What I like about this channel is that the answer is given early. I fot the answer in my head in less than a minute, but I appreciate the answer given to me without waiting for a 10-20 minute video. Love this channel.
Calculators changed the rules. The way I was taught sixty years ago, 39 would be the correct answer because an expression leading with a minus sign would be interpreted as a negative number, not a subtraction. If you want to have fun with PEMDAS ambiguities, find some very old textbooks from various regions and test them against excel, especially when it comes to various combinations of parentheses. The modern (computer) method is superior because it removes ambiguity.
@@blakeweigel6475Or never did any examples. I didn't. If you write it the other way round due to equivalence, 30-3² is more sensibly interpreted by 30-9. It would be very odd to answer 39 to that.
I entered this problem as written into Excel, ie, =-3^2+6*(4+1), and it gave 39 as the answer. I then entered the problem as =+6*(4+1)-3^2 and it gave 21 as the answer. My understanding of order of operations is that you must first enter a number then perform an operation on that number using another number. The leading sign in the expression should not be interpreted as an operation, but as the sign of the number to be squared. Excel seems to agree with this. Of course, in engineering school 50 years ago they taught us that in cases like this you should use additional parentheses to avoid ambiguity. The goal should be to accurately convey meaning and to avoid misunderstanding, not to test the reader's command of conventions.
A negative multiplied by a negative would give a positive answer, but that's not what we're doing here. We're multiplying a positive by a positive and then taking the negative of the result.
@@chrissullivan40It's not poorly written. It's intentionally written. It's a standard and common form of notation, but easily misinterpreted if you don't know what it means. So mathematics teachers NEED to teach what it means.
This is ridiculously stupid. Nobody ever means subtract (3^2) when writing -3^2 in the first term. That first term is absolutely (-3)^2. If you present a problem in this way meaning what you claim it means, then you failed at writing the equation in a way that clearly communicates to the reader what you meant.
This is basic sixth grade middle school math. Math problems are presented to students both past and present similarly; including PEMDAS usage. This is the proper way to solve exponents. (29 years, middle school teacher)
The first term is absolutely not (-3)². If it was then the general expression of commutativity a - b = -b + a would not work. 30 - 3² world not be equivalent to -3² + 30. Also, the answers to the questions What is -3²? and What is -x² for x=3? would not be the same.
@@gavindeane3670 This type of problem can be confusing for students. The negative sign is not manipulated. It remains the same. 3*3=9. Thus -9. (The video shows how -9 was arrived at.) -9 + 30 = 21 OR 30 -9 = 21
It is only 21. -3^2 = -(3x3)=-(9)=-9. Only (-3)^2= (-3)(-3)=9. The - is the coefficient of-1 and not part of the base that the exponent was on. There is only one solution.
@@blakeweigel6475 Yes this is indeed correct, that - sign is working as an integral part of the term and it works accordingly. Your comment is right and final and you could ignore anything on the contrary.
As suggested by another commenter, the oriblem should have been written less ambiguously. 6(4-1)-3^2 would have fixed the issue with this. Alternatively,-1*3^2 or 0-3^2+6(4+2) would also work so as to elominate confusion in the equation
@gavindeane3670 Admittedly so, just too used to having to 'dumb it down' for the various computer languages/spreadsheets/students to ensure what I wanted to occur did in fact occur. By rearranging the equation it becomes obvious that the -3^2 would remove 9 from the rest of the equation. By putting a 0 in front of the -3^2 this would give the negative 9 wanted to circumvent certain old calculators I have used in the past (without a change sign key you needed to be creative to get the desired outcome). Even the suggestion of "Mr RUclips Math Man" of changing the equation to -1 times the 3^2 eliminates the issue (although not for the aforementioned calculators). Any of these disambiguates the equation helping ensure the viewer/student can grasp & solve the equation without fear of failure. While working in the Army (decades ago admittedly) I had to write tests for our electronic students that would show they understood the concepts no matter who had taught them math in the past whether a parentheses around the -(3^2) or conversely a (-3)^2 type of instruction had been given. (This also required us to write at a 3rd grade reading level, figure that one out if you can try eliminating polysyllabic words to reduce the grade level). Poorly written equations which left room for multiple interpretations based on multiple states/cities/townships methods of instruction were kicked back to be rewritten by our supervisors. Each phase test would be analyzed to remove any of these problems, if a question was missed too often it was sent back repeatedly until the question could be passed easily by anyone who understood the concepts, proving their understanding of Ohm's Law, Moore's Law, Pythagorean Theory or any of the various basic trig/geometry work. We were always told to never make any question a 'gotcha' question, the one shown here would have fallen into that category. Not saying any of the work presented is wrong in any way, just pointing out there is a better way of showing the student/viewer that they know the PEMDAS concepts & give them confidence that they can continue their math journey.
