cstu
Footballguy
1860's?IIRC, I was taught this stuff in the early to mid 60s. The way I was taught was that -5^2 == -25
1860's?IIRC, I was taught this stuff in the early to mid 60s. The way I was taught was that -5^2 == -25
This isn't about geography or teaching style.-5² = 25 everywhere on the planet.So MrPack, Bewdude and I were all taught the same way, and we're decidedly not from the same geographic area. So I don't know where roly went to school, but he's either much younger, or his district was way ahead of its time.
When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
It's not asking for the square of 5. It's asking for the square of negative 5.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
Whereas some would argue that "-5" is a self-contained integer, a stand-alone unit. That the - is simply part of the number.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
(-5) squared is 25.- (5 squared) is -25.-5 squared is 25.
and negative 5 is negative 1 times 5It's not asking for the square of 5. It's asking for the square of negative 5.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
The -5 is a negative integer. We are squaring it.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
Hmm. I see the "-" as an operator.Whereas some would argue that "-5" is a self-contained integer, a stand-alone unit. That the - is simply part of the number.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
I do about as technical stuff as you can get. If you polled all 30 engineers in my building every one of them would say the teacher is wrong and Otis is dead on.Without the parenthesis in there at all "-5" is a self contained negative integer. There is no ambiguity here.This isn't about geography or teaching style.-5² = 25 everywhere on the planet.So MrPack, Bewdude and I were all taught the same way, and we're decidedly not from the same geographic area. So I don't know where roly went to school, but he's either much younger, or his district was way ahead of its time.
-(5²) is a different story.
0 - 5^2 ╘ -5^2edit to add the weird symbol above is supposed to be "not equal to"As a math geek, let me see if I can help you out. First, there is no such thing as "old math" or "new math". Math is math and the rules for doing calculations haven't changed in eons. My experience is that people who claim that "new math" is too confusing just don't remember things as well as they think they do. This is coming from a 35 year old that has been accused of having Alzheimer's by his wife. Let's see if I can clear this up a bit. Another way to look at this is to add a 0 at the beginning of the equations. Adding a zero will not change the value of the calculations but does clearly show that -5^2 = -25 and -6^2 = -36:
0 - 5^2 + 4 X 2^3 = -5^2 + 4 X 2^3 = -7
0 - 6^2 + 2 X 3^2 = -6^2 + 4 X 2^3 = 18
Now, all that said, when I first looked at it and added it up in my head, I rattled off 54 and 57 and figured the first post was someone being funny. Then I looked again and realized I just read it wrong.
Edit to add bolded part...
Yes it is, write it this way if you want:0 + -5^2 = -5^2 = -250 - 5^2 ╘ -5^2As a math geek, let me see if I can help you out. First, there is no such thing as "old math" or "new math". Math is math and the rules for doing calculations haven't changed in eons. My experience is that people who claim that "new math" is too confusing just don't remember things as well as they think they do. This is coming from a 35 year old that has been accused of having Alzheimer's by his wife. Let's see if I can clear this up a bit. Another way to look at this is to add a 0 at the beginning of the equations. Adding a zero will not change the value of the calculations but does clearly show that -5^2 = -25 and -6^2 = -36:
0 - 5^2 + 4 X 2^3 = -5^2 + 4 X 2^3 = -7
0 - 6^2 + 2 X 3^2 = -6^2 + 4 X 2^3 = 18
Now, all that said, when I first looked at it and added it up in my head, I rattled off 54 and 57 and figured the first post was someone being funny. Then I looked again and realized I just read it wrong.
Edit to add bolded part...
I would agree that these were written as trick questions and a good teacher would give partial credit for 54 and 57 unless they were just trying to be a ####.I would say:
-5^2 = -5 x -5 = 25
-1(5^2) = -1(5 x 5) = -1(25) = -25
-(5^2) = -(5 x 5) = -(25) = -25
I agree with Smoo in that I see -5 as a stand alone integer. I was in high school in the mid 90s and math was a strong point of mine. I say that given the way the teacher is expecting it to be worked out that it's either a very poorly written question or a trick question. In the case of the latter, I would expect that the teacher made a point during instructional time on how to interpreit -5^2.
If I were to add zero to the begining of the equation I would see:0 + -5^2 + 4 X 2^3As a math geek, let me see if I can help you out. First, there is no such thing as "old math" or "new math". Math is math and the rules for doing calculations haven't changed in eons. My experience is that people who claim that "new math" is too confusing just don't remember things as well as they think they do. This is coming from a 35 year old that has been accused of having Alzheimer's by his wife. Let's see if I can clear this up a bit. Another way to look at this is to add a 0 at the beginning of the equations. Adding a zero will not change the value of the calculations but does clearly show that -5^2 = -25 and -6^2 = -36:
0 - 5^2 + 4 X 2^3 = -5^2 + 4 X 2^3 = -7
0 - 6^2 + 2 X 3^2 = -6^2 + 4 X 2^3 = 18
Now, all that said, when I first looked at it and added it up in my head, I rattled off 54 and 57 and figured the first post was someone being funny. Then I looked again and realized I just read it wrong.
