-1 squared minus (- 1) squared =? A BASIC Math problem MANY will get WRONG!
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- Опубликовано: 28 фев 2024
- How to simplify a numeric expression with positive and negative numbers, subtraction and powers using the order of operations - PEMDAS.
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![[(4 - 3 squared -( - 9)] / (1 - 3)cubed =? Order of Operations Practice (PEMDAS)](http://i.ytimg.com/vi/g04wj7mDNlQ/mqdefault.jpg)
looking at this, this is about where the square applies, for the -1² it only applies to the 1, so that would be -1, but in the case of (-1)² it applies to the -1 which gives a positive 1, so this would be -1 - 1 = -2
Exactly. Not very difficult. :)
The odd thing is that if you used Excel and entered that same expression, the first minus has higher precedence than the exponentiation, thus the answer you would get is 0.
Yet Windows calculator gets it right. Someone at Microsoft needs to have a word with someone at Microsoft.
@@dazartingstall6680 At this stage of the game, there is no way they will change Excel to have the power have higher precedence tha the minus. Microsoft would assume (and probably correctly) that a lot of Excel formulas would be broken if they changed the way they did the math.
I am sorry but it doesn’t make sense as: minus 1 squared => minus 1 times minus 1 => -1 times -1 = 1.
So 1-1=0. A should be the correct answer.
@@TheSillybits The first term should be treated as zero minus the square of one. We could express it this way.:
−(1^2)
which expands to:
−(1×1)
which yields:
−1
The second term expands to:
(−1)×(−1)
which yields:
1
So we end up with:
−1−1 = −2
Edit: if I'm going to explain it, I may as well explain the "why" along with the "how." Just saying "we should" feels like a cop-out. So:
−x, with the minus sign just hanging there with no explicit previous term for x to be subtracted from, is implicitly preceded by a zero:
0−x
So let's work the problem "zero minus two-squared" I'm using two rather than one for reasons having to do with the avoidance of confusion. Yes, I've been here before. 😊 The principle is exactly the same though.
0−2^2
As, Pemdas and Bodmas, the gods of arithmetic, decreed, we deal with exponents before subtractions, so:
0−4
Now we deal with the subtraction:
0−4=−4
And that's why −x^y yields a negative number.
Depends on the calculator. Business calculators do not use PEMDAS
Thank you for what you are doing. You are helping A lot of us adults at The Excel Center adult high school in Springdale, AR.
Thanks to previous videos and having made the mistake once I can now say that this problem was easy.
Learning from our mistakes is part of the process. :)
I have one question. What do you think of the new math? I personally think it is very dumb I was needing to refresh my math skills and was using some online resources. I couldn't figure out what they were teach8ng.
c. (-2)
Which software you are using to teach ?
when the negative symbol isn't in parentheses with the number you're squaring, that's the same as saying "Negative, x squared" , not "negative x, squared"
So -1^2 is negative (1^2) = -1, not (negative 1)^2 +1
So -1 - 1 = -2
On that basis he should write {+1} squared so that we know it is not [-1} squared if need be
-1 squared is always 1
@@thenetsurferboy what? no, the 1^2 has implied brackets, so -1^2 is -(1^2), which is just -(1) = -1
Very nice licture
when writing computer code and when I input this equation the computer WILL GET IT RIGHT! But was it what I, MYSELF, expected and/or desired ? There a difference between:
-(1^2) = -1
and
(-1)^2 = +1
in both cases I also know what the answer is. The problem, here, is I don't readily understand:
-1^2
When I do a Google search of
-1^2
the response is an immediate
-(1^2) = -1
meaning the computer clarified the question....
Furthermore, when I write such equations I will ALWAYS employ parentheses to PREVENT confusion.
I understand there are those who seek to educate by presenting confusing problems. I.E. create UNNECESSARY ambiguity to test ability.
Yeah, I mentioned that Excel computes this differently than what was presented in the video.
at 7:40. John gives a decent explanation of how I think about it:
-1^2
means -1*1^2 = -1(1)(1)
=-1
while (-1)^2 means (-1)(-1) =1
edit _ saw Paul' post and I had Excel already open and he's right Excel outputs 0.
I tried
(-1)*(1)^2-(-1)^2 which gave -2
I think it is struggling with the implied -1 at the start.
@@vespa2860 I've not done Excel in forever.. but my experience then was Excel doesn't make mistakes... but in this case apparently it does.
