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Daughter's math homework (1 Viewer)
- Thread starter MrPack
- Start date
Let's go with this
leaseExcuse
My Dear
Aunt Sally
Multiplication and division are to be done at the same time from left to right. If you leave "My" on its own line, you may be inclined to multiply from left to right and then divide from left to right. Same thing with addition and subtraction.
Ex:
3 * 4 / 2 * 3
Multiplying and dividing from left to right, we get:
3 * 4 / 2 * 3
12 / 2 * 3
6 * 3
18
Multiplying from left to right and then dividing left to right, we get:
3 * 4 / 2 * 3
12 / 2 * 3
12 / 6
2
PC Load Letter
Irregardless.
This thread is rivaling the Myspace Hotties thread in terms of length.
This is madness!!
This is madness!!
A negative in front of whatever means the opposite of whatever.-5 is the opposite of 5I'm on Clayton's side, but I don't think that explanation resolves the ambiguity.The opposite of five squared can be read as:This is the best explanation...I am a math teacher and need to put this through the heads of kids every year. The TI calculator series does it the same way (ie. -5^2=-25). I go through this with kids and ask them what negative 5 squared is and they tell me 25...then I have them type it in and they say their calculator is broken. The easiest way to explain it is just the way Clayton explained it.
(The opposite of five) squared
or
The opposite of (five squared).
Just writing it out as a sentence doesn't solve the problem of where the implied parentheses should go.
-X is the opposite of X
-chair is the opposite of chair
-5^2 is the opposite of 5^2
Yes you we are.
Because we point out mistakes?
Kleck
Footballguy
Quite frankly, it bothers me when folks start to turn to Google and Microsoft when looking to definitions of how we should interpret -5^2. That may sound arrogant, but I hope we can all agree that the established mathematical world community should be the one to turn to in times of confusion like this.
Standardized notation and the order of operations are something that mathematicians don't want to debate. We won't mind educating folks, but after that it starts to become
for us.
If someone chooses not to accept the accepted definition, well, okay. I'm guessing they don't have a very high Erdos number.
Seems that some folks have gained some insight from this thread. Love when that happens on our boards.
Standardized notation and the order of operations are something that mathematicians don't want to debate. We won't mind educating folks, but after that it starts to become
for us.If someone chooses not to accept the accepted definition, well, okay. I'm guessing they don't have a very high Erdos number.
Seems that some folks have gained some insight from this thread. Love when that happens on our boards.
Actually just a guy that clearly hasn't taken math in a long time.Canadian math.Your order of operations has "Equation"? That makes no sense.I went to school in Vancouver. But that's neither here nor there. I learned the same order of operations as you. Our point is that -5 isn't an operation, it's a number.I went through the same school system as you Smoo in the Peg and I didn't learn it this way. It was BEDMAS. I had it ingrained into my head. I always said I would never use any of this stuff in the real world and so far I am pretty much correct in thinking that. Now I find out out not only do I not need to use it but it is wrong? WTF?
Equation
Division
Multiplication
Addition
Subtraction
I think it was supposed to be exponent not equation. labor = labourdefence = defense
offence = offense
case of beer = two four
check = cheque
couch = chesterfield
Canadian english
rolyaTy
You're Heinous
7-x^2=?This poses a question. If x is 2, what is the answer? Is it 3? or is it 10? It's clearly 3 and few would argue with that because they see the minus sign as subtraction and not a negative X. What about -x^2+x^2 =?Using the identities, you can rearrange the equation as: x^2-x^2=?because : -a+b=b-a.Now, if you extrapolate that out, you can only come to the conclusion that:-x^2+x^2=x^2-x^2 therefore(x)^2 - (x)^2 = ZERO.therefore -x^2 has to equal -(x)^2, according to some of the most basic mathematic principles any of us should've learned. Associative distribution? I forget, but maybe Shick! can help me out with the name of those things.
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PC Load Letter
Irregardless.
Couch? Ottoman?
Kleck
Footballguy
I can't argue the point. I've seen math teachers make students feel small. Not saying that you've done that here, but I've seen it happen. The biggest change I underwent as an educator was putting a stop to being judgmental with regard to my students abilities. Some of them suck at math. Its just a fact. I don't think less of them because of it. There are things I don't do so well.Because we point out mistakes?
This is not correct.- 4 + 5^2A negative in front of whatever means the opposite of whatever.-5 is the opposite of 5I'm on Clayton's side, but I don't think that explanation resolves the ambiguity.The opposite of five squared can be read as:
(The opposite of five) squared
or
The opposite of (five squared).
