Daughter's math homework (1 Viewer)

[rolyaTy]

OK, so now I'm convinced due to the order of operations that -5^2 should be -25.  However, I fear that most if not all computer programs ever written and interpreted on current processors is doing it wrong.

To force the processor to intrepret it correctly would mean changing every formula that includes exponentiation to check for a negative base number and if found change the formula from something like x^2 to (-1*(x)^2).  Otherwise, it comes out positive every time.

I think this could be a new Y2K for us programmers. 

Will one of you alert the news media?  I'll be getting my business cards ready.  Swapster, Negative Exponentiation Specialist.

No, just like with google, calculators and excel, one must understand how to use them before expecting them to churn out correct answers. If you were to use parentheses like you're supposed to, the computers do fine with them. Even without parenthesis, the computers do the calculations correctly...it's just that we think we're telling the computer to do one thing, when we're really telling it something else.

So, how would you put the original equation in code? Assuming intNumber is the variable to be taken to the 2nd power, I would code it as (intNumber^2). If intNumber is set to -5, the processor comes calculates this as 25 not -25. Same if you make it (intNumber)^2.

I would make a specific operator for negative values separate from a minus sign, like most calculators do. If someone uses the operator representing a sign...then it'd be -5, if they use the operator representing subtraction, it'd be -(5).

Programs don't work that way.I'm just saying... that any business apps that include exponentiation that could possibly be given a negative number are going to calculate incorrectly, based on what I have learned here.

To force them to calculate correctly would take a lot of programming changes, looking for a negative being fed into the equation (not by a human operator but from elsewhere in the program - it could be a result of a previous calculation done on numbers from a database, for instance).

You can make a program work most any way you want. If I wanted to write a program to do order of operations stuff, I would include a negative sign seperate from the minus sign. Programs can and do run that way, I have a calculator that does just that as proof.Again, a computer program is only as good as the person using it. If the person using it doesn't understand that there is a difference between writing -5^2 and (-5)^2, it's not the computers fault. The job of the person is to put the mathematical equation into terms that the computer can understand.

The computer program will not calculate incorrectly - the person would have INPUT the problem incorrectly.

There are plenty of calculators out there that don't follow PEMDAS, that calculate 100% correctly. The users have to know how to enter the info, and to do that they have to understand order of operations themselves, which apparently isn't as common as I suspected.

 

[rolyaTy]

It'd be something like:

NumVal = x

NumSign=y %either a -1 or a 1

Num=x*y

solution=Num^2

Solution would still be wrong.NumVal = 5

NumSign = -1

Num = 5 * -1

Num = -5

Solution = -5^2, interpreted by computer as 25.

(-5)^2 is 25.

 

[Maurile Tremblay]

I'm just saying... that any business apps that include exponentiation that could possibly be given a negative number are going to calculate incorrectly, based on what I have learned here.

They'd calculate it correctly. Let's say another function returns a value of -5, and the current program wants to square it. The answer is 25.There's no confusion on that point. We all agree that when you take negative five and square it, you get a positive number.

That's not what "-5^2" is asking us to do, though. It's not saying "take negative five and then square it." It's saying "take five, square it, and then multiply by negative one."

 

[Maurile Tremblay]

It'd be something like:

NumVal = x

NumSign=y %either a -1 or a 1

Num=x*y

solution=Num^2

Solution would still be wrong.NumVal = 5

NumSign = -1

Num = 5 * -1

Num = -5

Solution = -5^2, interpreted by computer as 25.

(-5)^2 is 25.

Exactly. If you're squaring Num (where Num = -5), you'll get 25, and that will be correct. There's no dispute about that.

 

[Swapster]

OK, so now I'm convinced due to the order of operations that -5^2 should be -25.  However, I fear that most if not all computer programs ever written and interpreted on current processors is doing it wrong.

To force the processor to intrepret it correctly would mean changing every formula that includes exponentiation to check for a negative base number and if found change the formula from something like x^2 to (-1*(x)^2).  Otherwise, it comes out positive every time.

I think this could be a new Y2K for us programmers. 

Will one of you alert the news media?  I'll be getting my business cards ready.  Swapster, Negative Exponentiation Specialist.

