- 3 squared plus 6 times the sum of 4 and 1 =? Many will GET WRONG!!
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- čas přidán 29. 08. 2024
- Order of operations practice problem with powers and exponents.
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-3 x -3. = 9 + 30= 39
Exponents first
-9 + 30 = 21
Two negatives beget a positive number
@@39wopstud-3² isn't multiplying two negatives. It's multiplying two positives and then taking the negative of the result.
@@gavindeane3670, I disagree but somehow, as usual, I’m wrong.
@@SkyBlue-i6c -3² means -(3²) not (-3)²
I think the point of confusion is using the "-" as an operator when in reality it is indicating that you are dealing with the integer -3 not negating the expression 3^2. The -3 is not a mathematical operation but rather a number as much 4 or 10 is a number and so should be interpreted the same as (-3). Negation is not a part of PEMDAS since it is not an arithmetic operation. BTW I did computer language parseas an exercise what you suggested and submitted it to my trusty old TI-36X Solar calculator... the order of my operations on the calculator:
c (to clear), 3 , +/- (at this point the display showed -3 ) , x^2 .... the display now showed 9 no need to proceed . So in computer language parlance the - used in the expression would be considered the unary minus and varies as to how it is interpreted... I would say to avoid all confusion, when in doubt use parens , so it would be better to write the expression -(3^2) +6(4+1) ..unless one is trying to be tricky..as a side note PEMDAS is not the only rule for order of operations...e.g., BEDMAS, BODMAS, and BIDMAS. As a teacher I would hope you would be clear when testing your students not to introduce problems that my be ambiguous :) BTW I have decades in Math with a BSEE, BSMath, and MSCOMPSCI not pull the degree card but just to indicate I do have a profeesional background for my commenst. Good job in the way you make your presentation ... very clear.
@brianmurphy NO, it's not very clear!! I am not a math genius like you and John. I don't understand powers at all, and he didn't explain how the -3 squared was still a -9. Before learning algebra, I thought I had a great understanding of positive and negative numbers and how they work, but that got thrown out the window with the pot here and I don't understand that. Can you explain that for me? Pretend that I'm 8yo.
the problem is that he applied the - to 3 AFTER it got squared but he shouldn't because as you observed -3 squared is 9 not -9 ... if you square -3 rather than 3 you would get 9 ... my position is that the minus is associated with 3 ... in otherwords you must keep it with the 3 when you square it... you are spot on.
:( i wish i read this before i went on my rant. would have saved me time.
@@brianmurphy4702 Thank you Brian, that helps!!
@@survivrslike all these click bait videos it starts with an ambiguous question. If you assume every mathematical equation starts at zero which we do. ie 0 +3 + +3 = +6 is the same as 3 + 3 = 6 as by convention only, the leading zero and + for positive numbers are omitted. As is the first operator after the leading zero if it is addition ie. 0 + +3 + +4 is written 3 + 4, but 0 - +3 + + 4 written -3 + 4
If a question seems ambiguous then the leading zero and + can be added back in where necessary to remove the ambiguity.
Then this becomes 0 - +3^2 + 6(4+1) = 21. Or if negative three squared was the intended term it would be written in full as 0 + (-3)^2 + 6(4+1) = 39
or (-3)^2 + 6(4+1) = 39 if by convention you omit the leading zero.
Poorly written problem. I will stand by it being 39.
I do as well.
I agree
Waaaaa😢
It's a very normal and ubiquitous form of notation. That's why teachers need to teach that -3² does not mean (-3)², it means -(3²).
Addition/Subtraction is at the same level and is reversable.
6(4 + 1) - 3²
6(5) - 9
30 - 9
21
Really surprised with all the comments stating that they were taught that is was 39.
21 or if you place parenthesis on -3, that would equal 39.
21 is what I got
You're right.
There are no parentheses on -3
Before I came to this channel I never repeat never heard of the order of operations. That cleared up a lot of problems that I had with doing math problems.
Is it possible you were taught order of operations in 5th grade but forgot it over time?
