Daughter's math homework (1 Viewer)

[(HULK)]

Can't we all agree that this equation:

-5^2

should never be used as it will cause confusion?

Why be ambiguous when you can be clear by using (-5)^2 or -(5^2)?

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable. For example -x^2 must equal -(x^2)... or else you get two possible values for x and that is undesirable. So, they made this decision.

However, it enters into the realm of abiguity because negative five is expressed as -5 when it is standing alone. For this reason, plenty of people see -5^2 and assume the equation is saying negative five squared, not the opposite of five squared.

Hence, its interpreted both ways by the general population. Someone somewhere down the line made the decision that one is accepted and the other is not to save time on using parenthesis. I call that intellectual laziness. I think the correct answer should've been to require parenthesis to make certain it was clear.

 

[Clayton Gray]

Smoo,

Is 5 a self-contained number?

Yes.

What is the opposite of 5?

-5

Then how can -5 be self-contained when it is nothing more than a modified 5?

What's the opposite of -5?

A self-contained number.

 

[Clayton Gray]

Let me start over...Are the numbers 1, 2, 3, etc self-contained numbers?

 

[rolyaTy]

-5 is the opposite of 5, but that's a static definition that's really without meaning in a math equation. An equation is a process (like a journey, with the distance between the start and end as the final answer), and a static definition doesn't help understand the process, that is why the concept that "negative" means "the opposite of" doesn't appeal to me. To me, the negative sign represents action, and it specifies direction. All math boils down to the distance from the origin to the final point of the equation, even vector math in 3 dimensions. The players in the equation are operators and magnitudes. Operators are x(times), -(minus), +(plus)...etc and get more and more advanced the further you go in math, but the basics still apply. Magnitudes are units such as five, six, eighty, etc. All that math equations do is tell you how to proceed on a number line. The magnitudes tell you how far to go, the neg/pos signs tell you direction, and the other signs tell you how to deal with more than 1 number, or what operations to perform on them.So in 2+(-2) you might know that -2 is the opposite of 2, but that doesn't tell you how to solve the problem. To solve the problem, you must reconcile the operators, use the magnitudes, and find the distance the equation takes you from the origin. That is why negative signs make the most sense being defined as a reversal of direction, rather than the "opposite" of a number.

 

[Maurile Tremblay]

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable.

I don't think that's the reason. I think it's just an application of the rule that exponentiation has priority over multiplication.

 

[Clayton Gray]

Can't we all agree that this equation:

-5^2

should never be used as it will cause confusion?

Why be ambiguous when you can be clear by using (-5)^2 or -(5^2)?

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable.  For example -x^2 must equal -(x^2)... or else you get two possible values for x and that is undesirable.  So, they made this decision.

However, it enters into the realm of abiguity because negative five is expressed as -5 when it is standing alone.  For this reason, plenty of people see -5^2 and assume the equation is saying negative five squared, not the opposite of five squared.

Hence, its interpreted both ways by the general population.  Someone somewhere down the line made the decision that one is accepted and the other is not to save time on using parenthesis.  I call that intellectual laziness.  I think the correct answer should've been to require parenthesis to make certain it was clear.

Did you see my reply to this?

 

[bryhamm]

Our point is that -5 isn't an operation, it's a number.

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).

While it is obvious that "-" can be an operator, the question is whether it can also act as part of a number (like "2" can).

The answer depends only on arbitrary convention, and is therefore rather unintersting. But either way, I would pour mustard on the textbook's front cover for neglecting to use parentheses.

My point is that, yes, a number can be negative. If it's labelled -5 then that means it's negative 5. If you want to make the - an operator, you have two options: use () or write it - 5^2 with a space in between. Using a space is ridiculous for real world purposes so if it's meant to be an operator then () have to be used. Otherwise it's assumed to mean the number is negative. A lot of people seem to be over thinking this since if you were asked verbally what negative 2 squared is you would say 4. I think many of you are looking at it on the screen and making it seem more complex than it is.