Just writing it out as a sentence doesn't solve the problem of where the implied parentheses should go.
-X is the opposite of X
-chair is the opposite of chair
-5^2 is the opposite of 5^2
is not the opposite of
4 + 5^2.
-4 + 5^2 is 21, but the opposite of 4 + 5^2 is -29.
Steel City
Footballguy
High school math teacher here.I really think the best way to see this is to put a zero in front of the operation like suggested earlier in the tread.If you can agree that 0 - 5^2 is the same as -5^2, then -25 is the only possible answer. Another way to think about it. There is a rule that allows us to change subtraction to addition by "adding the opposite". So, if I have 0 - 5^2, I could change this to addition by making the problem 0 + -5^2, which again is the same as -5^2.edit spelling
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Aussie Cowboy
Footballguy
GB the mathematical world community.
alert
Aussie Cowboy
Footballguy
Almost the same.Actually just a guy that clearly hasn't taken math in a long time.Canadian math.Your order of operations has "Equation"? That makes no sense.I went to school in Vancouver. But that's neither here nor there. I learned the same order of operations as you. Our point is that -5 isn't an operation, it's a number.I went through the same school system as you Smoo in the Peg and I didn't learn it this way. It was BEDMAS. I had it ingrained into my head. I always said I would never use any of this stuff in the real world and so far I am pretty much correct in thinking that. Now I find out out not only do I not need to use it but it is wrong? WTF?
Equation
Division
Multiplication
Addition
Subtraction
defence = defense
offence = offense
case of beer = two four Carton or Slab (Depending on where you were born)
check = cheque
couch = chesterfieldLounge or Lounge chair
Canadian Australian english
No -chair = stand.
Well, Wikipedia and PlanetMath were useless. What this comes down to is whether the "-" is treated as an operator or as part of the number. If it's an operator, it is subordinate to the exponentiation. If it is part of the number, the exponent operates over the whole "-5" as a defined value.Where does one look for the answer to whether the "-" is treated as an operator or as part of a number?
Excel and TI-85 give contrary answers. Several people searched the 'Net, and one person came up with the "Dr. Math" column that said to use parentheses (which seems to be good advice) since the expression was otherwise ambiguous.
I'm sure I did, but seeing as I'm an exeducator it's OK for me to be judgmental.I can't argue the point. I've seen math teachers make students feel small. Not saying that you've done that here, but I've seen it happen. The biggest change I underwent as an educator was putting a stop to being judgmental with regard to my students abilities. Some of them suck at math. Its just a fact. I don't think less of them because of it. There are things I don't do so well.Because we point out mistakes?
Aussie Cowboy
Footballguy
And the rest of this thread isn't?
A negative in front of whatever term means the opposite of whatever term.In that problem, the negative is in front of the 4. The 5^2 is a different term as it is separated by the addition sign.This is not correct.- 4 + 5^2A negative in front of whatever means the opposite of whatever.-5 is the opposite of 5I'm on Clayton's side, but I don't think that explanation resolves the ambiguity.The opposite of five squared can be read as:
(The opposite of five) squared
or
The opposite of (five squared).
Just writing it out as a sentence doesn't solve the problem of where the implied parentheses should go.
-X is the opposite of X
-chair is the opposite of chair
-5^2 is the opposite of 5^2
is not the opposite of
4 + 5^2.
-4 + 5^2 is 21, but the opposite of 4 + 5^2 is -29.
Yes, I'm rusty with my explanations.
And the rest of this thread isn't?
Hard to imagine that seven pages of negativity would be so
.
Smoo
Fear the Beaver
You're a hater. Negative numbers have as much right to individual identity as positive numbers. You're like a medieval land baron, forcing negative numbers to take the identity of their positive overlords. Or like some Third Reich demon lining up all the negative numbers to be branded with their negative operators for easy sorting into numerical Auschwitz.This kind of anti-negative bigotry will not be tolerated.We're right here, dude.
-5 is a self-contained unit and shall be afforded all of the rights and privileges of its positive brethren. Down with you, bourgeois pig, the proletariat are rising.
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NCCommish
Footballguy
Power to the negatives!You're a hater. Negative numbers have as much right to individual identity as positive numbers. You're like a medieval land baron, forcing negative numbers to take the identity of their positive overlords. Or like some Third Reich demon lining up all the negative numbers to be branded with their negative operators for easy sorting into numerical Auschwitz.This kind of anti-negative bigotry will not be tolerated.We're right here, dude.
