Daughter's math homework (1 Viewer)

[Otis]

Another vote for 57/54. Adding stuff that is not there by changing to "-1 X.." or "0 +.." etc.. is crazy.

6 is really an assumed 3*2, therefore 6^2 = 3*2^2 = 12. Insane!

It's not an operator b/c there's nothing in front to operate on! -5 is the number negative 5.

Huh?

 

[bryhamm]

Finally, an

 

[Smoo]

ATTENTION.

I have officially turned around on this topic. -5^2 is indeed -25. I accept this and deem it logically sound.

My apologies to those whom I have abandoned in this traitorous betrayal.

Sig update on the way.

 

[Psychopav]

Well done. Faster than most Canadians would have come around, I reckon.

 

[Smoo]

Oh, and there are those who have accused me of never admitting when I'm wrong. Please direct those people here.

 

[Thorn]

ATTENTION.I have officially turned around on this topic. -5^2 is indeed -25. I accept this and deem it logically sound.My apologies to those whom I have abandoned in this traitorous betrayal.Sig update on the way.

I do not know how to express my dismay at this. I have slept well konwing you agreed that -5 was an integer; an entity which existed without knowledge of -1 or any operation. Now you purport to remove its legitimacy? With nothing more than "ATTENTION"? Weak sauce, sir. Weak. sauce.

 

[sirelfman]

I was going to quote Smoo's post and ask him what changed his mind, but when I clicked the post button, it acted like the "top" button.

So, anyways, what changed your mind Smoo? I might use the same argument with my students.

 

[Mr. Pickles]

According to Google, -5^2 = 25.

Looks like they changed their mind five years later.

 

[Flying Spaghetti Monster]

According to Google, -5^2 = 25.

Looks like they changed their mind five years later.

See that is why I come to the FFA.

 

[Ignoratio Elenchi]

Good to see Google finally got this one right.

 

[Maurile Tremblay]

Good to see Google finally got this one right.

Do you think Google knows about this thread?What am I saying? Of course Google knows about this thread. It's Google! It knows everything about the internet.

 

[chet]

Good to see Google finally got this one right.

Do you think Google knows about this thread?What am I saying? Of course Google knows about this thread. It's Google! It knows everything about the internet.

Even Mr. Pickles?

 

[Ignoratio Elenchi]

Good to see Google finally got this one right.

Do you think Google knows about this thread?What am I saying? Of course Google knows about this thread. It's Google! It knows everything about the internet.

Google knows.

 

[bryhamm]

It looks like Google ends up putting the parenthesis around it where it is assumed. I wouldn't necessarily call that getting it right. More so it is simply clarifying what it is showing.

 

[Ignoratio Elenchi]

It looks like Google ends up putting the parenthesis around it where it is assumed. I wouldn't necessarily call that getting it right. More so it is simply clarifying what it is showing.

They're doing both; they're getting it right, and they're clarifying why it's right.-52 = -(52) = -25

 

[Chaka]

According to Google, -5^2 = 25.

Looks like they changed their mind five years later.

Microsoft Excel 2007 disagrees.

 

[the moops]

It looks like Google ends up putting the parenthesis around it where it is assumed. I wouldn't necessarily call that getting it right. More so it is simply clarifying what it is showing.

They're doing both; they're getting it right, and they're clarifying why it's right.-52 = -(52) = -25

You forgot -1(52) = -25

 

[Dexter]

People should always use parentheses in this situation.

There is a reason we have parentheses in math.

 

[joffer]

27 pages

 

[PlasmaDogPlasma]

27 pages

I believe you mean 1*(27) pages.

 

[Rick James]

-5^2 = 25

(-1)(-1)(5)(5)=25

 

[Ignoratio Elenchi]

-5^2 = 25(-1)(-1)(5)(5)=25

There aren't two negative signs.

 

[Maurile Tremblay]

According to Google, -5^2 = 25.

Looks like they changed their mind five years later.

Microsoft Excel 2007 disagrees.

Excel gives the unary minus priority over all other operators. The developer notes are quoted somewhere in this thread, and acknowledge that Excel gives a non-standard (i.e., wrong) answer in this case.

 

[Thorn]

-5^2 = 25(-1)(-1)(5)(5)=25

There aren't two negative signs.

There aren't any ones, either.

 

[Ignoratio Elenchi]

-5^2 = 25

(-1)(-1)(5)(5)=25

There aren't two negative signs.