No, just like with google, calculators and excel, one must understand how to use them before expecting them to churn out correct answers. If you were to use parentheses like you're supposed to, the computers do fine with them. Even without parenthesis, the computers do the calculations correctly...it's just that we think we're telling the computer to do one thing, when we're really telling it something else.

So, how would you put the original equation in code? Assuming intNumber is the variable to be taken to the 2nd power, I would code it as (intNumber^2). If intNumber is set to -5, the processor comes calculates this as 25 not -25. Same if you make it (intNumber)^2.

I would make a specific operator for negative values separate from a minus sign, like most calculators do. If someone uses the operator representing a sign...then it'd be -5, if they use the operator representing subtraction, it'd be -(5).

Programs don't work that way.I'm just saying... that any business apps that include exponentiation that could possibly be given a negative number are going to calculate incorrectly, based on what I have learned here.

To force them to calculate correctly would take a lot of programming changes, looking for a negative being fed into the equation (not by a human operator but from elsewhere in the program - it could be a result of a previous calculation done on numbers from a database, for instance).

You can make a program work most any way you want. If I wanted to write a program to do order of operations stuff, I would include a negative sign seperate from the minus sign. Programs can and do run that way, I have a calculator that does just that as proof.Again, a computer program is only as good as the person using it. If the person using it doesn't understand that there is a difference between writing -5^2 and (-5)^2, it's not the computers fault. The job of the person is to put the mathematical equation into terms that the computer can understand.

The computer program will not calculate incorrectly - the person would have INPUT the problem incorrectly.

There are plenty of calculators out there that don't follow PEMDAS, that calculate 100% correctly. The users have to know how to enter the info, and to do that they have to understand order of operations themselves, which apparently isn't as common as I suspected.

I understand GIGO.But (-5)^2 is interpreted the same as -5^2, at least from what I've tried in a vbscript and excel. I haven't tried in a compiled language tonight, but I'm assuming it would be the same. So to make this calculate correctly, you'd have to put in and if/then/else to force it to use the negative of the exponentiated number.

 

[rolyaTy]

It'd be something like:

NumVal = x

NumSign=y %either a -1 or a 1

Num=x*y

solution=Num^2

Solution would still be wrong.NumVal = 5

NumSign = -1

Num = 5 * -1

Num = -5

Solution = -5^2, interpreted by computer as 25.

(-5)^2 is 25.

The only reason to introduce a sign value is to eliminate, or try to, user error. There is obviously ambiguity here, and separating the sign from the number value is the way to get to the root of the issue.The whole problem here has been whether or not the number being squared was 5 or -5. Once that is cleared up, the problem is not confusing at all. Math teaches that -5^2 should be seen as -(5)^2. When you enter that into a computer, you must be sure that you're telling the computer the correct thing, based on what Math teaches you. If you enter the equivalent of (-5)^2, it's not the computer that has messed up when you get 25 out, it was you.

 

[Swapster]

I'm just saying...  that any business apps that include exponentiation that could possibly be given a negative number are going to calculate incorrectly, based on what I have learned here.

They'd calculate it correctly. Let's say another function returns a value of -5, and the current program wants to square it. The answer is 25.There's no confusion on that point. We all agree that when you take negative five and square it, you get a positive number.

That's not what "-5^2" is asking us to do, though. It's not saying "take negative five and then square it." It's saying "take five, square it, and then multiply by negative one."

Woah! Now I'm ! How do you know by looking at the original problem to assume that it is saying "take five, square it then multiply by -1"? If that is the case, how on earth do you write "take negative five and then square it"? If you tell me it's (-5)^2, what I am asserting is that a computer program will calcluate both the exact same way, with or without parentheses.

 

[rolyaTy]

OK, so now I'm convinced due to the order of operations that -5^2 should be -25.  However, I fear that most if not all computer programs ever written and interpreted on current processors is doing it wrong.

To force the processor to intrepret it correctly would mean changing every formula that includes exponentiation to check for a negative base number and if found change the formula from something like x^2 to (-1*(x)^2).  Otherwise, it comes out positive every time.