@@awcampbell2002I'm all for clarity, but it is completely standard and ubiquitous in mathematics to write like this. It will be familiar to anyone who got as far as doing since basic algebra. So students do need to be taught what it means. If they taught what it means then it IS clear.
@gavindeane3670 My main problem is that I have seen multiple methods of showing negativity if a number (one teacher insisted that if the - was not elevated like a superscript it wasn't a negative sign ... You had to write it above the center of the numbers ... He would not acknowledge it as a negative and would msrk your answers as an incorrect response. No other instructors ever did that, but you learned over the course to work with his quirk. Not being a math major, & having the multiple methods presented by Lotus (spreadsheets), Microsoft (also spreadsheets), various programming languages, ancient RPN calculators. I never found enough consistency to (in my mind) feel that this method of writing equations is the final, established way of indicating a negative of the result of exponentiation. At this time I am still gun-shy of taking one person's word about standardation (as indicated by the superscript negative sign instruction) in math. Watching these videos, I know what this instruction wants me to view the equation as asking. But, I haven't seen anyone except one other math video guy who says this same thing is standard. I guess I'll eventually come around if I find consistency among others, just might take a while. Almost 68 years old & it may take a bit of convincing to make it stick in my mind that this is the true standard. Until then I will still vote for clarity over what my bosses told me were 'gotcha' questions. We wanted to build our students confidence perhaps too well when the results of them failing meant they would be reclassified to another career path (including infantryman) at the army's convenience.
@@awcampbell2002It is absolutely standard. And ubiquitous. Anyone who has done some basic algebra knows that. Absolutely nobody writes, say, a quadratic with coefficients -1, 1, and 1 as -(x²) + x + 1 It's just -x² + x + 1 The point about using a high level - for a sign indicator for negative numbers, leaving mid level - to be an operator, is interesting. I have occasionally seen that too but it is certainly not standard. I think that's a shame. I think it would be a really good idea if we could distinguish these two different uses of the - symbol like that, but for whatever reason it hasn't caught on.
39 is not correct. Adding brackets and I've the 3 doesn't help. If you wanted to add brackets for clarity, you should write -(3²)+30. But since the entire point is to teach what -3² means without brackets, he obviously isn't going to add them.
@@sanmiguel3280-3² does not mean "calculate the square of -3". It means "take the negative of 3²". If you want to write "calculate the square of -3" then you need to write (-3)².
Thanks. Right away, I could see where it could be either 21 or 39. What I wasn’t sure was how to interpret the exponent situation. I probably knew this stuff years ago, but at 73 years of age, details like these have fallen by the wayside. N
Tell me if my logic is correct please... I see that the first sign is a minus, not a negative, followed by 3^2 ... am I correct in saying I can thus assume we are starting with zero, and thus rewrite the equation as... 0 - 3² + 6(4+1) ...? So then I end up with... 0 - 9 + 6(4 + 1) Then 0 - 9 + 6 x 5 Then 0 - 9 + 30 Then -9 + 30 = 21
You can think of this as equivalent to 0 - 3² + 30, but the - symbol in the question is not a subtraction operator. It's negation: taking the negative of its operand. You need to be careful if you're going to change the expression like that though. For example 90 / -3² is NOT 90 / 0 - 3²
-9+30=21. I didn't know how to square negative numbers properly until watching videos like this. It never came up in my maths lessons in the 80s that I recall.
@@gavindeane3670 I never said we were. I said I didn't know how to until I started watching lessons like this one. In this one, the difference is explained.
-1×3^2 = -3^2 No parentheses required. -3^2 can be restated as it was before just the same: -1×3^2. Order of operations dictates this. If you begin with -1×3 and apply ^2 it would need parentheses to clarify: (-1×3)^2, which reduces to (-3)^2. But to continue with -3^2 would be in error. -9 is not = to 9. (!)
One immediate consequence of arguing against this convention is the fact that viewers are going around with the idea in mind that two negatives multiplied give a negative product! Try using that bad idea working MATRICES or rocket propulsion. Elon Musk would have an interesting response to this nonsense.
