think our state of our educational systems show how effective that kind of teaching has been.Yes, well this is only going to happen to kids that aren't good at math to begin with. There are plenty of kids like this out there, who just plug and chug without ever actually grasping the underlying principals. Once these kids hit calculus and beyond, when knowledge of what the equations are actually saying matters, they begin to struggle. And that's when they'll realize that a future in something math related just isn't for them.It's not really a big deal. Like I said, school isn't about learning, it's about following directions. Right or wrong, that's the truth.I understand if a student taught that way would think it was right, but the bottom line is that it isn't. Credit should be given, but you can't go around teaching kids the wrong way to do things and have them grow up thinking it's right.It has nothing to do with knowing math. It has to do with following the conventions used in a given class. I can't imagine the teacher would give them that problem and expect them to do it the above way unless she had previously explained it to them.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.
Why write it that way if it's not meant to be assumed to be a negative number?Assumed by whom? That's the whole crux of the matter.-5 is assumed to be -5, not a mathmatical operation.
Oh, I agree. Whatcha gonna do?That may be, but it's unfortunate and I think our state of our educational systems show how effective that kind of teaching has been.Yes, well this is only going to happen to kids that aren't good at math to begin with. There are plenty of kids like this out there, who just plug and chug without ever actually grasping the underlying principals. Once these kids hit calculus and beyond, when knowledge of what the equations are actually saying matters, they begin to struggle. And that's when they'll realize that a future in something math related just isn't for them.It's not really a big deal. Like I said, school isn't about learning, it's about following directions. Right or wrong, that's the truth.I understand if a student taught that way would think it was right, but the bottom line is that it isn't. Credit should be given, but you can't go around teaching kids the wrong way to do things and have them grow up thinking it's right.It has nothing to do with knowing math. It has to do with following the conventions used in a given class. I can't imagine the teacher would give them that problem and expect them to do it the above way unless she had previously explained it to them.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.
May be, hell, I am so old that I can't rightly remember!1860's?IIRC, I was taught this stuff in the early to mid 60s. The way I was taught was that -5^2 == -25
May be, hell, I am so old that I can't rightly remember!1860's?IIRC, I was taught this stuff in the early to mid 60s. The way I was taught was that -5^2 == -25
-5 is a negative number. So is 0-5. That doesn't mean that -5^2 is a positive number any more than it means that 0-5^2 is a positive number.To answer your question, though, there's no good reason to write it that way (regardless of whatever assumptions are made). Parentheses should have been used.Why write it that way if it's not meant to be assumed to be a negative number?Assumed by whom? That's the whole crux of the matter.-5 is assumed to be -5, not a mathmatical operation.
Agreed.-5 is a negative number. So is 0-5. That doesn't mean that -5^2 is a negative number any more than it means that 0-5^2 is a negative number.To answer your question, though, there's no good reason to write it that way (regardless of whatever assumptions are made). Parentheses should have been used.Why write it that way if it's not meant to be assumed to be a negative number?Assumed by whom? That's the whole crux of the matter.-5 is assumed to be -5, not a mathmatical operation.
Man, you have no faith in Otis at all, do you?Most people would have written, "I agree with Otis, which means I'm definitely right."I agree with Otis, but I'm sure I could be wrong.
I would normally agree with you, but this thing has hit 4 pages, and there's still some discussion on what is the correct way. So I'll give her the benefit of the doubt, that and she has been a straight A student since entering middle school.I think you guys are missing the real issue here:
If your daughter can't explain to you why she got this problem wrong, then either (1) you teacher did a horrible job of explaining this, or (2) you daughter was not paying attention that day and didn't do the homework. I don't see any other options.
Stupid huh? And what do you call everyone still discussing this?Or sometimes kids are just stupid. I'm just saying.I think you guys are missing the real issue here:
If your daughter can't explain to you why she got this problem wrong, then either (1) you teacher did a horrible job of explaining this, or (2) you daughter was not paying attention that day and didn't do the homework. I don't see any other options.
Except you've reintroduced the same problem in your "proof". If they're claiming that -5^2 = -25 then they're also going to claim that -1^2 = -1.I see error in your math. Here's an example6^2 = 36Of coarse, because those items have brains of their own and are never wrong...
Personally I would have a hard time not giving credit to a student for either answer. If I were coding this for any reason I would use () to specify my meaning. If you go to order of operation in your version of 0 + -5^2 + ..., which you agree means the same as -5^2 + ... then I think you have to calculate it as 0+ -(5^2) + ... and get -7 but I also don't really think it is worth the arguement.
The point should be reiterated that the teacher was obviously trying to be ambigious and/or trying to prove a point instead of just teaching the rules.
