Daughter's math homework (1 Viewer)

[Clayton Gray]

So if I think that -5 ^ 2 = 25 was I mistaught back in the 70's, did I mislearn this back in the 70's, or has the convention on order of operations shifted in that time?

Probably one of the first two. It's most likely that this was covered for ten seconds because it only shows up as a single question on the test and geeky FF message boards.

 

[John 14:6]

This alludes back to an earlier post, but what would your answers be for these?

4 x 2³ - 5² =

2 x 3² - 6² =

4*8-25= 7But, had it been presented as -5^2 + 4*2^3 I would've said 25+32=57

But the two should be equal:4 x 2³ - 5² = -5² + 4 x 2³

 

[shadyridr]

Please, somebody solve the following problems:

5-*3

12*/4

6+*7

Those don't make sense, right? You don't put two operators in a row?

So why does this make sense?

0--5

The answer to that is clearly 5. You're subtracting -5 from 0, to get 5. Why is that?

Oh right. Because the negative in front of the 5 is NOT an operator! It's PART OF THE NUMBER!

Your comparing apples and oranges. This different rules for different operators. 5-*3 makes no sense but 5*-3 makes perfect sense.

 

[Clayton Gray]

Google calculator's answer

Please read the entire thread. We dismissed Google last night.

 

[Smoo]

Please, somebody solve the following problems:

5-*3

12*/4

6+*7

Those don't make sense, right? You don't put two operators in a row?

So why does this make sense?

0--5

The answer to that is clearly 5. You're subtracting -5 from 0, to get 5. Why is that?

Oh right. Because the negative in front of the 5 is NOT an operator! It's PART OF THE NUMBER!

Are these statements true?4 x 2³ - 5² = -5² + 4 x 2³

2 x 3² - 6² = -6² + 2 x 3²

Nope. And you don't even have to understand math to see why. On the left side of both, you've separated the negative operator from the number with a space. On the right you've nestled it in right next to the number with no space separator. Why did you do that? Oh, right, because on the right side the negative sign is being used as part of the number, not as an operator.

 

[rolyaTy]

Please, somebody solve the following problems:

5-*3

12*/4

6+*7

Those don't make sense, right? You don't put two operators in a row?

So why does this make sense?

0--5

The answer to that is clearly 5. You're subtracting -5 from 0, to get 5. Why is that?

Oh right. Because the negative in front of the 5 is NOT an operator! It's PART OF THE NUMBER!

It's the same as 0-(-1)(5) and the negative sign distributes out.

 

[shadyridr]

Here's the actuary thread:link

 

[P Boy]

There is a significant difference between how an interger is treated versus a variable.

In which math system? A variable is a number. It just has not been determined through process what number it is.

 

[Buckychudd]

What does this equation equal?

-x^2+x=

if x=5?

What does it equal if x=-5 ?

 

[P Boy]

So if I think that -5 ^ 2 = 25 was I mistaught back in the 70's, did I mislearn this back in the 70's, or has the convention on order of operations shifted in that time?

Probably one of the first two. It's most likely that this was covered for ten seconds because it only shows up as a single question on the test and geeky FF message boards.

Truth.

 

[(HULK)]

Google calculator's answer

Please read the entire thread. We dismissed Google last night.

I'm happy to join in an argue. But I'm not reading through 10 pages of prior arguement.Sorry for the honda.

 

[John 14:6]

Are these statements true?

4 x 2³ - 5² = -5² + 4 x 2³

2 x 3² - 6² = -6² + 2 x 3²

Nope. And you don't even have to understand math to see why. On the left side of both, you've separated the negative operator from the number with a space. On the right you've nestled it in right next to the number with no space separator. Why did you do that? Oh, right, because on the right side the negative sign is being used as part of the number, not as an operator.

OK, how about like this:4 x 2³ - 5² = - 5² + 4 x 2³

2 x 3² - 6² = - 6² + 2 x 3²

I don't think a space makes a difference in math.

 

[trout]

This alludes back to an earlier post, but what would your answers be for these?

4 x 2³ - 5² =

2 x 3² - 6² =

4*8-25= 7But, had it been presented as -5^2 + 4*2^3 I would've said 25+32=57

But the two should be equal:4 x 2³ - 5² = -5² + 4 x 2³

Left side is 7. Right side is 57.NO, the 2 are not equal.

 

[shadyridr]

Please, somebody solve the following problems:

5-*3

12*/4

6+*7

Those don't make sense, right?  You don't put two operators in a row?

So why does this make sense?

0--5

The answer to that is clearly 5.  You're subtracting -5 from 0, to get 5.  Why is that?

Oh right.  Because the negative in front of the 5 is NOT an operator!  It's PART OF THE NUMBER!