As written, some people THINK that -3² connotes (-3)(-3). The entire point of the video is to explain that that is NOT what it means. I don't think writing it as -(3)² does much good. If someone doesn't already know what -3² means then I don't think putting just the 3 in parentheses is going to help. To clarify it with parentheses you would write -(3²). But again, the entire point is to teach what it means without parentheses.
@@gavindeane3670 John tricked us by stating -3² without space and + 6... with space, compare: - 3² + 6(4 + 1) and -3² -6(4 + 1) = (-3)² + -6(4 + 1) ? Is it a negative value or an operation? I think the notation without the space between - and 3 is deceiving. Still I believe the exponent is on 3 and not on -3
@@panlomitoI can see how a space might make it more obvious that this is -(3²) not (-3)². It's still not subtraction though. And it's normal to write this without a space, as it's written in the video, so that's what he needs to teach. If he were to teach this with a space where the rest of the world doesn't use a space he would be doing his students a considerable disservice. He'd basically be teaching his own personal dialect instead of teaching the language everyone else uses. (This is a flaw in some of his other videos, where he uses completely non-standard, nonsensical notation. But in this case he is correct).
You're interpretation is correct but it's not really a PEMDAS/BODMAS interpretation. This negating operator is outside the scope of PEMDAS/BODMAS, although you can think of it like an implicit multiplication by -1.
In this world, where "negative three squared" is not sufficiently clear and precise wording to describe what we're doing. We are taking the negative of the square of three.
The way I interpreted it is: 1. 4+1 = 5 2. 6x5= 30 3. 32 = 9 4. 30 MINUS 9 = 21 I would love it if you'd explain why all this kind of thing is even necessary. It might be fun and interesting but it seems convoluted and unnecessary. What's the point of convoluted equations in the first place? Even your explanations with all this negative 9 or positive 9......why not just go: 3 squared is 9, moving to multiplication, 6x5 is 30, moving to subtraction 30 MINUS 9 is 21. Done. How about just 22 -1 = 21. Or 7x3 = 21. Why have all this other crap in there? Seems pointless. That's why I've never liked or cared about math. The reason for all these long winded multi step business has never been adequately explained.
Before you reach for PEMDAS you need to know that the - symbol is a negating operator. And you need to know that that operation, which isn't part of PEMDAS, has lower precedence than the exponentiation. Using PEMDAS goes like this: -3² + 6(4+1)... P -3² + 6(5)... E -9 + 6(5)... MD -9 + 30... AS 21
Wrong wrong wrong wrong. -3²is 9. The -3 there is understood to be * (-3)² or else it would be written as 0-3² There is no preambulatory number so the first number is negative. Not a positive number being subtracted. When you use the calculator you use the +/- key not minus key with the 3. Edit: I corrected(-3)² from the incorrect -1(3)² I initially had written.
I don't know what point you're trying to make, but -1(3)² is still -9. I would have thought that -1(3)² is more obviously -9 because it involves a multiplication and an exponentiation, and lots of people are familiar with the fact that exponentiation has higher precedence than multiplication. Yes, the first number is negative here. It is the negative of 3². 3² is 9 so the first number here is -9.
@@johnburke7756I'm not sure what distinction you're making with "negative three squared" vs "minus three squared". To me "minus three squared" sounds like squaring the negative number "minus three" to give a result of 9 and "negative three squared" sounds more like taking the negative of the quantity "three squared" to give a result of -9, but I think you might be using them the other way round. But anyway, the notation -3² means "take the negative of 3²" not "calculate the square of -3".
@gavindeane3670 You are right I incorrectly expressed myself. I meant to put(-3)² but I overthought. But you you are wrong in the problem. Because the minus is first the number is negative not being subtracted from zero or it would be written as 0 - 3². On a calculator you would NOT enter minus 3 squared. You would enter 3(+/- key) squared.
@gavindeane3670 read the problem. It starts as -3². For pedmas sake that is negative 3 squared so you square negative 3. What you are doing is arguing the problem starts 3² and subtract it from zero. Which would be written 0-3²... In other words on a number line. The first number is written as a negative but your Arguement is that it's a positive number squared and subtracted
The answer is 21, but I personally hate problems like these cause all they do is go viral and demonstrate either just how many people are bad at math or how badly people were taught math. The order of operations is easy to understand, and yet so many people are totally clueless on it, and that makes me sad. That’s my two cents.
Number sense is much more important. In this case, it doesn’t matter if you evaluate 6(4+1):or 3^2 first because they are separated by a low precedence operator.