2*3 = 6
(2*3)^2 = 2^2 * 3^2 (distributive property of exponents)
2^2 * 3^2 = 4 * 9 = 36
In this case, following the logic above
-5^2 = (-1*5)^2 = -1^2 * 5^2 = 1 * 25 = 25
I went through the same school system as you Smoo in the Peg and I didn't learn it this way. It was BEDMAS. I had it ingrained into my head. I always said I would never use any of this stuff in the real world and so far I am pretty much correct in thinking that. Now I find out out not only do I not need to use it but it is wrong? WTF? BracketYes. We've established that that's the right answer today. Do you remember, though, that that was not taught that way back when we were in school?It's an order of operations thing.
(-5)^2 is said as "Negative five squared"
-5^2 is said as "The negative of five squared" and as such, you square it first and then negate.
I went to school in Vancouver. But that's neither here nor there. I learned the same order of operations as you. Our point is that -5 isn't an operation, it's a number.I went through the same school system as you Smoo in the Peg and I didn't learn it this way. It was BEDMAS. I had it ingrained into my head. I always said I would never use any of this stuff in the real world and so far I am pretty much correct in thinking that. Now I find out out not only do I not need to use it but it is wrong? WTF? BracketYes. We've established that that's the right answer today. Do you remember, though, that that was not taught that way back when we were in school?It's an order of operations thing.
(-5)^2 is said as "Negative five squared"
-5^2 is said as "The negative of five squared" and as such, you square it first and then negate.
Equation
Division
Multiplication
Addition
Subtraction
Your order of operations has "Equation"? That makes no sense.I went to school in Vancouver. But that's neither here nor there. I learned the same order of operations as you. Our point is that -5 isn't an operation, it's a number.I went through the same school system as you Smoo in the Peg and I didn't learn it this way. It was BEDMAS. I had it ingrained into my head. I always said I would never use any of this stuff in the real world and so far I am pretty much correct in thinking that. Now I find out out not only do I not need to use it but it is wrong? WTF? BracketYes. We've established that that's the right answer today. Do you remember, though, that that was not taught that way back when we were in school?It's an order of operations thing.
(-5)^2 is said as "Negative five squared"
-5^2 is said as "The negative of five squared" and as such, you square it first and then negate.
Equation
Division
Multiplication
Addition
Subtraction
Somebody mentioned before that if we're going to read -5 as -1*5, then we should read 25 as 2*5.The obvious difference is that "2" is a numeral, while "-" is generally an operator (as in 26 - 13 = 13).Our point is that -5 isn't an operation, it's a number.
Canadian math.Your order of operations has "Equation"? That makes no sense.I went to school in Vancouver. But that's neither here nor there. I learned the same order of operations as you. Our point is that -5 isn't an operation, it's a number.I went through the same school system as you Smoo in the Peg and I didn't learn it this way. It was BEDMAS. I had it ingrained into my head. I always said I would never use any of this stuff in the real world and so far I am pretty much correct in thinking that. Now I find out out not only do I not need to use it but it is wrong? WTF? BracketYes. We've established that that's the right answer today. Do you remember, though, that that was not taught that way back when we were in school?It's an order of operations thing.
(-5)^2 is said as "Negative five squared"
-5^2 is said as "The negative of five squared" and as such, you square it first and then negate.
Equation
Division
Multiplication
Addition
Subtraction
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.
But it's not, because that'll go on forever. -1^2 * 1^2 * 1^2 ... every time you try to factor out that -1 you're going to just lengthen the equation, but remain with a -1 being squared somewhere in there. You can't get rid of it.Except you've reintroduced the same problem in your "proof". If they're claiming that -5^2 = -25 then they're also going to claim that -1^2 = -1.I see error in your math. Here's an example6^2 = 36Of coarse, because those items have brains of their own and are never wrong...
Personally I would have a hard time not giving credit to a student for either answer. If I were coding this for any reason I would use () to specify my meaning. If you go to order of operation in your version of 0 + -5^2 + ..., which you agree means the same as -5^2 + ... then I think you have to calculate it as 0+ -(5^2) + ... and get -7 but I also don't really think it is worth the arguement.
The point should be reiterated that the teacher was obviously trying to be ambigious and/or trying to prove a point instead of just teaching the rules.
2*3 = 6
(2*3)^2 = 2^2 * 3^2 (distributive property of exponents)
2^2 * 3^2 = 4 * 9 = 36
In this case, following the logic above
-5^2 = (-1*5)^2 = -1^2 * 5^2 = 1 * 25 = 25
case closedYou wouldn't treat -x^2 as (-x)^2. This is the same principal.
How is substituting a variable for an ambiguous integer proof of anything?case closedYou wouldn't treat -x^2 as (-x)^2. This is the same principal.
-5² + 4 x 2³ = 7
-6² + 2 x 3² = 18
End of discussion. I can't believe this made it to 4 pages.