No, if you were to say to someone verbally "negative 2 squared" and their answer was 4, then they were thinking (-2)^2.However, looking at -2^2 and saying "negative 2 squared" is incorrect. You should say "the negative of 2 squared" which would be -(2^2).

 

[Smoo]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

 

[Kleck]

Absolute worst case of arguing notation evah.

 

[Clayton Gray]

Our point is that -5 isn't an operation, it's a number.

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).

While it is obvious that "-" can be an operator, the question is whether it can also act as part of a number (like "2" can).

The answer depends only on arbitrary convention, and is therefore rather unintersting. But either way, I would pour mustard on the textbook's front cover for neglecting to use parentheses.

My point is that, yes, a number can be negative. If it's labelled -5 then that means it's negative 5. If you want to make the - an operator, you have two options: use () or write it - 5^2 with a space in between. Using a space is ridiculous for real world purposes so if it's meant to be an operator then () have to be used. Otherwise it's assumed to mean the number is negative. A lot of people seem to be over thinking this since if you were asked verbally what negative 2 squared is you would say 4. I think many of you are looking at it on the screen and making it seem more complex than it is.

No, if you were to say to someone verbally "negative 2 squared" and their answer was 4, then they were thinking (-2)^2.However, looking at -2^2 and saying "negative 2 squared" is incorrect. You should say "the negative of 2 squared" which would be -(2^2).

And since "of" means "multiply", you square 2 before taking the negative.

 

[(HULK)]

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable.

I don't think that's the reason. I think it's just an application of the rule that exponentiation has priority over multiplication.

I believe Dr. Math said that WAS the reason somewhere on his site. I can't remember where now though -x^2 definitely has to equal -(x^2) though, or else you get multiple possibilities for x, which is ungood.

 

[RoarinSonoran]

If you want to make the - an operator, you have two options: use () or write it - 5^2 with a space in between.

It is an operator. It's called a "unary minus", used to negate what follows it.

 

[Aaron Rudnicki]

I can't believe this has reached 31 pages.For the record, I think the teacher was wrong.

 

[(HULK)]

Can't we all agree that this equation:

-5^2

should never be used as it will cause confusion?

Why be ambiguous when you can be clear by using (-5)^2 or -(5^2)?

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable.  For example -x^2 must equal -(x^2)... or else you get two possible values for x and that is undesirable.  So, they made this decision.

However, it enters into the realm of abiguity because negative five is expressed as -5 when it is standing alone.  For this reason, plenty of people see -5^2 and assume the equation is saying negative five squared, not the opposite of five squared.

Hence, its interpreted both ways by the general population.  Someone somewhere down the line made the decision that one is accepted and the other is not to save time on using parenthesis.  I call that intellectual laziness.  I think the correct answer should've been to require parenthesis to make certain it was clear.

Did you see my reply to this?

 

[Clayton Gray]

-5 is the opposite of 5, but that's a static definition that's really without meaning in a math equation. An equation is a process (like a journey, with the distance between the start and end as the final answer), and a static definition doesn't help understand the process, that is why the concept that "negative" means "the opposite of" doesn't appeal to me. To me, the negative sign represents action, and it specifies direction.

All math boils down to the distance from the origin to the final point of the equation, even vector math in 3 dimensions. The players in the equation are operators and magnitudes. Operators are x(times), -(minus), +(plus)...etc and get more and more advanced the further you go in math, but the basics still apply. Magnitudes are units such as five, six, eighty, etc.

All that math equations do is tell you how to proceed on a number line. The magnitudes tell you how far to go, the neg/pos signs tell you direction, and the other signs tell you how to deal with more than 1 number, or what operations to perform on them.

So in 2+(-2) you might know that -2 is the opposite of 2, but that doesn't tell you how to solve the problem. To solve the problem, you must reconcile the operators, use the magnitudes, and find the distance the equation takes you from the origin. That is why negative signs make the most sense being defined as a reversal of direction, rather than the "opposite" of a number.

I understand what you are saying, but I don't see a big difference between reversal and opposite.