@@gavindeane3670 Retired mathematics teacher here and I would never write that equation without brackets as its too ambiguous, in fact seeing -3 written that way I immediately assumed that it was the negative number -3 and squaring that makes 9. Is the squared symbol "attacking" just the 3 or the - sign as well. Not clear enough!
@@WasimBarriIt's a standard and very common form of notation - even more so when you get as far as some basic algebra. Not teaching students what it means seems a surprising omission. I completely understand the potential for confusion. But once students have been taught what it means then it IS clear.
How so? -3^2 has multiplication and an exponent. Order of operations says the exponent goes first and then applies the negative sign. I'm teaching myself to read -a^b as -1 * (a^b)
@@wildgurgs3614I'm sure it's what you'd do anyway, but strictly you want to be teaching yourself to read it as (-1 × a^b) rather than -1 × a^b. It doesn't make a difference here but it would with, say, 90 / -3² That is 90 / (-1 × 3²) not 90 / -1 × 3²
@@gavindeane3670 I stand corrected! However if I may attempt to absolve myself, in the TOTAL absence of other nearby multiplication/division operations, (-1 × (a^b)) looks a little ridiculous. That being said, in the presence of other division/multiplication terms the extra set of parentheses offers a HUGE increase in clarity.
He's not wrong. -3² means "take the negative of 3²" not "calculate the square of -3". If you want to calculate the square of -3, that is written (-3)².
What I like about this channel is that the answer is given early. I fot the answer in my head in less than a minute, but I appreciate the answer given to me without waiting for a 10-20 minute video. Love this channel.
Calculators changed the rules. The way I was taught sixty years ago, 39 would be the correct answer because an expression leading with a minus sign would be interpreted as a negative number, not a subtraction. If you want to have fun with PEMDAS ambiguities, find some very old textbooks from various regions and test them against excel, especially when it comes to various combinations of parentheses. The modern (computer) method is superior because it removes ambiguity.
Indeed but a simple problem has caused a stellar conversation.
Agreed.
✨🕊️👍
Or maybe you just remember it incorrectly.
@@blakeweigel6475Or never did any examples. I didn't.
If you write it the other way round due to equivalence, 30-3² is more sensibly interpreted by 30-9.
It would be very odd to answer 39 to that.
So why didn't John write the problem as -(3)^2 + 6(4+1) ???
@terry_willis It's not necessary.
−3² + 6(4 + 1)
= −3² + 6(5)
= −9 + 6(5)
= −9 + 30
= 21
I entered this problem as written into Excel, ie, =-3^2+6*(4+1), and it gave 39 as the answer. I then entered the problem as =+6*(4+1)-3^2 and it gave 21 as the answer. My understanding of order of operations is that you must first enter a number then perform an operation on that number using another number. The leading sign in the expression should not be interpreted as an operation, but as the sign of the number to be squared. Excel seems to agree with this. Of course, in engineering school 50 years ago they taught us that in cases like this you should use additional parentheses to avoid ambiguity. The goal should be to accurately convey meaning and to avoid misunderstanding, not to test the reader's command of conventions.
39 . So I was wrong. I thought a negative times a negative would be a positive answer.
A negative multiplied by a negative would give a positive answer, but that's not what we're doing here. We're multiplying a positive by a positive and then taking the negative of the result.
@@gavindeane3670 poorly written
@@chrissullivan40It's not poorly written. It's intentionally written.
It's a standard and common form of notation, but easily misinterpreted if you don't know what it means. So mathematics teachers NEED to teach what it means.
it is, but the 3 is the base of that exponent and not the -1.
@@chrissullivan40 not poorly written. It is math you just forgot. -3^2 is actually -1(3)^2. This is textbook grade 9 curriculum (in Canada)
This is ridiculously stupid. Nobody ever means subtract (3^2) when writing -3^2 in the first term. That first term is absolutely (-3)^2. If you present a problem in this way meaning what you claim it means, then you failed at writing the equation in a way that clearly communicates to the reader what you meant.
His Pemdas examples are always like that. But I even firmly disagree even with Pemdas so 🤷
This is basic sixth grade middle school math. Math problems are presented to students both past and present similarly; including PEMDAS usage. This is the proper way to solve exponents. (29 years, middle school teacher)
The first term is absolutely not (-3)².
If it was then the general expression of commutativity a - b = -b + a would not work. 30 - 3² world not be equivalent to -3² + 30. Also, the answers to the questions
What is -3²?
and
What is -x² for x=3?
would not be the same.