There aren't any ones, either.

It doesn't make a difference how many ones you imagine there are. It certainly makes a difference when you start introducing extraneous negative signs.The convention is that -52 is treated as -(52). It didn't have to be that way, but that's the way it is.

 

[jon_mx]

I think the proper convention is not to write a number as.... -5^2....it is ambiguous, and thus improper. Confusing kids with bad convention is not teaching kids anything.

 

[Ilov80s]

I think the proper convention is not to write a number as.... -5^2....it is ambiguous, and thus improper. Confusing kids with bad convention is not teaching kids anything.

That is why simple rules are created to understand the language of math- just like the order of operations. If not for the order of operations, 5 + 4 x 3 is also very ambiguous.

 

[jon_mx]

I think the proper convention is not to write a number as.... -5^2....it is ambiguous, and thus improper. Confusing kids with bad convention is not teaching kids anything.

That is why simple rules are created to understand the language of math- just like the order of operations. If not for the order of operations, 5 + 4 x 3 is also very ambiguous.

I would say if -5^2 is written as a number, it would be 25. If it was written as part of an operation, it would be -25. That is why it is ambiguous and why only a crappy math book would write a number that way.

 

[Ignoratio Elenchi]

I think the proper convention is not to write a number as.... -5^2....it is ambiguous, and thus improper. Confusing kids with bad convention is not teaching kids anything.

That is why simple rules are created to understand the language of math- just like the order of operations. If not for the order of operations, 5 + 4 x 3 is also very ambiguous.

I would say if -5^2 is written as a number, it would be 25. If it was written as part of an operation, it would be -25. That is why it is ambiguous and why only a crappy math book would write a number that way.

It's only ambiguous if you're completely unfamiliar with the convention. If a math text explained the convention (or if it was sufficiently advanced that it safely assumed the student was already familiar with the convention), there would be no need to included the parentheses. -52 is -25. If you want to square the quantity (-5), you include the parentheses. Otherwise the exponent occurs before the negation.

 

[Ilov80s]

I think the proper convention is not to write a number as.... -5^2....it is ambiguous, and thus improper. Confusing kids with bad convention is not teaching kids anything.

That is why simple rules are created to understand the language of math- just like the order of operations. If not for the order of operations, 5 + 4 x 3 is also very ambiguous.

I would say if -5^2 is written as a number, it would be 25. If it was written as part of an operation, it would be -25. That is why it is ambiguous and why only a crappy math book would write a number that way.

Again, it is only ambiguous to someone who does not understand the accepted procedures for handling that situation...just as 1+2x3 would be ambiguous to someone who does not know about order of operations.

 

[Maurile Tremblay]

It's only ambiguous if you're completely unfamiliar with the convention. If a math text explained the convention (or if it was sufficiently advanced that it safely assumed the student was already familiar with the convention), there would be no need to included the parentheses. -52 is -25. If you want to square the quantity (-5), you include the parentheses. Otherwise the exponent occurs before the negation.

The fact that Excel gives an alternative answer, and Google used to, means that it's at least a little ambiguous, IMO.The order of operations is a matter of convention, and conventions are unambiguous only if there's widespread agreement about them. In this case, I think the agreement is sufficiently widespread to say that -25 is standard while 25 is non-standard; but I don't think it's sufficiently widespread to say that there's no ambiguity.

 

[Thorn]

-5^2 = 25

(-1)(-1)(5)(5)=25

There aren't two negative signs.

There aren't any ones, either.

It doesn't make a difference how many ones you imagine there are. It certainly makes a difference when you start introducing extraneous negative signs.The convention is that -52 is treated as -(52). It didn't have to be that way, but that's the way it is.

Well I suppose that's just it. I don't imagine any ones. -5 is an integer that exists without any operation at all.

 

[Short Corner]

The world needs ditch diggers too I guess.

 

[Maurile Tremblay]

Well I suppose that's just it. I don't imagine any ones. -5 is an integer that exists without any operation at all.

All integers exist independent of any operations. But not all of them can be expressed without any operators. Negative integers, for example, tend to take a unary minus.

 

[Ignoramus]

Wow, time sure does fly. Five years already?

 

[Bronco Billy]

I wonder if AMC can do a series on this thread? It's got more legs than the Walking Dead.

 

[Mjolnirs]

It's only ambiguous if you're completely unfamiliar with the convention.