 

[Kleck]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

Congrats, you've come up with your own "thing" and given it your own "definition". Self contained number? What is that?Mathematics is a language and science of patterns. Making up new terms and applying definitions because you don't know of a better way to describe it is a bad idea.

I've said it too many times, but you don't want to hear the reality of it. Clayton and I are not the ones you need here. We teach kids fundamentals. If you want to seek out the "why" of all this you need to move on to someone more qualified to discuss it.

If you want to try and torture one of us and label us as inadequate because we can't properly answer your questions, well, okay. I don't know how to kindly respond to that.

 

[Maurile Tremblay]

If you want to make the - an operator, you have two options: use () or write it - 5^2 with a space in between.

It is an operator. It's called a "unary minus", used to negate what follows it.

According to this page, "The - (unary minus) operator negates the value of the operand."Bingo.

 

[rolyaTy]

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable.

I don't think that's the reason. I think it's just an application of the rule that exponentiation has priority over multiplication.

Do you agree that multiplication is really just advanced addition, ie. it can be reduced to simple addition? If so, I don't see any particular benefit in stating that -5 is (-1)x(5) because that isn't any more clear when you break it down to addition. The only way I look at that is that it's a shortcut, like multiplication, an easy way to view things, but in essence, -5 is not (-1)x(5) but rather 5 in the reverse direction.

 

[Kleck]

I mentioned this before, but I think it got glossed over.Why is this a new thing? Why all the confusion? I believe it's directly related to the newer dynamics of the keyboard and graphing calculators. We routinely type out -5^2+10 into a calculator now, but this isn't something that didn't happen 15 years ago. Being able to type in a string like this is a fairly new concept.

 

[Smoo]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

Congrats, you've come up with your own "thing" and given it your own "definition". Self contained number? What is that?Mathematics is a language and science of patterns. Making up new terms and applying definitions because you don't know of a better way to describe it is a bad idea.

I've said it too many times, but you don't want to hear the reality of it. Clayton and I are not the ones you need here. We teach kids fundamentals. If you want to seek out the "why" of all this you need to move on to someone more qualified to discuss it.

If you want to try and torture one of us and label us as inadequate because we can't properly answer your questions, well, okay. I don't know how to kindly respond to that.

When did I torture you or call you inadequate? You're clearly following the current convention. I simply wanted you to explain why the convention was the way it was using logic and reason. I know you tried, but your approaches didn't resonate with me. Maurile's did, perhaps because we've spent lots of time in logic threads, so he probably has an idea for how I resolve problems like this.I think you're taking this a mite personally. Sounds like you need a man-hug.

 

[Maurile Tremblay]

Self contained number? What is that?

I gave a kick-### definition: it is a string of symbols that must be resolved into a value before any operators are applied to it.

 

[Smoo]

If you want to make the - an operator, you have two options: use () or write it - 5^2 with a space in between.

It is an operator. It's called a "unary minus", used to negate what follows it.

According to this page, "The - (unary minus) operator negates the value of the operand."Bingo.

 

[Bottomfeeder Sports]

:

:

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable.

:

:

Effectively yes I think this is what they are saying, but the only way for there to be real logic that is always consistent and not an rule which is an exception is for -5^2 to mean -(5)^2

The argument that -5 means the opposite of 5 seems to imply that -5 is always shorthand notation for -(5).

 

[thatguy]

-5 is the opposite of 5, but that's a static definition that's really without meaning in a math equation. An equation is a process (like a journey, with the distance between the start and end as the final answer), and a static definition doesn't help understand the process, that is why the concept that "negative" means "the opposite of" doesn't appeal to me. To me, the negative sign represents action, and it specifies direction.

All math boils down to the distance from the origin to the final point of the equation, even vector math in 3 dimensions. The players in the equation are operators and magnitudes. Operators are x(times), -(minus), +(plus)...etc and get more and more advanced the further you go in math, but the basics still apply. Magnitudes are units such as five, six, eighty, etc.