@@gavindeane3670 This type of problem can be confusing for students. The negative sign is not manipulated. It remains the same. 3*3=9. Thus -9. (The video shows how -9 was arrived at.) -9 + 30 = 21 OR
30 -9 = 21
@@Marsi5316I know it can be confusing. That's why he's teaching what it means.
-3² + 6(4 + 1) = ?
- [3]² + 6 x 4 + 6 x 1 --> distributieve eigenschap van vermenigvuldiging a(b + c) = ab + ac
-[9] + 24 + 6 = -9 + 30 = 21 ☑
Got 21
Cute setup with the -.
Thanks for the fun.
39
@irmavincent9546 21 it's -(3^2) not (-3^2).
No parenthesis
so it's a 3.
21 or 39, depending on how you interpret -3^2 as either -(3^2) or (-3)^2
It is only 21. -3^2 = -(3x3)=-(9)=-9. Only (-3)^2= (-3)(-3)=9. The - is the coefficient of-1 and not part of the base that the exponent was on. There is only one solution.
@@blakeweigel6475 yup 39
@@blakeweigel6475ever heard of negative numbers? In that case the - sign isn't an operation.
@@blakeweigel6475
Yes this is indeed correct, that - sign is working as an integral part of the term and it works accordingly.
Your comment is right and final and you could ignore anything on the contrary.
Currently, -3^2 is considered the same as -(3^2).
As suggested by another commenter, the oriblem should have been written less ambiguously. 6(4-1)-3^2 would have fixed the issue with this. Alternatively,-1*3^2 or 0-3^2+6(4+2) would also work so as to elominate confusion in the equation
Except the entire point is to teach what -3² means.
@gavindeane3670 Admittedly so, just too used to having to 'dumb it down' for the various computer languages/spreadsheets/students to ensure what I wanted to occur did in fact occur.
By rearranging the equation it becomes obvious that the -3^2 would remove 9 from the rest of the equation.
By putting a 0 in front of the -3^2 this would give the negative 9 wanted to circumvent certain old calculators I have used in the past (without a change sign key you needed to be creative to get the desired outcome).
Even the suggestion of "Mr RUclips Math Man" of changing the equation to -1 times the 3^2 eliminates the issue (although not for the aforementioned calculators).
Any of these disambiguates the equation helping ensure the viewer/student can grasp & solve the equation without fear of failure. While working in the Army (decades ago admittedly) I had to write tests for our electronic students that would show they understood the concepts no matter who had taught them math in the past whether a parentheses around the -(3^2) or conversely a (-3)^2 type of instruction had been given. (This also required us to write at a 3rd grade reading level, figure that one out if you can try eliminating polysyllabic words to reduce the grade level).
Poorly written equations which left room for multiple interpretations based on multiple states/cities/townships methods of instruction were kicked back to be rewritten by our supervisors. Each phase test would be analyzed to remove any of these problems, if a question was missed too often it was sent back repeatedly until the question could be passed easily by anyone who understood the concepts, proving their understanding of Ohm's Law, Moore's Law, Pythagorean Theory or any of the various basic trig/geometry work.
We were always told to never make any question a 'gotcha' question, the one shown here would have fallen into that category.
Not saying any of the work presented is wrong in any way, just pointing out there is a better way of showing the student/viewer that they know the PEMDAS concepts & give them confidence that they can continue their math journey.
@@awcampbell2002I'm all for clarity, but it is completely standard and ubiquitous in mathematics to write like this. It will be familiar to anyone who got as far as doing since basic algebra. So students do need to be taught what it means.
If they taught what it means then it IS clear.
@gavindeane3670 My main problem is that I have seen multiple methods of showing negativity if a number (one teacher insisted that if the - was not elevated like a superscript it wasn't a negative sign ... You had to write it above the center of the numbers ... He would not acknowledge it as a negative and would msrk your answers as an incorrect response. No other instructors ever did that, but you learned over the course to work with his quirk.
Not being a math major, & having the multiple methods presented by Lotus (spreadsheets), Microsoft (also spreadsheets), various programming languages, ancient RPN calculators. I never found enough consistency to (in my mind) feel that this method of writing equations is the final, established way of indicating a negative of the result of exponentiation. At this time I am still gun-shy of taking one person's word about standardation (as indicated by the superscript negative sign instruction) in math. Watching these videos, I know what this instruction wants me to view the equation as asking. But, I haven't seen anyone except one other math video guy who says this same thing is standard. I guess I'll eventually come around if I find consistency among others, just might take a while. Almost 68 years old & it may take a bit of convincing to make it stick in my mind that this is the true standard. Until then I will still vote for clarity over what my bosses told me were 'gotcha' questions. We wanted to build our students confidence perhaps too well when the results of them failing meant they would be reclassified to another career path (including infantryman) at the army's convenience.