Are these statements true?4 x 2³ - 5² = -5² + 4 x 2³

2 x 3² - 6² = -6² + 2 x 3²

Nope. And you don't even have to understand math to see why. On the left side of both, you've separated the negative operator from the number with a space. On the right you've nestled it in right next to the number with no space separator. Why did you do that? Oh, right, because on the right side the negative sign is being used as part of the number, not as an operator.

HUH?????????? Now your are saying those statements aren't equal? OK now I think your just fishing.

 

[Sid]

http://www.math.com/school/subject2/lessons/S2U2L2EX.html

 

[posty]

Please, somebody solve the following problems:

5-*3

12*/4

6+*7

Those don't make sense, right? You don't put two operators in a row?

So why does this make sense?

0--5

The answer to that is clearly 5. You're subtracting -5 from 0, to get 5. Why is that?

Oh right. Because the negative in front of the 5 is NOT an operator! It's PART OF THE NUMBER!

Are these statements true?4 x 2³ - 5² = -5² + 4 x 2³

2 x 3² - 6² = -6² + 2 x 3²

Nope. And you don't even have to understand math to see why. On the left side of both, you've separated the negative operator from the number with a space. On the right you've nestled it in right next to the number with no space separator. Why did you do that? Oh, right, because on the right side the negative sign is being used as part of the number, not as an operator.

I don't think you are right on that Smoo...4 x 2³ - 5² = -5² + 4 x 2³

4 x 8 - 25 = -25 + 4 x 8

32 - 25 = -25 + 32

7 = 7

2 x 3² - 6² = -6² + 2 x 3²

2 x 9 - 36 = -36 + 2 x 9

18 - 36 = -36 + 18

-18 = -18

At least that is what I think and what my wife confirmed (7th and 8th grade math teacher)...

 

[P Boy]

Left side is 7. Right side is 57.NO, the 2 are not equal.

Hence the 99.9% in math....

 

[Clayton Gray]

I have come to the conclusion that the way it's written, BOTH sets of answers are correct since it's not written very clearly.

I still say -5 can be the base number here.

That conclusion is wrong, even though it doesn't make sense to you why it is Teachers give students those types of problems SPECIFICALLY to make sure they understand the difference between -5^2 and (-5)^2 , because there is a difference and it's important to know and to remember that they aren't the same. (Although apparently many people can go through their lives oblivious to this and not suffer from it).

 

[Smoo]

There is a significant difference between how an interger is treated versus a variable.

In which math system? A variable is a number. It just has not been determined through process what number it is.

A negative sign next to a variabe is clearly an operator. A negative sign next to a number is part of the number unless explicitly indicated as an operator.

 

[MrPack]

Pack--pls print this out and give it to your daughter to bring to her teacher.

Trust me, the thought has crossed my mind.I sent these problems out to all the engineers here at work, and everyone but 1 came back with the right answers. They all came up with the same answer I did.

Yea I reread that. Nice catch... What I MEANT to say is that the ones that answered, came back with my original answers (57, 54) A lot of them just got out of a meeting, and so far the answers are split.

 

[MrPack]

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.

 

[Smoo]

I don't think you are right on that Smoo...4 x 2³ - 5² = -5² + 4 x 2³

4 x 8 - 25 = -25 + 4 x 8

32 - 25 = -25 + 32

7 = 7

2 x 3² - 6² = -6² + 2 x 3²

2 x 9 - 36 = -36 + 2 x 9

18 - 36 = -36 + 18

-18 = -18

At least that is what I think and what my wife confirmed (7th and 8th grade math teacher)...

- 5^2 <> -5^2

 

[shadyridr]

This alludes back to an earlier post, but what would your answers be for these?

4 x 2³ - 5² =

2 x 3² - 6² =

4*8-25= 7But, had it been presented as -5^2 + 4*2^3 I would've said 25+32=57

But the two should be equal:4 x 2³ - 5² = -5² + 4 x 2³

Yes they are its simple math.

Left side is 7. Right side is 57.NO, the 2 are not equal.

 

[(HULK)]

There is a significant difference between how an interger is treated versus a variable.

In which math system? A variable is a number. It just has not been determined through process what number it is.

Its simple.X isn't a set number or defined on its own. -X is defined as the opposite of X.

However 5 is a set number and is defined on its own. -5 is also a set number (unless you don't believe in intergers). 5 and -5 are opposites of each other. The difference is that -5 exists in its own right whereas -x does not exist in its own right.

 

[John 14:6]

This alludes back to an earlier post, but what would your answers be for these?