Agreed, the problem for some of us is that the convention changed within the last 30 years.I graduated high school in '82 so learned my mat in the late 70s and early 80s.

I was taught that -5^2 = negative five squared = -5*-5 = 25

It is now taught that -5^2 = negative of five squared = -(5*5) = 25

I've seen the text books now and understand how the answer of -25 is achieved. It just seems unnatural to me and I will always see it as 25.

 

[Thorn]

Well I suppose that's just it. I don't imagine any ones. -5 is an integer that exists without any operation at all.

All integers exist independent of any operations. But not all of them can be expressed without any operators. Negative integers, for example, tend to take a unary minus.

Please do not circumvent the language filter.

 

[Ignoratio Elenchi]

It's only ambiguous if you're completely unfamiliar with the convention. If a math text explained the convention (or if it was sufficiently advanced that it safely assumed the student was already familiar with the convention), there would be no need to included the parentheses. -52 is -25. If you want to square the quantity (-5), you include the parentheses. Otherwise the exponent occurs before the negation.

The fact that Excel gives an alternative answer, and Google used to, means that it's at least a little ambiguous, IMO.The order of operations is a matter of convention, and conventions are unambiguous only if there's widespread agreement about them. In this case, I think the agreement is sufficiently widespread to say that -25 is standard while 25 is non-standard; but I don't think it's sufficiently widespread to say that there's no ambiguity.

Yeah, it's a fine distinction. It's obviously ambiguous to most of the general population. But in the specific context of a math textbook or a math test, it's probably assumed that the math student is already familiar with the convention. So on the one hand it's not surprising that there would be a great deal of confusion when it's discussed on a fantasy football message board, but I suspect there probably shouldn't have been any confusion in the classroom (assuming it had already been covered in class).

 

[Psychopav]

It's only ambiguous if you're completely unfamiliar with the convention. If a math text explained the convention (or if it was sufficiently advanced that it safely assumed the student was already familiar with the convention), there would be no need to included the parentheses. -52 is -25. If you want to square the quantity (-5), you include the parentheses. Otherwise the exponent occurs before the negation.

The fact that Excel gives an alternative answer, and Google used to, means that it's at least a little ambiguous, IMO.The order of operations is a matter of convention, and conventions are unambiguous only if there's widespread agreement about them. In this case, I think the agreement is sufficiently widespread to say that -25 is standard while 25 is non-standard; but I don't think it's sufficiently widespread to say that there's no ambiguity.

Isn't all mathematics ultimately a matter of convention?I would be willing to wager that this -5^2 = +25 is a relatively recent development. I'd love to see any evidence from anyone that a textbook or even a popular source prior to, say, 1960 represents -5^2 as anything other than -25.

 

[Ignoratio Elenchi]

Well I suppose that's just it. I don't imagine any ones. -5 is an integer that exists without any operation at all.

Sure. -5 is an integer that exists. In an abstract sense, there's no such thing as a "subtraction" operator anyway, there's just addition. What we call subtraction is really just addition with negative integers. In that sense, it's not really correct to say -5 is really shorthand for "zero minus five" (an analogy someone made earlier in the thread, I think) because "minus" isn't a well-defined concept. -5 is just -5, you can't really separate the - sign from the 5.Perhaps, then, it should be the case that we should treat -52 as (-5)2. But we don't. It's probably because we do treat the negative sign as an operator on a natural number (i.e. "-5" isn't a number, it's a negative sign applied to the number 5; it's 0 minus 5, or -1 times 5), in which case it makes sense to slot it in after the exponent in the order of operations, unless you include the parentheses.

I don't know how math was taught 30 years ago. If it really has changed in that time, that's interesting. But as it stands now, -52 = -25.

 

[squidrope]

Maybe I'm    but here goe.......

Solve this problem:

-5² + 4 x 2³ =

-6² + 2 x 3² =

My answers57 and 54

<{POST_SNAPBACK}>

1. 572. 54

Order of operations. First resolve the exponents, then the multiplication, then the addition.

 

[Thorn]

-5 is just -5, you can't really separate the - sign from the 5.

Perhaps, then, it should be the case that we should treat -52 as (-5)2.

Welcome aboard.

 

[The Iguana]

It's only ambiguous if you're completely unfamiliar with the convention.

Agreed, the problem for some of us is that the convention changed within the last 30 years.I graduated high school in '82 so learned my mat in the late 70s and early 80s.