@@awcampbell2002It is absolutely standard. And ubiquitous. Anyone who has done some basic algebra knows that. Absolutely nobody writes, say, a quadratic with coefficients -1, 1, and 1 as
-(x²) + x + 1
It's just
-x² + x + 1
The point about using a high level - for a sign indicator for negative numbers, leaving mid level - to be an operator, is interesting. I have occasionally seen that too but it is certainly not standard. I think that's a shame. I think it would be a really good idea if we could distinguish these two different uses of the - symbol like that, but for whatever reason it hasn't caught on.
39 is a correct answer given the written equation. To make it clear that it is the negative of 3 squared it should be written as -(3)^2.
No, the default interpretation has changed. Do exponentiation first, then negation. ie 3^2.... then made negative.
39 is not correct.
Adding brackets and I've the 3 doesn't help. If you wanted to add brackets for clarity, you should write -(3²)+30.
But since the entire point is to teach what -3² means without brackets, he obviously isn't going to add them.
@@gavindeane3670 -3 squared is 9 not -9.
@@sanmiguel3280-3² does not mean "calculate the square of -3". It means "take the negative of 3²".
If you want to write "calculate the square of -3" then you need to write (-3)².
I agree. It should be 39. At least the way I learned it
-3^2 + 6(4+1)
-9 + 30= 21
21
Thanks. Right away, I could see where it could be either 21 or 39. What I wasn’t sure was how to interpret the exponent situation. I probably knew this stuff years ago, but at 73 years of age, details like these have fallen by the wayside. N
Back when we went to school, -3^2 was (-3)^2. Today, it's -(3^2).
Tell me if my logic is correct please...
I see that the first sign is a minus, not a negative, followed by 3^2 ... am I correct in saying I can thus assume we are starting with zero, and thus rewrite the equation as...
0 - 3² + 6(4+1) ...?
So then I end up with... 0 - 9 + 6(4 + 1)
Then 0 - 9 + 6 x 5
Then 0 - 9 + 30
Then -9 + 30
= 21
You can think of this as equivalent to 0 - 3² + 30, but the - symbol in the question is not a subtraction operator. It's negation: taking the negative of its operand.
You need to be careful if you're going to change the expression like that though. For example
90 / -3²
is NOT
90 / 0 - 3²
-9+30=21. I didn't know how to square negative numbers properly until watching videos like this. It never came up in my maths lessons in the 80s that I recall.
in the 80's, -3^2 was considered the same as (-3)^2. This has changed, it's now seen as -(3^2).
We're not squaring a negative number - that's the entire point.
We're squaring a positive number and taking the negative of the result.
@@laurendoe168 I recall no such thing being taught.
@@gavindeane3670 I never said we were. I said I didn't know how to until I started watching lessons like this one. In this one, the difference is explained.
@@RustyWalker Back then, it wasn't. Back then, negativity was considered an inherent property of a number. Now, it's not.
Should have been written -(3)^2 to avoid confusion. As written, -3^2 connotes (-3)(-3) = 9, and hence the answer is 39.
-1×3^2 = -3^2
No parentheses required. -3^2 can be restated as it was before just the same: -1×3^2.
Order of operations dictates this.
If you begin with -1×3 and apply ^2 it would need parentheses to clarify: (-1×3)^2, which reduces to (-3)^2. But to continue with -3^2 would be in error. -9 is not = to 9. (!)
One immediate consequence of arguing against this convention is the fact that viewers are going around with the idea in mind that two negatives multiplied give a negative product! Try using that bad idea working MATRICES or rocket propulsion. Elon Musk would have an interesting response to this nonsense.
To be clear, the answer is 21.
To argue it's 39 puts more than a fly in the ointment!
As written, some people THINK that -3² connotes (-3)(-3). The entire point of the video is to explain that that is NOT what it means.
I don't think writing it as -(3)² does much good. If someone doesn't already know what -3² means then I don't think putting just the 3 in parentheses is going to help. To clarify it with parentheses you would write -(3²). But again, the entire point is to teach what it means without parentheses.
- 5² - 5.( - 4 - 1 ) ^ -3 = without calculator is much nicer.
Why does a very easy basic problem need to take 14 minutes to explain
9+6x5= 39
21 it's -(3^2) not (-3^2).
No parenthesis
so it's a 3.
My imaginary ( ) have betrayed me.