4 x 2³ - 5² =

2 x 3² - 6² =

4*8-25= 7But, had it been presented as -5^2 + 4*2^3 I would've said 25+32=57

But the two should be equal:4 x 2³ - 5² = -5² + 4 x 2³

Left side is 7. Right side is 57.NO, the 2 are not equal.

As mentioned in this earlier post by Iguana, they should be:

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!

 

[Gamblor]

No. It's not. I was taught that -5*-5 = 25. I get all the rigamarole about the parentheses, etc. But I was taught to look at -5 squared as -5*-5. And so I did.

What's worse is I'm going to be preparing to take the Praxis II for elementary content in the spring and now I wonder how much other math isn't what it was when I was 12.

Sounds like you have a gripe to pick with your teacher.

 

[P Boy]

A negative sign next to a variabe is clearly an operator. A negative sign next to a number is part of the number unless explicitly indicated as an operator.

Unless the negative leads the problem, in which case an understood 0 has been omitted from the beginning of the problem.I hate to admit this smoo, but you have a strong argument that math geeks who have no room for compromise need to explain.Geez - I feel so dirty now...

 

[MrPack]

This alludes back to an earlier post, but what would your answers be for these?

4 x 2³ - 5² =

2 x 3² - 6² =

I get 7 and -18

 

[PC Load Letter]

This alludes back to an earlier post, but what would your answers be for these?

4 x 2³ - 5² =

2 x 3² - 6² =

4*8-25= 7But, had it been presented as -5^2 + 4*2^3 I would've said 25+32=57

But the two should be equal:4 x 2³ - 5² = -5² + 4 x 2³

Left side is 7. Right side is 57.NO, the 2 are not equal.

As mentioned in this earlier post by Iguana, they should be:

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!

OH SNAP! He broke out the commutative property on your ###!

 

[John 14:6]

- 5^2 <> -5^2

I don't think spaces have any meaning in math...

 

[(HULK)]

There is a significant difference between how an interger is treated versus a variable.

In which math system? A variable is a number. It just has not been determined through process what number it is.

A negative sign next to a variabe is clearly an operator. A negative sign next to a number is part of the number unless explicitly indicated as an operator.

 

[Smoo]

-5² + 4 x 2³ = 4 x 2³ + -5²

Now it should be obvious that:

4 x 2³ + -5² = 4 x 2³ - 5² = -7

No no, you've disobeyed the order of operations laws here.You can't convert "... + -5^2" to "... - 5^2" until after you resolve the exponent.

 

[Clayton Gray]

I have come to the conclusion that the way it's written, BOTH sets of answers are correct since it's not written very clearly.

I still say -5 can be the base number here.

That conclusion is wrong, even though it doesn't make sense to you why it is Teachers give students those types of problems SPECIFICALLY to make sure they understand the difference between -5^2 and (-5)^2 , because there is a difference and it's important to know and to remember that they aren't the same. (Although apparently many people can go through their lives oblivious to this and not suffer from it).

Why are they different? Because you, and some math scholars say so?I say there is a difference between -5^2 and -(5)^2.

Why are -5 and 5 different? Because they are defined to be different.Why are square and square root different? Because they are defined to be different.

Why are chair and football different? Because they are defined to be different.

Why are -5^2 and (-5)^2 different? Because they are defined to be different.

-5^2 always equals -25, and (-5)^2 always equals 25.

 

[shadyridr]

What does this equation equal?

-x^2+x=

if x=5?

What does it equal if x=-5 ?

If x=-5 it equals -30 if x=5 it equals -20. According to some people in this thread if x=5 it would equal 30 and if x=-5 it would equal 20.

 

[P Boy]

Its simple.X isn't a set number or defined on its own. -X is defined as the opposite of X.However 5 is a set number and is defined on its own. -5 is also a set number (unless you don't believe in intergers). 5 and -5 are opposites of each other. The difference is that -5 exists in its own right whereas -x does not exist in its own right.

You're kidding, right?x can represent either a positive number, a negative number, or 0. Therefore there is no need for a (-x).

 

[rolyaTy]

A negative sign next to a number is part of the number unless explicitly indicated as an operator.

In Smoo Math maybe, in real math, it's just the opposite.

 

[John 14:6]

No no, you've disobeyed the order of operations laws here.

You can't convert "... + -5^2" to "... - 5^2" until after you resolve the exponent.

I still think they're the same because a space doesn't mean anything in math.

 

[posty]

[QUOTE=']

Please, somebody solve the following problems:

5-*3

12*/4

6+*7

Those don't make sense, right? You don't put two operators in a row?

So why does this make sense?

0--5

The answer to that is clearly 5. You're subtracting -5 from 0, to get 5. Why is that?

Oh right. Because the negative in front of the 5 is NOT an operator! It's PART OF THE NUMBER!