I think this could be a new Y2K for us programmers. 

Will one of you alert the news media?  I'll be getting my business cards ready.  Swapster, Negative Exponentiation Specialist.

No, just like with google, calculators and excel, one must understand how to use them before expecting them to churn out correct answers. If you were to use parentheses like you're supposed to, the computers do fine with them. Even without parenthesis, the computers do the calculations correctly...it's just that we think we're telling the computer to do one thing, when we're really telling it something else.

So, how would you put the original equation in code? Assuming intNumber is the variable to be taken to the 2nd power, I would code it as (intNumber^2). If intNumber is set to -5, the processor comes calculates this as 25 not -25. Same if you make it (intNumber)^2.

I would make a specific operator for negative values separate from a minus sign, like most calculators do. If someone uses the operator representing a sign...then it'd be -5, if they use the operator representing subtraction, it'd be -(5).

Programs don't work that way.I'm just saying... that any business apps that include exponentiation that could possibly be given a negative number are going to calculate incorrectly, based on what I have learned here.

To force them to calculate correctly would take a lot of programming changes, looking for a negative being fed into the equation (not by a human operator but from elsewhere in the program - it could be a result of a previous calculation done on numbers from a database, for instance).

You can make a program work most any way you want. If I wanted to write a program to do order of operations stuff, I would include a negative sign seperate from the minus sign. Programs can and do run that way, I have a calculator that does just that as proof.Again, a computer program is only as good as the person using it. If the person using it doesn't understand that there is a difference between writing -5^2 and (-5)^2, it's not the computers fault. The job of the person is to put the mathematical equation into terms that the computer can understand.

The computer program will not calculate incorrectly - the person would have INPUT the problem incorrectly.

There are plenty of calculators out there that don't follow PEMDAS, that calculate 100% correctly. The users have to know how to enter the info, and to do that they have to understand order of operations themselves, which apparently isn't as common as I suspected.

I understand GIGO.But (-5)^2 is interpreted the same as -5^2, at least from what I've tried in a vbscript and excel. I haven't tried in a compiled language tonight, but I'm assuming it would be the same. So to make this calculate correctly, you'd have to put in and if/then/else to force it to use the negative of the exponentiated number.

You know that some languages or programs perform math according to order of operations, and some don't. It's the job of the person using the program to understand how the program itself works, and then to tailor the input accordingly.So if the computer doesn't recognize order of operations, it almost has to use parentheses for guidance, and the user must use parentheses to organize the equation so that the program will output the correct answer. The user will organize the equation by arranging things in parentheses so that PEMDAS is followed.

 

[Swapster]

It'd be something like:

NumVal = x

NumSign=y %either a -1 or a 1

Num=x*y

solution=Num^2

Solution would still be wrong.NumVal = 5

NumSign = -1

Num = 5 * -1

Num = -5

Solution = -5^2, interpreted by computer as 25.

(-5)^2 is 25.

The only reason to introduce a sign value is to eliminate, or try to, user error. There is obviously ambiguity here, and separating the sign from the number value is the way to get to the root of the issue.The whole problem here has been whether or not the number being squared was 5 or -5. Once that is cleared up, the problem is not confusing at all. Math teaches that -5^2 should be seen as -(5)^2. When you enter that into a computer, you must be sure that you're telling the computer the correct thing, based on what Math teaches you. If you enter the equivalent of (-5)^2, it's not the computer that has messed up when you get 25 out, it was you.

OK, I see what you are saying. I was looking at plain old -5^2. If I had a formula such as savings to the 2nd power where x is savings, I would calcluate it as savings^2. BUT, if I wanted to calculate the negative of savings to the 2nd power then I certainly would code it as -1 * (savings)^2. But I still don't see how you know the original equation meant negative 5 to the 2nd power without any parentheses!

However, my brain is fried and I'm going to bed.

 

[rolyaTy]

I'm just saying...  that any business apps that include exponentiation that could possibly be given a negative number are going to calculate incorrectly, based on what I have learned here.

They'd calculate it correctly. Let's say another function returns a value of -5, and the current program wants to square it. The answer is 25.There's no confusion on that point. We all agree that when you take negative five and square it, you get a positive number.