Edit to add bolded part...
Especially if you do this in any kind of real world situation.I think anybody who writes the expression (no matter which interpretation they intend) is nuts for not using parentheses.
And in writing it the way you did, you should see that the correct answer is -7 and 18. I still think it all boils down to the teacher being a butthead and trying to trick people up by making it somewhat ambigious. As previously posted anyone that needs to create such an equation and needs it to be calculated correctly would include () regardless of their meaning to prevent any possibility of error.If I were to add zero to the begining of the equation I would see:0 + -5^2 + 4 X 2^3As a math geek, let me see if I can help you out. First, there is no such thing as "old math" or "new math". Math is math and the rules for doing calculations haven't changed in eons. My experience is that people who claim that "new math" is too confusing just don't remember things as well as they think they do. This is coming from a 35 year old that has been accused of having Alzheimer's by his wife. Let's see if I can clear this up a bit. Another way to look at this is to add a 0 at the beginning of the equations. Adding a zero will not change the value of the calculations but does clearly show that -5^2 = -25 and -6^2 = -36:
0 - 5^2 + 4 X 2^3 = -5^2 + 4 X 2^3 = -7
0 - 6^2 + 2 X 3^2 = -6^2 + 4 X 2^3 = 18
Now, all that said, when I first looked at it and added it up in my head, I rattled off 54 and 57 and figured the first post was someone being funny. Then I looked again and realized I just read it wrong.
Edit to add bolded part...
0 + -6^2 + 2 X 3^2
I believe this boils down to what Smoo and Maurile noticed about seeing -5 as a stand alone integer vs as an operator. At best, the problem is poorly written. MrPack's daughter got the problem wrong not because she couldn't do math or didn't understand the order of operations, but based on a technical misinterpreitation. If the lesson here was order of operations, the teacher did a bad job IMHO. If the point of the lesson was to treat a negative number as a positive number with an operator (which I'm not convinced is correct), then I can buy it.
So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.Hmm. I see the "-" as an operator.Whereas some would argue that "-5" is a self-contained integer, a stand-alone unit. That the - is simply part of the number.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
I don't see it that way. I'll work the first one out:0 + -5^2 + 4 X 2^3And in writing it the way you did, you should see that the correct answer is -7 and 18. I still think it all boils down to the teacher being a butthead and trying to trick people up by making it somewhat ambigious. As previously posted anyone that needs to create such an equation and needs it to be calculated correctly would include () regardless of their meaning to prevent any possibility of error.
-5 is a stand alone integer IMO. If it were meant to be an operator the () should have been used. Case closed.If I were to add zero to the begining of the equation I would see:0 + -5^2 + 4 X 2^3As a math geek, let me see if I can help you out. First, there is no such thing as "old math" or "new math". Math is math and the rules for doing calculations haven't changed in eons. My experience is that people who claim that "new math" is too confusing just don't remember things as well as they think they do. This is coming from a 35 year old that has been accused of having Alzheimer's by his wife. Let's see if I can clear this up a bit. Another way to look at this is to add a 0 at the beginning of the equations. Adding a zero will not change the value of the calculations but does clearly show that -5^2 = -25 and -6^2 = -36:
0 - 5^2 + 4 X 2^3 = -5^2 + 4 X 2^3 = -7
0 - 6^2 + 2 X 3^2 = -6^2 + 4 X 2^3 = 18
Now, all that said, when I first looked at it and added it up in my head, I rattled off 54 and 57 and figured the first post was someone being funny. Then I looked again and realized I just read it wrong.
Edit to add bolded part...
0 + -6^2 + 2 X 3^2
I believe this boils down to what Smoo and Maurile noticed about seeing -5 as a stand alone integer vs as an operator. At best, the problem is poorly written. MrPack's daughter got the problem wrong not because she couldn't do math or didn't understand the order of operations, but based on a technical misinterpreitation. If the lesson here was order of operations, the teacher did a bad job IMHO. If the point of the lesson was to treat a negative number as a positive number with an operator (which I'm not convinced is correct), then I can buy it.
Smoo, we're right on this one. I'm really by the people that see it another way. It's almost like they can't see that numbers can be negative.So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.Hmm. I see the "-" as an operator.Whereas some would argue that "-5" is a self-contained integer, a stand-alone unit. That the - is simply part of the number.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
I agree. There are negative numbers. Negative numbers should not need parentheses in order to have their identities understood. It should be the other way around.Smoo, we're right on this one. I'm really by the people that see it another way. It's almost like they can't see that numbers can be negative.So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.Hmm. I see the "-" as an operator.Whereas some would argue that "-5" is a self-contained integer, a stand-alone unit. That the - is simply part of the number.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
There are definitely negative integers. Negative five, for example, is a negative integer. You can write negative five as -5, (0-5), -1*5, 20-25, -1/((-5)^(1/2)), ((5^3)*(5^-2))/-1, etc.So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.