All that math equations do is tell you how to proceed on a number line. The magnitudes tell you how far to go, the neg/pos signs tell you direction, and the other signs tell you how to deal with more than 1 number, or what operations to perform on them.

So in 2+(-2) you might know that -2 is the opposite of 2, but that doesn't tell you how to solve the problem. To solve the problem, you must reconcile the operators, use the magnitudes, and find the distance the equation takes you from the origin. That is why negative signs make the most sense being defined as a reversal of direction, rather than the "opposite" of a number.

This is the right answer. So, what's the over/under on how many pages this thread will reach?

 

[Clayton Gray]

Can't we all agree that this equation:

-5^2

should never be used as it will cause confusion?

Why be ambiguous when you can be clear by using (-5)^2 or -(5^2)?

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable.  For example -x^2 must equal -(x^2)... or else you get two possible values for x and that is undesirable.  So, they made this decision.

However, it enters into the realm of abiguity because negative five is expressed as -5 when it is standing alone.  For this reason, plenty of people see -5^2 and assume the equation is saying negative five squared, not the opposite of five squared.

Hence, its interpreted both ways by the general population.  Someone somewhere down the line made the decision that one is accepted and the other is not to save time on using parenthesis.  I call that intellectual laziness.  I think the correct answer should've been to require parenthesis to make certain it was clear.

Did you see my reply to this?

Probably because I never did. Confused it with another. Anyway, I would not agree that would should stop using the notation. I believe we should do a better job of teaching the correct method of computation.

 

[Whatevaman15]

I understand that at some point, mathmaticians decided that

-5^2 should be assumed to mean -(5^2) because of its similarity to the use with a variable.

I don't think that's the reason. I think it's just an application of the rule that exponentiation has priority over multiplication.

I believe Dr. Math said that WAS the reason somewhere on his site. I can't remember where now though -x^2 definitely has to equal -(x^2) though, or else you get multiple possibilities for x, which is ungood.

What happens when you sub in x=5?

 

[rolyaTy]

-5 is the opposite of 5, but that's a static definition that's really without meaning in a math equation. An equation is a process (like a journey, with the distance between the start and end as the final answer), and a static definition doesn't help understand the process, that is why the concept that "negative" means "the opposite of" doesn't appeal to me. To me, the negative sign represents action, and it specifies direction.

All math boils down to the distance from the origin to the final point of the equation, even vector math in 3 dimensions. The players in the equation are operators and magnitudes. Operators are x(times), -(minus), +(plus)...etc and get more and more advanced the further you go in math, but the basics still apply. Magnitudes are units such as five, six, eighty, etc.

All that math equations do is tell you how to proceed on a number line. The magnitudes tell you how far to go, the neg/pos signs tell you direction, and the other signs tell you how to deal with more than 1 number, or what operations to perform on them.

So in 2+(-2) you might know that -2 is the opposite of 2, but that doesn't tell you how to solve the problem. To solve the problem, you must reconcile the operators, use the magnitudes, and find the distance the equation takes you from the origin. That is why negative signs make the most sense being defined as a reversal of direction, rather than the "opposite" of a number.

I understand what you are saying, but I don't see a big difference between reversal and opposite.

It makes no difference to us because we know what happens when -2 and 2 are combined. But try teaching that to someone who doesn't know what math is, and explain to them how the - sign means "the opposite", and whether or not that helps them come to the correct answer. You may be successful, but I can't figure a way to explain that without simply telling them that it is true that a number plus it's opposite equals zero...rather than showing them it is, using my explanation.

 

[Mr.Happy]

31 pages......If this passes the short skit thread, the terrorists have won.

 

[Clayton Gray]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

But how did we come up with the numbers -1, -2, -3, etc? Did some dude look at the sky and say, "Seems like something is amiss today. Looks like there are negative three birds flying around"?

 

[Smoo]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

But how did we come up with the numbers -1, -2, -3, etc? Did some dude look at the sky and say, "Seems like something is amiss today. Looks like there are negative three birds flying around"?

Black holes were discovered on chalkboards long before they were ever discovered in reality.