That's not what "-5^2" is asking us to do, though. It's not saying "take negative five and then square it." It's saying "take five, square it, and then multiply by negative one."

Woah! Now I'm ! How do you know by looking at the original problem to assume that it is saying "take five, square it then multiply by -1"? If that is the case, how on earth do you write "take negative five and then square it"? If you tell me it's (-5)^2, what I am asserting is that a computer program will calcluate both the exact same way, with or without parentheses.

That is based on how it views the number and the sign, not on the order of operations. I think you are confusing two issues. One is how a computer identifies a value, and the other is how Mathematical Order of Operations should be performed.

 

[Clayton Gray]

Well this suddenly turned into a fest.

 

[NCCommish]

Well this suddenly turned into a fest.

Suddenly?

 

[Kleck]

Random thought... When you were a student, how often were you typing mathematical expressions into a keyboard or a graphing calculator? Probably not at all. Its sort of a new medium for students to work in that didn't really exist on a large scale before (if at all). I can see how acknowledging the difference between (-5)^2 and -5^2 has become a more important concept due to technology.Like I mentioned before, this isn't about right or wrong. Its about agreeing upon a standardized way for us to communicate mathematically.

 

[Miggity]

I was told there would be no math.

 

[tommyboy]

You wouldn't treat -x^2 as (-x)^2. This is the same principal.

Yes, I would - as any person who knows math would do.

no kidding...sheesh you can really tell peoples education levels in this thread.NEVER EVER is a -5 the same as -(5)

-5 is= Negative 5

Negative 5 squared equals positive twenty ####### five.

 

[Miggity]

Random thought... When you were a student, how often were you typing mathematical expressions into a keyboard or a graphing calculator? Probably not at all. Its sort of a new medium for students to work in that didn't really exist on a large scale before (if at all). I can see how acknowledging the difference between (-5)^2 and -5^2 has become a more important concept due to technology.

Like I mentioned before, this isn't about right or wrong. Its about agreeing upon a standardized way for us to communicate mathematically.

I read posts 1-5, then posted. I was lucky enough that ! posted above me. -5^2 is confusing. (-5)^2 is not.

 

[HarryManback]

-(5)^2 and (-5)^2 would be the best way to to do them both, -5^2 can really be interpreted either way.

 

[crewmember]

1) 57

2) 54

Parentheses

Exponents

Multiplication

Division

Addition

Subdtraction

you're done

A good way to remember this is Please Exuse My Dear Aunt SallyI've also got some sayings to help you tie your shoes, let me know if your interested

 

[Sweet J]

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 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.

The answer to my querry is not related to the the amount of discussion on this board, or how hard the question is, really.But it IS related to your daughter being a straight A student. If that is true, and she pays attention in class, this is a screw-up by teach.

Lemme explain: This problem is one of those "you only have to explain it once" problems. It's less related to actual MATH and more related to how you interpret a specific mathmatical function. I think Maurile called it "syntax." Is that the same as "wording"? Anyway, the math teacher should have explained how a person "reads" -Xsquared. Once explained -- as long as you trust your teacher -- this is NOT a hard concept to accept. The reason everybody in this thread is throwing a hissy-fit is because they were taught a different way of doing it. If this is the ONLY way you've been taught, then it doesn't really seem hard.

SO -- because this isn't really a difficult mathmatical concept, either the teacher did a bad job of explaining, or your daughter wasn't paying attention. If you trust your daughter and she's a straight-A student, then maybe you might want to send a note to the teach.

 

[MrPack]

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.

If it had been written like -(5²) it would have made it a hell of a lot clearer to me.

For those saying the parentheses make it more clear, I am 100% in agreement.

Were there any like this: (-5)^2?

I will look when i get home. I believe there were a few problems similar. I do know there was one that was something like this:(-2³) + (-2)³ This may not be exact, but the answer was -16 and she/we got it right. Now the reason I got it correct is that when you put any negative number into a calculator and cube it, it comes out negative.