Regardless, I just promote that there's less confusion if parentheses are always used. ALWAYS AND FOREVER!
My default answer is 0, but that is assuming the -1 is negative one and not minus one...
You are correct
My human computer came up with zero however, my little Sharp EL-501X agrees with you Mr.Math Man.
Didn't get me this time. This is why I use these refreshers.
What is this math style used for in life. What job would this math be useful for?
A teacher
Ans. 0
Of course it is 0
Using 1 as the base makes it so much more complicated. If we did the same problem using 4 as the base instead of 1 would the answer be -32?
Yes
Good
Considering I haven't done this kind of math regularly since a couple of years prior to Panic at the Disco, I feel pretty good!
I originally got 0, not taking the parentheses into account.
A teacher that teaches to think from the multiple answers forward, instead of solving the problem, is not a teacher.
Very True.
He is an EDUCATOR!!!
super easy -1^2 is NOT (-1)^2 so there for we just square the first number and keep the negative sign. Now for the second part the () is used to show the negative 1 is being squared with the negative sign.
This means the problem is actually -1 + -1 which is like saying I owe my friend one dollar then another friend reminded me I owe them a dollar as well. So I owe a total of 2 dollars. Or -2. (Simplest way to relate to negative numbers when they are as basic as this is to think of it as money. Example I owe the government $5000 in back taxes, but I gave them $4000 when I sold my old car. This means I still owe them $1000. This can be written as either -5000 + 4000, or 4000 - 5000. the important think is to keep track of where the sign is. Also if you have two negative numbers like -5 and -3 you can think of it as -5 + -3. Remember when adding and subtracting if the signs are the same you add and keep the sign if the signs are different you subtract and keep the sign of the bigger number.)
There are several things that break PEDMAS/BEDMAS - implied addition, the solidus and confusion regarding the binary operator minus (-) versus the unary operator denoting a negative number (-) (even more difficult when the exact same glyph is used.) The equation above is ambiguous because the leading '-' could be a minus (i.e. 0 - 1^2 - (-1)^2) or a unary negation -1^2 - (-1)^2. When there is no number before, a unary negation is implied, but it is not definitive. This is why many people will get zero. Also, there is NO governing body when relating to math equations, and while PEDMAS/BEDMAS has its religious followers, it is not definitive, and care should be taken to understand the meaning or reason behind the equation to avoid mistakes. A more complete standard would be the C operator precedence charts. GEMS (Groupings, Exponents, Multiplication or Division, Subtraction or Addition) is another competitor. TLDR; The author's intent is what defines the equation - this equation was written to be ambiguous. Keep up the good work! 😉
This expression is unambiguous.
The issue with interpreting -1² is not about whether the - is a binary subtraction operator or a unary negation operator. Plainly it is not a binary operator.
The issue is whether it's a unary negation operator, in which case -1² equals -1, or it's a character in the numeric literal "minus one", in which case -1² equals -1.
And the convention we use is that it's a negation operator, not a character in a numeric literal. This keeps the notation consistent with things like -x² and -(1+2)² where the - symbol cannot be anything other than a negation operator.
If the - symbol in -1² was a character in the number "minus 1" then the answers to the questions
"What is -1²?"
and
"What is -x² for x=1?"
would not be the same. Which would be a bit weird.
Mr. Math teacher, I haven't seen this since 1999 when I was a senior in high school. But I guessed A because I thought negative 1 to 2nd power=1 so I got 1-1=0
The answer is A, not C. You do no need to encapsulate -1 in parenthesis if it is the leading term and it is not preceded by another term. You do not assume that there is a 0 in front of the minus sign, which is what you are doing here. -1^2 is equivalent to (-1)^2 You need the parenthesis around the second -1 because it is preceded by an operator and another term. If the leading term was supposed to be interpreted as -(1 * 1) then it would have been written -(1)^2. Were that the case, you would be correct.
-(1)² and -1² are exactly the same. Putting parentheses around just the 1 changes nothing.
The - symbol in -1² is the unary negation operator. That has lower precedence than exponentiation and so -1² means "take the negative of 1²" not "calculate the square of -1".