 

[(HULK)]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

But how did we come up with the numbers -1, -2, -3, etc? Did some dude look at the sky and say, "Seems like something is amiss today. Looks like there are negative three birds flying around"?

Zero and negative numbers are pretty much conceptual only. That doesn't mean they don't exist though. I'm sure LarryBoy believes in them.

 

[rolyaTy]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

But how did we come up with the numbers -1, -2, -3, etc? Did some dude look at the sky and say, "Seems like something is amiss today. Looks like there are negative three birds flying around"?

-1,-2 and -3 are positions on a number line, with the - sign representing their position with respect to the origin, which is 0. The magnitudes, of 1,2 and 3 represent their distance from the origin.

 

[cstu]

If you want to make the - an operator, you have two options: use () or write it - 5^2 with a space in between.

It is an operator. It's called a "unary minus", used to negate what follows it.

According to this page, "The - (unary minus) operator negates the value of the operand."Bingo.

No one is disputing that, what we're disputing is that the - is operating on the 5, which written the way the equation was, it's not. If you have -5 on a Cartesian plane, you aren't doing any crazy mathmatics on it like -1 * 5.

-5 is a number and that's final.

 

[Kleck]

I think you're taking this a mite personally.

Of course I am. This is my livelihood. Its what I do for a living. There are folks in this thread telling me that I'm flat our wrong. That bothers me. Might as well start arguing about the earth being round.Again, there's not right or wrong in this. Its a translation of symbols into meaning. It just is.

 

[Maurile Tremblay]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

But how did we come up with the numbers -1, -2, -3, etc? Did some dude look at the sky and say, "Seems like something is amiss today. Looks like there are negative three birds flying around"?

I'd say that negative numbers exist in mathematics just as fundamentally as positive numbers do.The concept of negative five is a self-contained number.

It's just that the expression of that concept, when we write it as "-5", is not self-contained (under my definition, which I think captures Smoo's usage). It is an operator applied to a numeral.

Part of the problem in this thread as that some people were mistaking the concept of negative five with a particular expression of it.

Negative five, when it is squared, becomes 25. But in the expression "-5^2" there is no negative five. "-5" doesn't mean negative five when there's a "^2" after it any more than "23" means twenty three when there's a "5" after it (as in "235").

I'm just trying to get us to 50 pages . . .

 

[Clayton Gray]

I'm with Shick!. I don't have enough knowledge to properly explain the reason why the convention is true.

 

[Chase Stuart]

Is this thread seriously 37 pages long?Has anyone read this?Or is it just Carlton and Shick just sending porn links back and forth?

 

[cstu]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

But how did we come up with the numbers -1, -2, -3, etc? Did some dude look at the sky and say, "Seems like something is amiss today. Looks like there are negative three birds flying around"?

I'd say that negative numbers exist in mathematics just as fundamentally as positive numbers do.The concept of negative five is a self-contained number.

It's just that the expression of that concept, when we write it as "-5", is not self-contained (under my definition, which I think captures Smoo's usage). It is an operator applied to a numeral.

Part of the problem in this thread as that some people were mistaking the concept of negative five with a particular expression of it.

Negative five, when it is squared, becomes 25. But in the expression "-5^2" there is no negative five. "-5" doesn't mean negative five when there's a "^2" after it any more than "23" means twenty three when there's a "5" after it (as in "235").

I'm just trying to get us to 50 pages . . .

Ok, let's all just agree that the equation was written poorly and move on...

 

[rolyaTy]

Let me start over...

Are the numbers 1, 2, 3, etc self-contained numbers?

Of course. And Maurile's demonstrated that simply modifying a self-contained number doesn't necessarily mean that the result is not a self-contained number.

But how did we come up with the numbers -1, -2, -3, etc? Did some dude look at the sky and say, "Seems like something is amiss today. Looks like there are negative three birds flying around"?

I'd say that negative numbers exist in mathematics just as fundamentally as positive numbers do.The concept of negative five is a self-contained number.