 

[MrPack]

^2 means to multiply the base number by itself.  Here, the base number is -5, or if you prefer (0-5).  So, when you add the 0- in front of it you should get:  (0-5) * (0-5) = 25.  Otherwise, you are changing the equation.

The base number is 5. You do the squaring before you do the negativing since exponents have priority over multiplication. (The negative sign means to multiply by negative one. You do this after exponentializing, not before.) (I'm making up words left and right here.)

But they're cool words

 

[MrPack]

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".

I must say, I have never thought of it like this. I will admit to this too....... My daughter had both problems right the first time, but as I was checking it over last night, I told her they were wrong. She questioned me a little bit, but was confused, and changed them.

When I got home from work today I faced one angry daughter as she got them both marked wrong, and those were the only 2 she had wrong.

MrPack: Do you need any help?

LittlePack: No thanks. I'm waiting on mom.

Actually I am the mathmetician in our house.

 

[The Iguana]

Solve this problem:

-5² + 4 x 2³ =

-6² + 2 x 3² =

My answers57 and 54

I thought it was just a sure sign of my math geekiness that I woke up this morning thinking about this thread but the fact that it grew from 5 pages to 10 since I last logged in means I'm ok! Either that or it verifies that all FF players really are just geeks. Anyway, I didn't take the time to read pages 6 to 10 but I will work the program again and show once and for all that there is only 1 answer to these problems. The answer lies in the commutative property of addition.Given that a + b = b + a:

-5² + 4 x 2³ = 4 x 2³ + -5²

Now it should be obvious that:

4 x 2³ + -5² = 4 x 2³ - 5² = -7

For you to work this problem as:

4 x 2³ + -5² = 4 x 2³ + 25 = 54 !WRONG!

You have to break the basic rules of math by changing the order of operation or fill in an assumed set of parenthesis that just are present in the problem. Therefore, it should be apparenent that the correct answers to the problems are -7 and 18!

 

[Otis]

I think anybody who writes the expression (no matter which interpretation they intend) is nuts for not using parentheses.

Especially if you do this in any kind of real world situation.

I disagree. The problem as written has a very clear and definite meaning. There is no ambiguity here.

 

[Otis]

How did this go on for 7 more pages after we cleared it up?

 

[Gatorman]

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 = -25

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.

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=25

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.

I gotta tell you shick, that I would fight to the death against you on this argument. when I see -5^2 I think of it as x^2 with x = -5, and I have been doing this before calculators made it easy to do. Now I could be wrong (and probably am), but this just seems to go against my way of looking at things. Then again, I am an Optometrist so to me the number -2 means I am treating someone who is nearsighted.So you need the parentheses to tell you this is a negative number and not the other way around...hmm.

 

[NCCommish]

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".

I must say, I have never thought of it like this. I will admit to this too....... My daughter had both problems right the first time, but as I was checking it over last night, I told her they were wrong. She questioned me a little bit, but was confused, and changed them.

When I got home from work today I faced one angry daughter as she got them both marked wrong, and those were the only 2 she had wrong.

MrPack: Do you need any help?

LittlePack: No thanks. I'm waiting on mom.

Actually I am the mathmetician in our house.

Were

 

[MrPack]

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".

I must say, I have never thought of it like this. I will admit to this too....... My daughter had both problems right the first time, but as I was checking it over last night, I told her they were wrong. She questioned me a little bit, but was confused, and changed them.

When I got home from work today I faced one angry daughter as she got them both marked wrong, and those were the only 2 she had wrong.

MrPack: Do you need any help?

LittlePack: No thanks. I'm waiting on mom.

Actually I am the mathmetician in our house.

Were Was

 

[Sweet J]

Were Was

Actually,I was --- You were.

You are both right.

 

[Clayton Gray]

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 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.

The answer to my querry is not related to the the amount of discussion on this board, or how hard the question is, really.But it IS related to your daughter being a straight A student. If that is true, and she pays attention in class, this is a screw-up by teach.

Lemme explain: This problem is one of those "you only have to explain it once" problems. It's less related to actual MATH and more related to how you interpret a specific mathmatical function. I think Maurile called it "syntax." Is that the same as "wording"? Anyway, the math teacher should have explained how a person "reads" -Xsquared. Once explained -- as long as you trust your teacher -- this is NOT a hard concept to accept. The reason everybody in this thread is throwing a hissy-fit is because they were taught a different way of doing it. If this is the ONLY way you've been taught, then it doesn't really seem hard.