@@gavindeane3670 Yeah, we're going to have to disagree here. -1 is negative 1. it is a signed number, one less than zero. It doesn't require being placed in parenthesis in order to count as the sign of the number. So, -1^2 is -1 * -1 or 1. -(1)^2 is not the same, as the exponent is higher precedence than the negation. The 'unary negation operator' is, by convention, how we denote a negative number. If the minus sign were not coupled with the numbers it negates, ther would be no signed numbers, only positive numbers that were understood to be nagated. Every use of them would need to pass a pemdas check and there would be no imaginary numbers because the radical sysmtol has a higher order precedence than the negation, so i would = -1, not the Sqrt(-1), as it should be.
@@llywyllngryffyn8053 There are two ways you can parse the notation -1. The distinction is perhaps quite subtle because in many contexts it makes no difference, but in this context it’s critical.
You can read the notation -1 as a single thing: the number “minus one”, which requires two characters to write it. By that interpretation, the notation -1² contains two separate entities: a negative number followed by a superscript 2 for squaring. And so -1² would involve a single mathematical operation. It would mean “calculate the square of -1” so it would equal 1.
Or you can read -1 as a positive number preceded by the negation operator. In that case the notation -1² contains three separate entities: a negation operator then a positive number then a superscript 2 for squaring. By this interpretation, -1² involves two separate mathematical operations. As you have correctly noted, exponentiation has higher precedence than negation, so by this interpretation -1² means “take the negative of 1²” and it equals -1.
Given this potential confusion, we cannot use the notation -1² unless we have a convention for which interpretation to use. And we do. You are reading it the first way but the standard convention is that it is read the second way - and for good reason. This convention keeps the notation consistent with things like -x² and -(1+2)² and indeed your example of -(1)², where the - symbol cannot be anything other than the negation operator.
If -1² meant “calculate the square of -1” then the answers to the questions
“What is -1²?”
and
“What is -x² for x=1?”
would not be the same. Which would be a bit weird.
@@gavindeane3670 Again, I have to disagree with some of what you have said. Your final statement, for one. -1^2 and -x^2 where x=1 are identical. Substitution of the value of x is not an operation that has an order of precedecne in the PEMDAS list. If x=1 then -x = -1. -(x) also = -1 except that the parenthesis must be evaluated. Since there is no other operation going on, the result is the same. However, -x^2 and -(x)^2 are not identical. It might be clearer if we rewrote the first one as (-1)^2 but it isn't necessary. The 'unary negation operator' is the same as the 'minus sign' when writing a negative number. As you said in 'the first interpretation' they are bascially one thing with two characters becasue we don't have another way, in our number system, of denoting negative numbers.
@@llywyllngryffyn8053 I think this statement is the root of the misunderstanding: “The 'unary negation operator' is the same as the 'minus sign' when writing a negative number”
The - character used as a sign indicator when writing negative numbers and the negation operator are completely different things. I think that point is not always understood, because the distinction is of no consequence in many contexts. When you write -1 in isolation, it makes no difference at all whether you think of that as writing a negative number that requires two characters, or a positive number that requires one character with an operator in front of it.
Much of the time it doesn’t matter within the context of a larger expression either. For example, -1+2 or -1×4 or the latter part of the expression in this video (-1)². In all of those expressions it makes no difference whether the - symbol is the sign character in a negative number, or an operator preceding a positive number. It’s not something you need to think about and many people probably don’t even appreciate the distinction exists.
But with -1² the distinction is critical. It makes all the difference in the world. Performing a single operation on a negative number is completely different to performing an operation on a positive number and then performing another operation on the result.
-1² and -x² where x=1 are indeed identical. The result of both is -1. In -x² the - symbol cannot be anything other than a negation operator. In -1² the - symbol *could* be something else. It *could* be a character in a negative number. But for consistency we don’t treat it as that. We treat it as a negation operator in front of a positive number.
-x² and -(x)² are identical. Those parentheses have no effect whatsoever. They are completely redundant visual clutter. Anyone who is competent with school level algebra will know that a quadratic with coefficients -1, 1 and 2 is not written as -(x)² + x + 2. It is simply written as -x² + x + 2. And they will know that when x = 1 that expression evaluates to 2 because the -x² bit is -1 not 1.
0
-1^2-(-1)^2=1-1=-1 (x+1x-1)
1-1=0
With 2 negative you add, ...-, + rule
-1-1=-2 ,So answer is (c)
a
Everything is like,a riddle and a apuzzle,at least 'fun'
C-2
C. -2
A
a) 0
You TAUGHT Mathematics? In PUBLIC School? In the same manner as you did in this video? EXPLAINS A LOT.