I was taught that -5^2 = negative five squared = -5*-5 = 25

It is now taught that -5^2 = negative of five squared = -(5*5) = 25

I've seen the text books now and understand how the answer of -25 is achieved. It just seems unnatural to me and I will always see it as 25.

The math never changes. Sometimes as you get older you just don't remember things as well as you think you do.

 

[The Iguana]

2 thoughts.... First, I really can't believe this discussion is this old. 2nd, while I understand that there would be amibguity in a public discussion of this, it amazes me how many people continue to try to "prove" that 25 is correct after have the "math facts" presented rather clearly. I just want a count of how many of those folks are stirring the pot verses how many truly believe they are correct.

 

[Ignoratio Elenchi]

-5 is just -5, you can't really separate the - sign from the 5.

Perhaps, then, it should be the case that we should treat -52 as (-5)2.

Welcome aboard.

It's a convention. Neither way is necessarily more or less "right" than the other, we pick one we all agree on and go with it. With that said, it's been agreed that -52 is -25, unless you specify otherwise with parentheses. I think that's probably a good way to handle it, given the way we usually think about and teach concepts like negative numbers and the commutativity of addition, etc. We typically treat the - sign as an operator on the natural number 5, and not as an inseperable part of the integer -5.

 

[Mjolnirs]

It's only ambiguous if you're completely unfamiliar with the convention.

Agreed, the problem for some of us is that the convention changed within the last 30 years.I graduated high school in '82 so learned my mat in the late 70s and early 80s.

I was taught that -5^2 = negative five squared = -5*-5 = 25

It is now taught that -5^2 = negative of five squared = -(5*5) = 25

I've seen the text books now and understand how the answer of -25 is achieved. It just seems unnatural to me and I will always see it as 25.

The math never changes. Sometimes as you get older you just don't remember things as well as you think you do.

you can all you want, but my statement is true. I've presented this question to a friend that teaches math in college and he agrees the answer is -25, but also states that when he and I learned it the convention was 25. I presented this question to my former boss that has a Doctorate in Math and is in his 60s and he said that 25 was what he was taught, but the convention now is -25. So, I'm pretty sure I'm not remembering things incorrectly.

 

[Short Corner]

It's only ambiguous if you're completely unfamiliar with the convention.

Agreed, the problem for some of us is that the convention changed within the last 30 years.I graduated high school in '82 so learned my mat in the late 70s and early 80s.

I was taught that -5^2 = negative five squared = -5*-5 = 25

It is now taught that -5^2 = negative of five squared = -(5*5) = 25

I've seen the text books now and understand how the answer of -25 is achieved. It just seems unnatural to me and I will always see it as 25.

The math never changes. Sometimes as you get older you just don't remember things as well as you think you do.

you can all you want, but my statement is true. I've presented this question to a friend that teaches math in college and he agrees the answer is -25, but also states that when he and I learned it the convention was 25. I presented this question to my former boss that has a Doctorate in Math and is in his 60s and he said that 25 was what he was taught, but the convention now is -25. So, I'm pretty sure I'm not remembering things incorrectly.

"Please excuse my dear aunt sally" has been the convention for at least a few hundred years.

 

[The Iguana]

Could be but I'm of a similar age and a math geek and a friend of much bigger math geeks myself. Some have been momentarily stumped by the problem and/or not seen it clearly but none have tried to argue the math has changed or anything of the sort. MT puts it pretty clearly in that it is somewhat ambiguous from a general population stand point. I'd guess it was put on the test as a "trick question" as well but the rules of math are still the same as they always have been. I still think the easiest way to see it is in the "proof" I put forth long ago...

-5^2 = x

you can add anything you want to one side as long as you do it to the other as well...

5 + -5^2 = 5 + x

doing should make it obvious that the answer is -25 to me. the only way that it = 25 is if you express it this way:

5+ (-5)^2 = 5 + x

That is to say that the - can't be seperated from the 5. For this to have ever been true, there would have to be some kind of "implied ()" around the -5 to begin with and/or you have to change the rules of accepted math principles.

I can still picture my high school math teacher writing this kind of thing on the board and then immediately erasing it saying that it "would burn your eyes out" if he left it up there too long. he was an odd guy but a funny one.

 

[Thorn]

We typically treat the - sign as an operator on the natural number 5, and not as an inseperable part of the integer -5.