By Excel, Google, the Windows Calculator, and quite a few posters here. But that we have to make an assumption is the reason why everyone on both sides agrees that parenthesis should've been used anyway. After looking it up, it appears that our feelings are right that parenthesis should've been used to avoid confusion. According to the link, it's only assumed when using variables (I'll be the first one to admit that I probably would've treated a variable the same way, but I see now why it's clear with variables and not so with real numbers).Assumed by whom? That's the whole crux of the matter.-5 is assumed to be -5, not a mathmatical operation.
Squaring Negative Numbers
Date: 02/19/2002 at 10:59:10
From: Thanh Phan
Subject: Squaring negative numbers
Hello,
I would like to know: does -9^2 = 81 or -81?
--------------------------------------------------------------------------------
Date: 02/19/2002 at 12:38:08
From: Doctor Rick
Subject: Re: Squaring negative numbers
Hi, Thanh.
You really should be precise about what you are asking in this case,
since (-9)^2 means -9 times -9, but the expression -9^2 could also be
taken to mean -(9^2), that is, the negative of the square of 9, which
is -81.
When we're working with variables, if we see -x^2, we interpret it in
the second way, as -(x^2), because squaring (or any exponentiation)
takes precedence over negation (or any multiplication; -x is treated
as -1*x.
When you have numbers only, as in -9^2, it's not at all clear that we
should treat it differently from -x^2. However, some will argue that
it should, because -9 represents a single number, not an operation on
a number. Thus, some will interpret -9^2 as (-9)^2, while others will
read it as -(9^2).
Because of the difference of opinion, I highly recommend that you put
in the parentheses explicitly whenever this situation arises.
- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
Squaring Negative Numbers
Date: 02/19/2002 at 10:59:10
From: Thanh Phan
Subject: Squaring negative numbers
Hello,
I would like to know: does -9^2 = 81 or -81?
--------------------------------------------------------------------------------
Date: 02/19/2002 at 12:38:08
From: Doctor Rick
Subject: Re: Squaring negative numbers
Hi, Thanh.
You really should be precise about what you are asking in this case,
since (-9)^2 means -9 times -9, but the expression -9^2 could also be
taken to mean -(9^2), that is, the negative of the square of 9, which
is -81.
When we're working with variables, if we see -x^2, we interpret it in
the second way, as -(x^2), because squaring (or any exponentiation)
takes precedence over negation (or any multiplication; -x is treated
as -1*x.
When you have numbers only, as in -9^2, it's not at all clear that we
should treat it differently from -x^2. However, some will argue that
it should, because -9 represents a single number, not an operation on
a number. Thus, some will interpret -9^2 as (-9)^2, while others will
read it as -(9^2).
Because of the difference of opinion, I highly recommend that you put
in the parentheses explicitly whenever this situation arises.
- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
Easy there, I wasn't talking about your daughter. I'm just saying that sometimes kids are just stupid. That's a fact.Stupid huh? And what do you call everyone still discussing this?Or sometimes kids are just stupid. I'm just saying.I think you guys are missing the real issue here:
If your daughter can't explain to you why she got this problem wrong, then either (1) you teacher did a horrible job of explaining this, or (2) you daughter was not paying attention that day and didn't do the homework. I don't see any other options.
Yes. It has always been "that way" assuming your teachers were competent.Yes. We've established that that's the right answer today. Do you remember, though, that that was not taught that way back when we were in school?It's an order of operations thing.
(-5)^2 is said as "Negative five squared"
-5^2 is said as "The negative of five squared" and as such, you square it first and then negate.
XYes, I would - as any person who knows math would do.You wouldn't treat -x^2 as (-x)^2. This is the same principal.
Hey, I agree with you. I'm just pointing out that your proof won't look like proof to those guys because they'll just say that -1^2 = -1.But it's not, because that'll go on forever. -1^2 * 1^2 * 1^2 ... every time you try to factor out that -1 you're going to just lengthen the equation, but remain with a -1 being squared somewhere in there. You can't get rid of it.Except you've reintroduced the same problem in your "proof". If they're claiming that -5^2 = -25 then they're also going to claim that -1^2 = -1.I see error in your math. Here's an example6^2 = 36Of coarse, because those items have brains of their own and are never wrong...
Personally I would have a hard time not giving credit to a student for either answer. If I were coding this for any reason I would use () to specify my meaning. If you go to order of operation in your version of 0 + -5^2 + ..., which you agree means the same as -5^2 + ... then I think you have to calculate it as 0+ -(5^2) + ... and get -7 but I also don't really think it is worth the arguement.
The point should be reiterated that the teacher was obviously trying to be ambigious and/or trying to prove a point instead of just teaching the rules.
2*3 = 6
(2*3)^2 = 2^2 * 3^2 (distributive property of exponents)
2^2 * 3^2 = 4 * 9 = 36
In this case, following the logic above
-5^2 = (-1*5)^2 = -1^2 * 5^2 = 1 * 25 = 25