✨🕊️
I did the same thing. Lol. Damnit
Yea, I got. 1.)-3^2+6(4+1)=? 2.)-9+6(5)=? 3.) -9+30= 21
I did the same thing with the exponent. My bad.
- (3)² + 6 . 5 = - 9 + 30 = 21 while pEmdas precedes pemdaS
There's no subtraction here.
Understanding whether -3² is 9 or -9 is beyond the scope of PEMDAS.
@@gavindeane3670 John tricked us by stating -3² without space and + 6... with space, compare:
- 3² + 6(4 + 1) and -3² -6(4 + 1) = (-3)² + -6(4 + 1) ?
Is it a negative value or an operation?
I think the notation without the space between - and 3 is deceiving. Still I believe the exponent is on 3 and not on -3
@@panlomitoI can see how a space might make it more obvious that this is -(3²) not (-3)². It's still not subtraction though.
And it's normal to write this without a space, as it's written in the video, so that's what he needs to teach. If he were to teach this with a space where the rest of the world doesn't use a space he would be doing his students a considerable disservice. He'd basically be teaching his own personal dialect instead of teaching the language everyone else uses. (This is a flaw in some of his other videos, where he uses completely non-standard, nonsensical notation. But in this case he is correct).
-3^2 == -(3^2) == Negative OF square of three, by PEMDAS/BODMAS. Change my mind
You're interpretation is correct but it's not really a PEMDAS/BODMAS interpretation. This negating operator is outside the scope of PEMDAS/BODMAS, although you can think of it like an implicit multiplication by -1.
-9 +30 whoa
I got 75😂❤
Good stuff 👍👏🙏💪😎🌎
21
-9+6.5=-9+30=21
I got it right!
I think the answer is 39.
It would be more challenging to solve, by using a calculator.
I get 39 maybe I’m doing it wrong in my head
-39
In what world does negative three squared equal negative nine?
In this world, where "negative three squared" is not sufficiently clear and precise wording to describe what we're doing.
We are taking the negative of the square of three.
My answer is 39. Isnt it -3 square is 9 and not -9?
We are not squaring -3. We are squaring positive 3 and then taking the negative of the result.
The answer is 21
Oh I meant 21
21...
well, my calculator says you are wrong and so does my 74 year old brain. -3 squared is 9 not -9
Of course the square of -3 is 9. But we're not squaring -3 here. We're squaring positive 3 and then taking the negative of the result.
The way I interpreted it is:
1. 4+1 = 5
2. 6x5= 30
3. 32 = 9
4. 30 MINUS 9 = 21
I would love it if you'd explain why all this kind of thing is even necessary. It might be fun and interesting but it seems convoluted and unnecessary. What's the point of convoluted equations in the first place?
Even your explanations with all this negative 9 or positive 9......why not just go: 3 squared is 9, moving to multiplication, 6x5 is 30, moving to subtraction 30 MINUS 9 is 21. Done.
How about just 22 -1 = 21. Or 7x3 = 21. Why have all this other crap in there? Seems pointless. That's why I've never liked or cared about math. The reason for all these long winded multi step business has never been adequately explained.
It's not subtraction. Subtraction is a binary operation: it requires TWO operands.
30 1/9
9
-.6
The snail in my goldfish bowl solved this one in 2 seconds. Just sayn.
And you didn't, because the snail told you the answer first?
@@panlomito No, I didn't answer it first because it was Curly's turn to solve John's next math quiz. 🤩
39 (Please excuse my dear aunt Sally).
-3^2 is viewed as 0-3^2. First do exponentiation, then subtraction.
@@laurendoe168There is no subtraction in this expression.
Before you reach for PEMDAS you need to know that the - symbol is a negating operator.
And you need to know that that operation, which isn't part of PEMDAS, has lower precedence than the exponentiation.
Using PEMDAS goes like this:
-3² + 6(4+1)... P
-3² + 6(5)... E
-9 + 6(5)... MD
-9 + 30... AS
21
@@gavindeane3670 You obviously don't believe what I said. This is the reason that "negation" is not a recognized operation.
@ And - a negative time a negative equals a positive! Therefore, my answer.
I thought it was 20
Wrong wrong wrong wrong. -3²is 9. The -3 there is understood to be * (-3)² or else it would be written as 0-3²
There is no preambulatory number so the first number is negative. Not a positive number being subtracted.
When you use the calculator you use the +/- key not minus key with the 3.
Edit: I corrected(-3)² from the incorrect -1(3)² I initially had written.
I don't know what point you're trying to make, but -1(3)² is still -9.