SO -- because this isn't really a difficult mathmatical concept, either the teacher did a bad job of explaining, or your daughter wasn't paying attention. If you trust your daughter and she's a straight-A student, then maybe you might want to send a note to the teach.

You missed the post where Pack says his daughter originally answered the questions correctly but he told her they were wrong. She ended up changing the answers and now has a 99.9% in the class.

 

[Clayton Gray]

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.

If it had been written like -(5²) it would have made it a hell of a lot clearer to me.

For those saying the parentheses make it more clear, I am 100% in agreement.

Were there any like this: (-5)^2?

I will look when i get home. I believe there were a few problems similar. I do know there was one that was something like this:(-2³) + (-2)³ This may not be exact, but the answer was -16 and she/we got it right. Now the reason I got it correct is that when you put any negative number into a calculator and cube it, it comes out negative.

Yes, but you do realize that you are cubing a positive 2 in the first term. Then you are making that answer negative. It ends up being -8 + -8 = -16.

 

[Clayton Gray]

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".

I must say, I have never thought of it like this. I will admit to this too....... My daughter had both problems right the first time, but as I was checking it over last night, I told her they were wrong. She questioned me a little bit, but was confused, and changed them.

When I got home from work today I faced one angry daughter as she got them both marked wrong, and those were the only 2 she had wrong.

MrPack: Do you need any help?

LittlePack: No thanks. I'm waiting on mom.

Actually I am the mathmetician in our house.

Rut Roh.You'll be #2 pretty soon (if not already).

 

[P Boy]

I disagree. The problem as written has a very clear and definite meaning. There is no ambiguity here.

And I respectfully disagree. As an engineering firm participating in real world problems where we do in fact have to submit calculations & drawings to local jurisdictions, I can state that it is company policy to ALWAYS use parenthesis to avoid ambiguous interpretations of signs & quantities.The negative sign out front is ambiguous - especially to a child learning operations.

The teacher should have used either -(5^2) or (-5)^2 to avoid any confusion. While you are correct about the proper order of operations on this problem, it is borderline a trick question with the placement of the negative sign without any parenthesis. I'm not sure we ought to be teaching sneaky tricks to kids - we ought to be teaching them proper use of mathematical processes. In fact, the problems should have been written as subtraction problems rather than adding negative problems.

And as an addition, I'll add that I was a teacher of math & physics for 12 years before getting my engineering degrees & opening our own company. I never would have used a confusing question like this in class or on a test. Your goal as a teacher isn't to try to trip kids up.

 

[Buckychudd]

If someone chooses not to accept the accepted definition, well, okay. I'm guessing they don't have a very high Erdos number.

Ummm, wouldn't you want a low Erdos number?

 

[Clayton Gray]

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 = -25

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.

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=25

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.

I gotta tell you shick, that I would fight to the death against you on this argument. when I see -5^2 I think of it as x^2 with x = -5, and I have been doing this before calculators made it easy to do. Now I could be wrong (and probably am), but this just seems to go against my way of looking at things. Then again, I am an Optometrist so to me the number -2 means I am treating someone who is nearsighted.So you need the parentheses to tell you this is a negative number and not the other way around...hmm.

You need the parenthesis to tell you to square the negative.Just like ab^2 is not a^2 b^2, but (ab)^2 is a^2 b^2.

 

[Sam Quentin]

I disagree.  The problem as written has a very clear and definite meaning.  There is no ambiguity here.

And I respectfully disagree. As an engineering firm participating in real world problems where we do in fact have to submit calculations & drawings to local jurisdictions, I can state that it is company policy to ALWAYS use parenthesis to avoid ambiguous interpretations of signs & quantities.The negative sign out front is ambiguous - especially to a child learning operations.