@@marcredgate7288 I wasn't either. I had an amazing teacher for algebra I but never heard of the order of operations.
To make equation clearer the 3 and square 2 should have been in brackets. That way 3 squared gives you 9 with the negative outside making it -9
But that's the point, to show how to get the right answer when parentheses aren't given. Yes, adding parentheses would make it clearer, and I probably would use them myself. But even without them, as written, the correct answer is well-defined and unambiguous. Order of operations is always PEMDAS, Parentheses, Exponentiation, Multiplication/Division, and finally Addition/Subtraction. With no parentheses present, the exponent is handled before the sign, so treat it as -(3^2), not (-3)^2. As others have observed, switch the order of the two terms, and it becomes clearer, also: 6(4+1) - 3^2 = 21.
@@typicalhguy9290 I th ink what we're in agreement on is that if we want to see if someone can solve a problem, we'd us the (). But if we were looking to maximize the number of wrong answers, we wouldn't.
It's similar to a question I had on an ultrasound physics class. There was a diagram of a transducer emitting a beam straight forward. The transducer's design revealed that it had the capability of steering the beam, rather than simply aiming it in a fixed direction.
The question was "Does this transducer have steering?" I asked the instructor (I won't call her an educator, for this very reason), whether it was asking if it was USING it, or if it was CAPABLE of it. She gave me the look typical of the instructors there, as though every question from a student was an attempt at tripping them up, and refused to answer. So, I answered it correctly given the language of the question, she counted it wrong, I went over two sets of heads and got my 97% instead of a 95%.
Triflin' b!tches. Rarely allow tech people to word their own exams. 🤣
@@typicalhguy9290 -3*-3 = 9. There is no operation on that to make it a negative after the 9.
@@steveklemetti8035 Sigh. No. PEMDAS. The exponentiation takes precedence over the subtraction. Always. The point of the entire video, and stated explicitly at 10:00. Put a leading zero in front of it if it helps you to see the difference: 0 - 3^2 + 6(4+1). Or rearrange the terms as shown: 6(4+1) - 3^2 = 30 - 9 = 21. Therefore, there is an operation to make it negative after the 3 is squared. If it was written as (-3)^2, *then* the parentheses would take precedence over the exponentiation, and the first term would be a positive 9, and the sum 39. But nothing as written here causes the negation to be applied first.
@@typicalhguy9290 Do you know why exponents are done first? And why there is no such thing as subtraction? No, we don't put a leading 0 in front of anything. No, people need to stop putting parenthesis in where it is not stated.
As it is written it is -3*-3 which is 9. If it is anything else, then it would say -3*3. People need to stop putting parenthesis where they are not and go by as it is written.
work inside braket
(4+1) = 5
Then Exponent
3x3=9
However you made it -
So the Exponent is -9
Then multiplication
6x5=30
Then -9 + 30 = 21
Answer 21
I recently saw a video by Dr Brian Greene where he was talking about this very type of thing. He said as far as his opinion, PEMDAS is very imprecise. And this is a good example. If they want you to square the three, and then add the negative sign, The 3^2 should be is parenthesis. I see this as one of those "gotcha" problems that math Instructors are very famous for.
Also no student should be exposed to ambiguity. Like any question should be given with proper fraction lines as one example. Not using / or ÷ ever
I had an algebra instructor in high school who would pull crap like this just to mess with kids. When they argued that he was not doing it the way he had taught them, and showed him where he was wrong, he would just tell them in a loud voice, "I don't care...YOU"RE WRONG!" Made a lot of kids hate math.
It IS imprecise. It's just usually "good enough" for the level of the people learning it. Those who go further in math learn to expand on it a bit.
@@afre3398 personally, I don't mind the / or ÷ or unary - *if the operator and its rules are clearly described.* Otherwise, any ambiguous expression can have multiple answers.
I for instance handle implied multiplication (juxtaposition) before regular multiplications/divisions. That's the way I was taught decades ago and if some people decide to change the language, it's their problem if the rocket crashes on the moon instead of performing a landing. ¯\_(ツ)_/¯
@@silverhammer7779 If he was working for me as a programmer he would put parentheses in to make it clear or he would be fired.