Are these statements true?4 x 2³ - 5² = -5² + 4 x 2³

2 x 3² - 6² = -6² + 2 x 3²

Nope. And you don't even have to understand math to see why. On the left side of both, you've separated the negative operator from the number with a space. On the right you've nestled it in right next to the number with no space separator. Why did you do that? Oh, right, because on the right side the negative sign is being used as part of the number, not as an operator.

I don't think you are right on that Smoo...4 x 2³ - 5² = -5² + 4 x 2³

4 x 8 - 25 = -25 + 4 x 8

32 - 25 = -25 + 32

7 = 7

2 x 3² - 6² = -6² + 2 x 3²

2 x 9 - 36 = -36 + 2 x 9

18 - 36 = -36 + 18

-18 = -18

At least that is what I think and what my wife confirmed (7th and 8th grade math teacher)...

- 5^2 <> -5^2
[/QUOTE]White space doesn't make a difference in this case cause you can write it like...4x2³-5²=-5²+4x2³

That is the same... White space is moot in this case. If you want to make it different, you have to use parenthesis...

 

[MrPack]

What does this equation equal?

-x^2+x=

if x=5?

Applying the principles I have learned in this thread (Using Claytons et al explanations) I get -20

 

[Smoo]

- 5^2 <> -5^2

I don't think spaces have any meaning in math...

Then why use them? They were inserted into the last problem for a reason: to separate operators from numbers. So why did the -5^2 not receive the same space? Because the - isn't an operator in that case.

 

[Ditkaless Wonders]

A negative sign next to a variabe is clearly an operator.  A negative sign next to a number is part of the number unless explicitly indicated as an operator.

Unless the negative leads the problem, in which case an understood 0 has been omitted from the beginning of the problem.I hate to admit this smoo, but you have a strong argument that math geeks who have no room for compromise need to explain.

Geez - I feel so dirty now...

So who should I get to design and engineer my depression in the ground, Smoo or PonyBoy, or both? Up to now I've just been getting by on whatever indentation my massive ### makes.

 

[trout]

http://www.math.com/school/subject2/lessons/S2U2L2EX.html

when I used the calculator linked at the top I got 25 as the answer to -5^2

 

[P Boy]

OH SNAP! He broke out the commutative property on your ###!

 

[Smoo]

What does this equation equal?

-x^2+x=

if x=5?

Applying the principles I have learned in this thread (Using Claytons et al explanations) I get -20

Agreed. In this case you square before negating because the presence of a variable clearly makes the negation an operator.However, the original problem is simply x^2 where x = -5.

 

[Clayton Gray]

Please, somebody solve the following problems:

5-*3

12*/4

6+*7

Those don't make sense, right? You don't put two operators in a row?

So why does this make sense?

0--5

The answer to that is clearly 5. You're subtracting -5 from 0, to get 5. Why is that?

Oh right. Because the negative in front of the 5 is NOT an operator! It's PART OF THE NUMBER!

Not in the case of -5^2.

 

[rick6668]

There is a significant difference between how an interger is treated versus a variable.

In which math system? A variable is a number. It just has not been determined through process what number it is.

A negative sign next to a variabe is clearly an operator. A negative sign next to a number is part of the number unless explicitly indicated as an operator.

A negative sign next to a variable is clearly an operator. A negative sign next to a number is an operator unless explicitly indicated as part of the number.

 

[(HULK)]

Its simple.

X isn't a set number or defined on its own.  -X is defined as the opposite of X.

However 5 is a set number and is defined on its own.  -5 is also a set number (unless you don't believe in intergers).  5 and -5 are opposites of each other.  The difference is that -5 exists in its own right whereas -x does not exist in its own right.

You're kidding, right?x can represent either a positive number, a negative number, or 0. Therefore there is no need for a (-x).

Exactly. Hence -x is defined as the opposite of x because x is not clearly defined.However, -5 does not necessitate that since it is defined in its own right.

 

[shuke]

You can't convert "... + -5^2" to "... - 5^2" until after you resolve the exponent.

You are completely wrong here.

 

[Clayton Gray]

From the Prentice Hall "Middle Grades Math - Tools for Success" Course 2 - 1999 Edition, Page 157:

When you use an exponent with a negative numer as the base, it is important to use grouping symbols to avoid confusion.

Example 3: Simply each expression.

a. (-5)^4 = (-5)(-5)(-5)(-5) = 625

b. -5^4 = -(5*5*5*5) = -625

Well that's all well and good for ^4 problems, but this a ^2 problem.

Damn

 

[rolyaTy]

What does this equation equal?

-x^2+x=

if x=5?

Applying the principles I have learned in this thread (Using Claytons et al explanations) I get -20