I would have thought that -1(3)² is more obviously -9 because it involves a multiplication and an exponentiation, and lots of people are familiar with the fact that exponentiation has higher precedence than multiplication.
Yes, the first number is negative here. It is the negative of 3². 3² is 9 so the first number here is -9.
@@johnburke7756I'm not sure what distinction you're making with "negative three squared" vs "minus three squared".
To me "minus three squared" sounds like squaring the negative number "minus three" to give a result of 9 and "negative three squared" sounds more like taking the negative of the quantity "three squared" to give a result of -9, but I think you might be using them the other way round.
But anyway, the notation -3² means "take the negative of 3²" not "calculate the square of -3".
@gavindeane3670 You are right I incorrectly expressed myself. I meant to put(-3)² but I overthought.
But you you are wrong in the problem. Because the minus is first the number is negative not being subtracted from zero or it would be written as 0 - 3². On a calculator you would NOT enter minus 3 squared. You would enter 3(+/- key) squared.
@gavindeane3670 read the problem. It starts as -3². For pedmas sake that is negative 3 squared so you square negative 3. What you are doing is arguing the problem starts 3² and subtract it from zero. Which would be written 0-3²... In other words on a number line. The first number is written as a negative but your Arguement is that it's a positive number squared and subtracted
-3²is read negative 3 squared. -3²is not the difference of 0-3² as there is no number before the minus sign
The answer is 21, but I personally hate problems like these cause all they do is go viral and demonstrate either just how many people are bad at math or how badly people were taught math. The order of operations is easy to understand, and yet so many people are totally clueless on it, and that makes me sad. That’s my two cents.
Number sense is much more important. In this case, it doesn’t matter if you evaluate 6(4+1):or 3^2 first because they are separated by a low precedence operator.
I feel sorry for you in Trumpland😂 Your math teachers haven’t heard about parentheses, but makes it much harder by the pemdas bs!
Change order to 6(4+1) -3^2 and almost everyone would get it right first time.
@@osgubben Huh?
@ Examples like this encourage ambiguity. Math, like prose, should communicate.
Should have used brackets around the 3 squared. ie -(3 squared) to make it clearer
Currently, -3^2 is interpreted as being equivalent to -(3^2). If you want to square negative three, THEN you need brackets (-3)^2.
He's teaching what -3² means without brackets. Adding brackets would completely defeat the object.
@@gavindeane3670 Retired mathematics teacher here and I would never write that equation without brackets as its too ambiguous, in fact seeing -3 written that way I immediately assumed that it was the negative number -3 and squaring that makes 9. Is the squared symbol "attacking" just the 3 or the - sign as well. Not clear enough!
@@WasimBarriIt's a standard and very common form of notation - even more so when you get as far as some basic algebra. Not teaching students what it means seems a surprising omission.
I completely understand the potential for confusion. But once students have been taught what it means then it IS clear.
Clear as mud. 👎
How so?
-3^2 has multiplication and an exponent. Order of operations says the exponent goes first and then applies the negative sign.
I'm teaching myself to read -a^b as -1 * (a^b)
@@wildgurgs3614I'm sure it's what you'd do anyway, but strictly you want to be teaching yourself to read it as (-1 × a^b) rather than -1 × a^b.
It doesn't make a difference here but it would with, say,
90 / -3²
That is
90 / (-1 × 3²)
not
90 / -1 × 3²
@@gavindeane3670 I stand corrected!
However if I may attempt to absolve myself, in the TOTAL absence of other nearby multiplication/division operations, (-1 × (a^b)) looks a little ridiculous. That being said, in the presence of other division/multiplication terms the extra set of parentheses offers a HUGE increase in clarity.
He's wrong? The brackets are not around the 3^2 that answer is +9
He's not wrong. -3² means "take the negative of 3²" not "calculate the square of -3".
If you want to calculate the square of -3, that is written (-3)².
Poorly written problem. Answer should be 39, regardless. There is nothing separating the negative sign from the 3. -3x-3 is nine all day long.
-3^2 is treated as if it was 0-3^2. The answer to 0-3^2 is -9. Exponentiation first, then subtraction.
It's perfectly well written. The point of it is to teach what -3² means, because it's a standard and ubiquitous form of notation.
39
21
39
-3 squared is +9 plus 5x6 =39
@@BrianLelievreWe're not squaring -3. We're squaring 3 and then taking the negative of the result.
To square -3 you would write (-3)².
39
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39
21
21
21
39
21
21
21
21
CORRECT