Ambiguity in a mathematical expression is inexcusable!!
Real mathematicians use parenteses to avoid it.
Write _either_ −(3^2) _or_ (−3)^2
But then he wouldn't have been able to say "You got this wrong, and you got this wrong, and you got this wrong..."
The reason is -3 squared is 9 is because there is NOT parenthesis around the 3 squared with the negative on the outside. If it was -(3squared) then it would be -9, therefore it would be -1(3^) = -9, -1 x (9) = -9
There was nothing ambiguous about that equation.
No real mathematician would bother with that. Once you've done a little bit of algebra at school, the meaning of this notation is so common and familiar that no misunderstanding remains.
I doubt you'll find a mathematician on the planet who would bother to write a quadratic with coefficients -1, 1 and 1 as
-(x²) + x + 1
Writing it simply as
-x² + x + 1
is completely standard and normal and ubiquitous.
@@debbybrown6943That's exactly backwards.
The reason -3² is -9 is because there are no parentheses around the -3.
-3² means "take the negative of 3²" not "calculate the square of -3".
The - symbol is a negation operator and negation has lower precedence than exponentiation. The ² only applies to the 3, and the - is applied afterwards.
If you want to do the square of -3 you have to write (-3)².
Unless the order of operations has changed, it is 39. I am an engineer and went through calculus and differential equations. Granted that was the 80s, but unless this is new math, it is 39.
People keep trying to blame "new math".
I also did math in the 80s. Three squared with a negative symbol in front of it has always been -9.
@@RichSmith77 Ah yes, but minus 3 squared is: minus 3 multiplied by minus 3, which equals plus 9. The person setting this equation has missed out parentheses in the appropriate place.
@@user-cw9qn1nb2n And because there are no parentheses, it's 3 being squared, with a minus in front. It's not (-3)².
@@RichSmith77 Ah yes, but the minus 3 comes before the symbol for squared. Therefore I read it as minus 3 multiplied by minus 3. I can't help it if 5 years of a grammar school education NEVER introduced to me to PEMDAS at all, if that is relevant here. And I got a very good grade at maths "O" level, so my maths teachers can't have been all bad. And I am not the only one getting 39 as the answer, as you can see. I think the way this equation has been set out is open to different interpretations and, to me, the answer 39 is more valid than 21.
@@user-cw9qn1nb2n The question is designed to catch people out, no doubt about it. They wouldn't be making a video about it if everyone agreed what the answer was. However, there is only one correct interpretation. It's easy to read the -3² as being (minus three) squared, but that's not how mathematical notation works. In Einstein's famous equation E=mc², the exponent only applies to the symbol it is attached to, the c. It's the same as E=m(c²), not E=(mc)². It's similar to the expression -3². This is the same as -(3²) and not (-3)². If it had been written the other way around, as 6(4+1) - 3², then I think a lot more people would have got the answer 21. But -3²+6(4+1) is the same expression, just with the terms reversed.
I agree that it is 39. You do the operation in the () first, then multiply by 6 m, resulting in 30. -3 times -3 is 9. 30 plus 9 equals 39.
try the expression on wolframalpha - or better yet, graph out y = -x² + 6(1+4) on desmos, and notice it is a downward pointing parabola with vertex at y = 30, and the value at x = 3, is 21, not 39.
I did it that way too
Negative 3 times Negative 3 is 9 ???
@@Kerry-xu7fqnegative 3 multiple by itself is certainly 9.
But that's not what we're doing here. We're multiplying positive 3 by positive 3 (which gives 9) then taking the negative of the result (which gives -9).
My question is: isn't -3 an integer? If so, then -3 squared is -3 x -3 which = 9. The negative is part of the integer, not a prefix to the integer.
As a teacher of Algebra at the college level, you are absolutely correct and the simplicity with which you explained your position was quite elegant.