It's just that the expression of that concept, when we write it as "-5", is not self-contained (under my definition, which I think captures Smoo's usage). It is an operator applied to a numeral.

Part of the problem in this thread as that some people were mistaking the concept of negative five with a particular expression of it.

Negative five, when it is squared, becomes 25. But in the expression "-5^2" there is no negative five. "-5" doesn't mean negative five when there's a "^2" after it any more than "23" means twenty three when there's a "5" after it (as in "235").

I'm just trying to get us to 50 pages . . .

What does the concept of -5 represent?I say it represents a position on a 1-d number line, 5 units to the left of 0. What say you?

 

[Maurile Tremblay]

If you want to make the - an operator, you have two options: use () or write it - 5^2 with a space in between.

It is an operator. It's called a "unary minus", used to negate what follows it.

According to this page, "The - (unary minus) operator negates the value of the operand."Bingo.

No one is disputing that,

Yes, the main proponents of the -5^2=25 group were saying that the unary minus is not an operator.

what we're disputing is that the - is operating on the 5, which written the way the equation was, it's not.

It operates on the value to the right of it. We all agree on this -- we just disagree on what is to the right of it: the "5" or the "5^2". The answer depends on the order of operations. If the ^ operates first, then the unary minus operates over "5^2". If the unary minus operates first, then it operates only over the "5".By convention, the ^ has priority over the -, so -5^2=-25.

 

[Clayton Gray]

-5 is the opposite of 5, but that's a static definition that's really without meaning in a math equation.  An equation is a process (like a journey, with the distance between the start and end as the final answer), and a static definition doesn't help understand the process, that is why the concept that "negative" means "the opposite of" doesn't appeal to me. To me, the negative sign represents action, and it specifies direction. 

All math boils down to the distance from the origin to the final point of the equation, even vector math in 3 dimensions.  The players in the equation are operators and magnitudes.  Operators are x(times), -(minus), +(plus)...etc and get more and more advanced the further you go in math, but the basics still apply.  Magnitudes are units such as five, six, eighty, etc. 

All that math equations do is tell you how to proceed on a number line.  The magnitudes tell you how far to go, the neg/pos signs tell you direction, and the other signs tell you how to deal with more than 1 number, or what operations to perform on them.

So in 2+(-2) you might know that -2 is the opposite of 2, but that doesn't tell you how to solve the problem.  To solve the problem, you must reconcile the operators, use the magnitudes, and find the distance the equation takes you from the origin.  That is why negative signs make the most sense being defined as a reversal of direction, rather than the "opposite" of a number.

I understand what you are saying, but I don't see a big difference between reversal and opposite.

It makes no difference to us because we know what happens when -2 and 2 are combined. But try teaching that to someone who doesn't know what math is, and explain to them how the - sign means "the opposite", and whether or not that helps them come to the correct answer. You may be successful, but I can't figure a way to explain that without simply telling them that it is true that a number plus it's opposite equals zero...rather than showing them it is, using my explanation.

We used two-sided disks (red and yellow). The yellow side was positive and the red was negative. A positive and a negative cancel each other.4 + (-7) is -3 because the four positives are canceled by four of the negatives which leaves three remaining negatives.

 

[Maurile Tremblay]

What does the concept of -5 represent?

It is the value of negative one added to itself five times.

 

[Clayton Gray]

Or is it just Carlton and Shick just sending porn links back and forth?

I wish.

 

[rolyaTy]

-5 is the opposite of 5, but that's a static definition that's really without meaning in a math equation. An equation is a process (like a journey, with the distance between the start and end as the final answer), and a static definition doesn't help understand the process, that is why the concept that "negative" means "the opposite of" doesn't appeal to me. To me, the negative sign represents action, and it specifies direction.

All math boils down to the distance from the origin to the final point of the equation, even vector math in 3 dimensions. The players in the equation are operators and magnitudes. Operators are x(times), -(minus), +(plus)...etc and get more and more advanced the further you go in math, but the basics still apply. Magnitudes are units such as five, six, eighty, etc.