The teacher should have used either -(5^2) or (-5)^2 to avoid any confusion. While you are correct about the proper order of operations on this problem, it is borderline a trick question with the placement of the negative sign without any parenthesis. I'm not sure we ought to be teaching sneaky tricks to kids - we ought to be teaching them proper use of mathematical processes. In fact, the problems should have been written as subtraction problems rather than adding negative problems.

And as an addition, I'll add that I was a teacher of math & physics for 12 years before getting my engineering degrees & opening our own company. I never would have used a confusing question like this in class or on a test. Your goal as a teacher isn't to try to trip kids up.

I disagree

the child needs to know ALL of the rules.

I also agree that when communicating mathematical ideas to others, you should use parentheses to avoid any perceived ambiguity, but in the real world, everybody will not do this, so it's important to know the rules.

 

[IvanKaramazov]

I didn't read the whole thread, but I just wanted to chime in and say that issues like this probably contribute to why American kids don't see the value in math. What has your daughter learned from this assignment? That math is all about little tricks and blindly following arbitrary algorithms. If you want somebody to calculate the square of the number "negative 5", then write (-5)^2 to clear up the ambiguity. If you want somebody to calculate the negative of the square of 5, then write -(5^2). Then get on with it. Math is fundamentally about logic, and logical analysis shouldn't tolerate the ambiguity in the way this was written originally.Edit: Seeing as how there are actually a bunch of posts on this exact topic 11 pages into the thread, I'm guessing my thoughts on this aren't exactly original. NM.

 

[playin4beer]

Holy Crap!! 10-pages on a MATH PROBLEM??? GB being a math idiot and not caring one way or another

 

[MrPack]

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.

If it had been written like -(5²) it would have made it a hell of a lot clearer to me.

For those saying the parentheses make it more clear, I am 100% in agreement.

Were there any like this: (-5)^2?

I will look when i get home. I believe there were a few problems similar. I do know there was one that was something like this:(-2³) + (-2)³ This may not be exact, but the answer was -16 and she/we got it right. Now the reason I got it correct is that when you put any negative number into a calculator and cube it, it comes out negative.

Yes, but you do realize that you are cubing a positive 2 in the first term. Then you are making that answer negative. It ends up being -8 + -8 = -16.

A positive 2? No it's a -2, it's in parentheses so that makes it negative right?.

 

[P Boy]

Holy Crap!! 10-pages on a MATH PROBLEM???

GB being a math idiot and not caring one way or another

Many, many geeks wandering these halls....

 

[Clayton Gray]

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.

If it had been written like -(5²) it would have made it a hell of a lot clearer to me.

For those saying the parentheses make it more clear, I am 100% in agreement.

Were there any like this: (-5)^2?

I will look when i get home. I believe there were a few problems similar. I do know there was one that was something like this:(-2³) + (-2)³ This may not be exact, but the answer was -16 and she/we got it right. Now the reason I got it correct is that when you put any negative number into a calculator and cube it, it comes out negative.

Yes, but you do realize that you are cubing a positive 2 in the first term. Then you are making that answer negative. It ends up being -8 + -8 = -16.

A positive 2? No it's a -2, it's in parentheses so that makes it negative right?.

The parenthesis in the first term change nothing.(-2³) is the exact same problem as -2³ just as (2+3) is the same as 2+3

 

[Clayton Gray]

Holy Crap!! 10-pages on a MATH PROBLEM??? 

GB being a math idiot and not caring one way or another 

Many, many geeks wandering these halls....

Yes, but we tolerate them.

 

[John 14:6]

Solve this problem:

-5² + 4 x 2³ =

-6² + 2 x 3² =

My answers57 and 54

I thought it was just a sure sign of my math geekiness that I woke up this morning thinking about this thread but the fact that it grew from 5 pages to 10 since I last logged in means I'm ok! Either that or it verifies that all FF players really are just geeks. Anyway, I didn't take the time to read pages 6 to 10 but I will work the program again and show once and for all that there is only 1 answer to these problems. The answer lies in the commutative property of addition.Given that a + b = b + a:

-5² + 4 x 2³ = 4 x 2³ + -5²

Now it should be obvious that:

4 x 2³ + -5² = 4 x 2³ - 5² = -7

For you to work this problem as:

4 x 2³ + -5² = 4 x 2³ + 25 = 54 !WRONG!