-5 is a self-contained unit and shall be afforded all of the rights and privileges of its positive brethren. Down with you, bourgeois pig, the proletariat are rising.
Smoo
Fear the Beaver
I have a dream!Power to the negatives!You're a hater. Negative numbers have as much right to individual identity as positive numbers. You're like a medieval land baron, forcing negative numbers to take the identity of their positive overlords. Or like some Third Reich demon lining up all the negative numbers to be branded with their negative operators for easy sorting into numerical Auschwitz.This kind of anti-negative bigotry will not be tolerated.We're right here, dude.
-5 is a self-contained unit and shall be afforded all of the rights and privileges of its positive brethren. Down with you, bourgeois pig, the proletariat are rising.
Rooster
Footballguy
I appreciate your and Clayton's input into the situation. Despite the fact that I'm not convinced it's the logical way to approach it, I'll concede that it is the standard based on the opinions of many math teachers here and hopefully I'll remember that in the future. I doubt it'll make a difference because 1) I'm not a teacher and 2) I always use parenthesis to avoid confusion.We're right here, dude.
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.
Awesome discussion here tonight, and I'm learning a lot. I am going to make sure to have her read some of this stuff too.
Swapster
Footballguy
I haven't read the entire thread, but it seems that the mathematicians have determined the answer to be -25, which is contrary to what I thought. After reading the first few pages of "old math" (me) vs. "new math", I checked with my 8th grade honor student. He has been taught -5^2 = -5 * -5 = 25. I've been thinking in computer terms so long that that is how I interpret all math problems, how a computer would. If I put this code into a program it returns 25. However, if I change it to 0-5^2 it returns -25. The question to me then is, does "negative x" always mean "zero minus x"?
Serenity Now
Footballguy
Absolutely. What a stupid change to the rules. That was supposed to be the beauty of math. It follows rules. Change is bad.
Swapster
Footballguy
But wait a minute!^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.
If you put (0-5)^2 in excel you get 25, the same as you do when you enter -5^2. By changing -5^2 to 0-5^2 you are changing the equation. You are not multiplying -5 * -5 you are multiplying 5*5 then subtracting it from 0. That's a different equation altogether.
rolyaTy
You're Heinous
I understand what he's saying there, but if the person meant to write negative five squared, that doesn't answer the question because the negative sign isn't meant to be the opposite of 5^2, but rather the opposite of five, squared.Maybe that's a good way to look at it. If you need a comma to convey your true meaning if you were saying it to someone, you need parentheses to show that...but if you read it without a comma (ie. the opposite of five squared) then you have to find out what 5 squared is first before you take the opposite.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.
Awesome discussion here tonight, and I'm learning a lot. I am going to make sure to have her read some of this stuff too.
So to me, a math equation doesn't have commas (parentheses) unless they are explicitly stated. So -5² + 4 x 2³ = is read "the opposite of five squared plus four times two to the third" and you apply the order of operations to how that is read.
Were there any like this: (-5)^2?
For those saying the parentheses make it more clear, I am 100% in agreement.
Kleck
Footballguy
As the founding father of the negative post club, I can comfortably say you're barking up the wrong tree.You're a hater. Negative numbers have as much right to individual identity as positive numbers. You're like a medieval land baron, forcing negative numbers to take the identity of their positive overlords. Or like some Third Reich demon lining up all the negative numbers to be branded with their negative operators for easy sorting into numerical Auschwitz.This kind of anti-negative bigotry will not be tolerated.We're right here, dude.
-5 is a self-contained unit and shall be afforded all of the rights and privileges of its positive brethren. Down with you, bourgeois pig, the proletariat are rising.
bentley
Footballguy
I hope this doesn't come out wrong, but I have never loved you as much as I love you now.You're a hater. Negative numbers have as much right to individual identity as positive numbers. You're like a medieval land baron, forcing negative numbers to take the identity of their positive overlords. Or like some Third Reich demon lining up all the negative numbers to be branded with their negative operators for easy sorting into numerical Auschwitz.This kind of anti-negative bigotry will not be tolerated.We're right here, dude.
-5 is a self-contained unit and shall be afforded all of the rights and privileges of its positive brethren. Down with you, bourgeois pig, the proletariat are rising.
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.)
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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.
I hope he hasn't been taught that.
Do you have a graphing calculator?