This seals it. If "-" is only an operator and not part of a number then the number i cannot exist.So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.Hmm. I see the "-" as an operator.Whereas some would argue that "-5" is a self-contained integer, a stand-alone unit. That the - is simply part of the number.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
Yes, I think there needs to be an absolute way of expressing any single number as a self-contained unit, free of operators. There are all those other ways of expressing it with operators, sure, but there needs to be a way without one, too. For negative numbers, that's done by putting a negation symbol in front of it.Otherwise, why can't we just answer math problems like this?There are definitely negative integers. Negative five, for example, is a negative integer. You can write negative five as -5, (0-5), -1*5, 20-25, -1/((-5)^(1/2)), ((5^3)*(5^-2))/-1, etc.So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.
It's just that I see all of those different ways of writing it as expressions with operators, including the first one.
But if you see the "-" in "-5" as just being part of the numeral instead of being an operator, then -5^2 would be 25.
Of coarse, because those items have brains of their own and are never wrong...Personally I would have a hard time not giving credit to a student for either answer. If I were coding this for any reason I would use () to specify my meaning. If you go to order of operation in your version of 0 + -5^2 + ..., which you agree means the same as -5^2 + ... then I think you have to calculate it as 0+ -(5^2) + ... and get -7 but I also don't really think it is worth the arguement.If -5^2 were meant to be -25 and that interprietation was standard, I would think Excel, Google, and Scientific Calculators would identify it as such.
Assuming -5 to be -1(5) to me is akin to saying 25 = 10, because I see that as 2(5). I think if someone wrote a problem saying 25 - 10 and expected the answer of 0, they'd be in the wrong. I think if you're counting on a nonstandard interpreitation (and based on Google, Excel, and Scientific Calculators it seems nonstandard) that it's your responsibility to make it clear through the use of parenthesis.There are definitely negative integers. Negative five, for example, is a negative integer. You can write negative five as -5, (0-5), -1*5, 20-25, -1/((-5)^(1/2)), ((5^3)*(5^-2))/-1, etc.So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.
It's just that I see all of those different ways of writing it as expressions with operators, including the first one.
But if you see the "-" in "-5" as just being part of the numeral instead of being an operator, then -5^2 would be 25.
Interesting point, but it can be easily countered by invoking an implied parenthetical. (-1)^0.5This seals it. If "-" is only an operator and not part of a number then the number i cannot exist.So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.Hmm. I see the "-" as an operator.Whereas some would argue that "-5" is a self-contained integer, a stand-alone unit. That the - is simply part of the number.When I was in school, nobody would have written this problem without clearing up the ambiguity with parentheses.But if there were no parentheses, I would go by the order of operations (which is arbitrary convention). Exponents come before multiplication. The "^2" is an exponent. The "-" is multiplication. So I'd square the five before making it negative.New math says to think of "-5" as "5 x (-1)". So when you see "-5^2", you're actually seeing "-1 x 5^2".
Actually, 25-10 is 521. 2(5) - 1(0) = 5(2)(1)Assuming -5 to be -1(5) to me is akin to saying 25 = 10, because I see that as 2(5). I think if someone wrote a problem saying 25 - 10 and expected the answer of 0, they'd be in the wrong. I think if you're counting on a nonstandard interpreitation (and based on Google, Excel, and Scientific Calculators it seems nonstandard) that it's your responsibility to make it clear through the use of parenthesis.There are definitely negative integers. Negative five, for example, is a negative integer. You can write negative five as -5, (0-5), -1*5, 20-25, -1/((-5)^(1/2)), ((5^3)*(5^-2))/-1, etc.So what you're saying is that there's no such thing as a negative integer, only a negative operation performed on a cardinal number? I disagree. I will fight to the death for the rights of negative integers.
It's just that I see all of those different ways of writing it as expressions with operators, including the first one.
But if you see the "-" in "-5" as just being part of the numeral instead of being an operator, then -5^2 would be 25.
I do but then again I already confessed to being a math geek. Also when I see the number 1, I always think 34938475950009987663^0.i find it hard to believe that anyone could look at -5 and think -1 * 5. when you see the number 7 do you think 7^1?
I see error in your math. Here's an example6^2 = 36Of coarse, because those items have brains of their own and are never wrong...
Personally I would have a hard time not giving credit to a student for either answer. If I were coding this for any reason I would use () to specify my meaning. If you go to order of operation in your version of 0 + -5^2 + ..., which you agree means the same as -5^2 + ... then I think you have to calculate it as 0+ -(5^2) + ... and get -7 but I also don't really think it is worth the arguement.
The point should be reiterated that the teacher was obviously trying to be ambigious and/or trying to prove a point instead of just teaching the rules.
I think the standard way to write it would be to use parentheses no matter which interpretation you favored.If I were a calculator, I might reject "-5^2" as a syntax error. But if I were a calculator I'd probably be a real *******.I think if you're counting on a nonstandard interpreitation (and based on Google, Excel, and Scientific Calculators it seems nonstandard) that it's your responsibility to make it clear through the use of parenthesis.
Looks like it was photocopied from a text.did the teacher write the problem down or is it in a textbook?