You have to break the basic rules of math by changing the order of operation or fill in an assumed set of parenthesis that just are present in the problem. Therefore, it should be apparenent that the correct answers to the problems are -7 and 18!

 

[Sam Quentin]

I didn't read the whole thread, but I just wanted to chime in and say that issues like this probably contribute to why American kids don't see the value in math. What has your daughter learned from this assignment? That math is all about little tricks and blindly following arbitrary algorithms.

If you want somebody to calculate the square of the number "negative 5", then write (-5)^2 to clear up the ambiguity. If you want somebody to calculate the negative of the square of 5, then write -(5^2). Then get on with it.

Math is fundamentally about logic, and logical analysis shouldn't tolerate the ambiguity in the way this was written originally.

Edit: Seeing as how there are actually a bunch of posts on this exact topic 11 pages into the thread, I'm guessing my thoughts on this aren't exactly original. NM.

should it have been written as:-(5²) + [4 x (2³)] ?

 

[Foosball God]

If they just used proper paraenthasis then there wouldn't even be an issue.

 

[Sam Quentin]

Holy Crap!! 10-pages on a MATH PROBLEM??? 

GB being a math idiot and not caring one way or another 

Many, many wannabe geeks wandering these halls....

fixed

 

[IvanKaramazov]

I didn't read the whole thread, but I just wanted to chime in and say that issues like this probably contribute to why American kids don't see the value in math.  What has your daughter learned from this assignment?  That math is all about little tricks and blindly following arbitrary algorithms. 

If you want somebody to calculate the square of the number "negative 5", then write (-5)^2 to clear up the ambiguity.  If you want somebody to calculate the negative of the square of 5, then write -(5^2).  Then get on with it. 

Math is fundamentally about logic, and logical analysis shouldn't tolerate the ambiguity in the way this was written originally.

Edit: Seeing as how there are actually a bunch of posts on this exact topic 11 pages into the thread, I'm guessing my thoughts on this aren't exactly original.  NM.

should it have been written as:-(5²) + [4 x (2³)] ?

The brackets around the second term are probably unneccessary.

 

[Sam Quentin]

I didn't read the whole thread, but I just wanted to chime in and say that issues like this probably contribute to why American kids don't see the value in math.  What has your daughter learned from this assignment?  That math is all about little tricks and blindly following arbitrary algorithms. 

If you want somebody to calculate the square of the number "negative 5", then write (-5)^2 to clear up the ambiguity.  If you want somebody to calculate the negative of the square of 5, then write -(5^2).  Then get on with it. 

Math is fundamentally about logic, and logical analysis shouldn't tolerate the ambiguity in the way this was written originally.

Edit: Seeing as how there are actually a bunch of posts on this exact topic 11 pages into the thread, I'm guessing my thoughts on this aren't exactly original.  NM.

should it have been written as:-(5²) + [4 x (2³)] ?

The brackets around the second term are probably unneccessary.

but isn't it ambiguous as to which you do first? multiply or add?

 

[John 14:6]

I didn't read the whole thread, but I just wanted to chime in and say that issues like this probably contribute to why American kids don't see the value in math.  What has your daughter learned from this assignment?  That math is all about little tricks and blindly following arbitrary algorithms. 

If you want somebody to calculate the square of the number "negative 5", then write (-5)^2 to clear up the ambiguity.  If you want somebody to calculate the negative of the square of 5, then write -(5^2).  Then get on with it. 

Math is fundamentally about logic, and logical analysis shouldn't tolerate the ambiguity in the way this was written originally.

Edit: Seeing as how there are actually a bunch of posts on this exact topic 11 pages into the thread, I'm guessing my thoughts on this aren't exactly original.  NM.

should it have been written as:-(5²) + [4 x (2³)] ?

The brackets around the second term are probably unneccessary.

Only because it is accepted by most everyone that multiplication is done before addition. But since there can be ambigouity over the exponent/negating issue, there could be over that as well.

 

[Fred Lane]

When I enter both equations into Excel without any parens, I get 57 and 54.So, we know what Bill Gates answer would be...