The state of the world.
-2
Many will get wrong”. hah! A false come-on!
got it -2 thanks for the fun
I disagree with the your interpretation of the first part. -1 squared should be -1 x -1. Not discount the negative sign and call it - ( 1 x 1 ). First part is 1. Then subtract positive 1 . Therefore the answer is zero.
-1² does not mean "calculate the square of -1". It means "take the negative of 1²".
The exponentiation has higher precedence than the negation.
-1
Zero 0
a. 0
I still don't understand why -1 squared is not -1 x -1. Why is it -1 x 1
After reading @chifghfh1949 's reply, I think I understand the very subtle, yet very important, distinction. I'll forget in a year... at 66 years old my brain is -x squared (rounded down),
He is wrong
So isn’t -1 x -1 = +1?
Isn’t it +1 (-) +1? Isn’t the answer 0?
The first 1 isn’t in parentheses so the squaring of the 1 wouldn’t include the negative sign. The second 1 is in parentheses with the negative sign so it’s (-1)x(-1). So we end up with -1 - 1 which equals -2.
Read what you wrote
You are talking crap. -1 was and always will be -1, a number
So you square it and get +1@@Ron_DeForest
I do math when I have to accomplish something, not to prove that I can.
0 is the answer
c) -2
1-1=0=-1
My first response was 0. But after looking at it further I decided -2. Now time to check.
D) 2
NO
2
Got me on this one, the first term got me, it should be -1, so it is -1- 1 = -2
2, I think?
What a complete BS. 0, and do not listen to the man, just solve the problem.
C) -2
YOU MAKE THINGS BOARING
you talk too much
5 seconds mental problem
@dhtyler. We love him teaching us math,so go away? Nobody is forcing you to watch his very helpful math videos!
Longer they talk more financial value given by RUclips.
Shakespeare said:
“All the work’s a stage.”
I say: These days,
“All the world’s a WHORE.”
His channel works with the assumption you have extremely basic math knowledge so the describes everything.
Does he think they do not go to school?
The lack of extreme basics on all similar posts astounds me@@Ron_DeForest
Why use this crazy and bad rule. Why doesn't PEMDAS mean
P
E
MDA
S
or
PE
MDA
S
Why is it
P
E
MD
AS
?
The rule itself gives no reason at all for that choice!
M and D are equal because they are the same thing. Division is really just multiplication by the reciprocal.
Similarly, subtraction is really just addition of the negative.
@@gavindeane3670 The point is that if you say that M and D are equal but that you can't see that in the rule. In PEMDAS M comes before D and that makes it confusing. That's why PE(MD)(AS) is a more correct way to write the rule.
Students often say If M and D have to be performed in the order in which they appear why is M before D in the rule? The rule suggests something else than that M and D are of the same "level". And that's why the rule is confusing for a lot of students. Using parenthesis prevents that.
@@henkhu100 Teaching students the rules instead of teaching stupid acronyms would also prevent that confusion.
The rules are not complicated and personally I think all the acronyms should just get in the bin. But if you want to use an acronym for this stuff then the 4 letter variations like PEMA are better for exactly this reason.
-1 squared is just badly written out. Should be -(1 squared).
He wrote -1 squared
= 1
Not what he says
Teacher is wrong. He confused negative sign with subtraction. The negative sign is inherent to the number. The negative sign is not an operator.
By definition a = (a)
-1^2 -(1x1)
I do not think so
I agree. When I was taught this back about 1965 zero would have been the correct answer as the first negative sign would be part of the number, not an operator. To get the answer he did it should have been written: -(1^2)- (-1)^ to show the negative sign was applied to the already squared number.
@@richdiddens4059He's telling us what the convention is now. So he's doing it correctly.
It is an operator.
There are similar constructs like -(1+2)² and -x² where the - cannot be anything other than a negation operator, so for consistency that's how it's treated in -1² as well.
you did not explain that very well, sorry. Quit saying it just the opposite, That is confusing. Just to the exercise win staright forware ways. you did a poor job on this one. this iwas the worst explanation ever
I give up
This is rubbish. 1i-1i=0 where i = square root of -1.
c.
-1- 1=-2
The subtle difference is that it’s -(1 x 1) = -1
0
-2
2
0
0
0
0
-2
-2
0
-2
-2
0
-2
-2