All that math equations do is tell you how to proceed on a number line. The magnitudes tell you how far to go, the neg/pos signs tell you direction, and the other signs tell you how to deal with more than 1 number, or what operations to perform on them.

So in 2+(-2) you might know that -2 is the opposite of 2, but that doesn't tell you how to solve the problem. To solve the problem, you must reconcile the operators, use the magnitudes, and find the distance the equation takes you from the origin. That is why negative signs make the most sense being defined as a reversal of direction, rather than the "opposite" of a number.

I understand what you are saying, but I don't see a big difference between reversal and opposite.

It makes no difference to us because we know what happens when -2 and 2 are combined. But try teaching that to someone who doesn't know what math is, and explain to them how the - sign means "the opposite", and whether or not that helps them come to the correct answer. You may be successful, but I can't figure a way to explain that without simply telling them that it is true that a number plus it's opposite equals zero...rather than showing them it is, using my explanation.

We used two-sided disks (red and yellow). The yellow side was positive and the red was negative. A positive and a negative cancel each other.4 + (-7) is -3 because the four positives are canceled by four of the negatives which leaves three remaining negatives.

But why are the positives canceled by the negatives? That's still a definition learned, that 1 positive cancels 1 negative. Why is that true?

 

[rolyaTy]

What does the concept of -5 represent?

It is the value of negative one added to itself five times.

What does the value of -1 represent?

 

[Smoo]

I think you're taking this a mite personally.

Of course I am. This is my livelihood. Its what I do for a living. There are folks in this thread telling me that I'm flat our wrong. That bothers me. Might as well start arguing about the earth being round.Again, there's not right or wrong in this. Its a translation of symbols into meaning. It just is.

No, they weren't telling you that you were wrong. They were telling you that they believed that the convention which you were correctly following was ill-conceived.Big difference.

 

[thatguy]

Every math equation has as its foundation some predetermined spatial world and some predetermined origin, regardless of the number of variables, or in other words, the number of dimensions. Let's assume we're talking about a 2-dimensional world, since this is the most commonly encountered in high school algebra. We set 'up' on the y-axis and 'right' on the x-axis as going forward, or as positive numbers. In the problem being discussed there is only one dimension, and thus, a number line, but this really doesn't matter. The same convention apply, except there is only one axis. From here, everything we do is relative to this origin and the conventions we set for it. Therefore, only whole numbers actually exist on their own. Without the conventions set by the x- and y-axis, it would be impossible to define a negative number. Negative numbers exist only because we need them to be able to communicate mathematically, or in other words, as Royalty (spelling, sorry) has been trying to tell you all, to specify a direction in space relative to our conventions.This may be confusing, as it is much more difficult to express mathematical thoughts in words than I thought it would be when I began this post, and and had I realized that to begin with, I probably would not have bothered.

 

[Kleck]

This makes me think of one of my favorite things to teach. Adding integers.We make a ninja battle out of every problem. Why? Because ninjas are freakin cool.5 + (-4) = 1Why? Positive numbers represent good guys. Negative numbers represent bad guys. One good/bad ninja is not more powerful than any other ninja. If they battle, who wins? The four bad ninjas above are defeated by the good ninjas, but they take out four of the good ninjas in the process. Only one good ninja remains after the battle.High school freshman that have struggled in their previous math classes eat this up. They love it.

 

[rolyaTy]

I think you're taking this a mite personally.

Of course I am. This is my livelihood. Its what I do for a living. There are folks in this thread telling me that I'm flat our wrong. That bothers me. Might as well start arguing about the earth being round.Again, there's not right or wrong in this. Its a translation of symbols into meaning. It just is.

No, they weren't telling you that you were wrong. They were telling you that they believed that the convention which you were correctly following was ill-conceived.Big difference.

Thread title "I beleive the teacher is wrong", shick agreed with the teacher, by the distributive property, the original poster probably thought shick was wrong too for a while, along with others.

 

[Kleck]

Or is it just Carlton and Shick just sending porn links back and forth?

I wish.

PM sent.