Exactly
@@Liam1HAs a teacher of algebra at college, it is astonishing that you don't know that, for example, a quadratic with coefficients of -1, 1 and 1 would be written
-x² + x + 1
Absolutely nobody writes that as
-(x²) + x + 1
-3² is -9 because the "-3" part is NOT a negative number. It is a positive number with a negative operator before it. And as we all know from elementary algebra, negation has lower precedence than exponentiation.
Good question, and in principle the notation absolutely could be read that way.
But we don't read it that way. We don't treat the - as one of the characters used to write a negative number. We treat the - as a negation operation, separate to the number.
And negation has lower precedence than exponentiation, so we square the 3 first to get 9, THEN we apply the negation, to get -9.
-3² means -(3²) not (-3)². This keeps the notation consistent with things like -(1+2)² and -x² where the - symbol cannot be anything other than a negation operator.
I know you say the value is 21 (I am guessing) but I still say, the way I was taught in the early 1980s, that is 39. I think the problem is that the person writing the issue is not being clear enough. Because calculators when programmed give 21, it is apparent that now that is considered 21. But when I went to school, we couldn't use calculators, even in advanced High School math. Arrrgghhh.
And you're correct. The problem is written ambiguously. If a problem has to be interpreted by the one solving it, and the answer differs depending on how one interprets the problem, then we know with certainty that the issue is unclear writing of the problem. Just remember that calculators are programmed to evaluate good and bad problems alike. GIGO.
Me too. Taught to get 39.
Simply switch position to 30 minus 3 squared. Math trickery.
-x^2≠(-x)^2
Calculators are programmed different ways. So they are useful if one knows proper order of operations. Some people seem to think that the Calculator on Google is proper program for algebraic equations NOT‼️‼️‼️‼️
There seems to be some disagreement here. I was taught that -3^2 = -3 * -3 = +9 I would be interested in hearing from someone qualified to make a ruling on this
I taught math at one of the top 3 private schools at the time (a long time ago), and also at university. You are correct, at least per every text book I taught out of.
This person is effectively stating that negative numbers don't exist unless you multiply a positive number by -1. That is ludicrous, as we have temperatures below, zero, while companies some years lose money, and the next year have a profit, for which we don't express a loss as a profit multiplied by negative 1. If a company's earnings for two years is calculated by adding the earnings for both years, and one year is a loss, effectively a negative number is being added.
This channel often makes terrible errors and misinforms, based upon teaching of pre-algebra that per my assessment began to change sometime in the last decade or two.
For those who take algebra and beyond, some of what is on this channel is simply wrong, while, you are right.
@@randylazer2894 Thank you for putting this in practical terms. So many want to deal with imaginary numbers and equations on one line. Losses are negative numbers and are added and multiplied. I don't base anything on what I've learned in school. I research and think upon it.
@@steveklemetti8035 Well shared, particularly of trusting your judgment. From what I have seen, school curriculum in the 1970's, 1980', and early 1990's, most assuredly had some flaws, but was basically reliable, particularly with math.
Yet, in the last five years or so, it seems that schools are simply engaged in wrongful instruction.
Thank you Steve. You have a good head on your shoulders, and your instincts will typically almost always be right on. I can't believe people make a living by sometimes giving wrongful answers to math that 5th and sixth graders, learn.
@@randylazer2894 There are websites that say that multiplication and addition is commutative but subtraction is not. They say that 9-5 is not = 5-9. I write them and correct them that subtraction is in reality adding a negative. 9-5 is 9+ -5 which is equal to -5+9. When they say that "that 9-5 is not = 5-9", they are comparing 4 numbers and not 2. +9 and -5 and +5 and -9, they don't understand the big picture of how they are not equal.
@@steveklemetti8035 My gosh I didn't know of the huge misinformation of basic math. As you shared 9-5 is 9 plus negative five. That astounds me as addition and subtraction are commutative, in as you had written the order of the numbers doesn't affect the result. This world is falling apart in every direction. Thanks of sharing. I guess I am glad that I retired from teaching decades ago, and thankfully pursued a career involving economics, finance, and real estate.
If "many get this wrong", then the school system has failed them... badly.
No matter how much a school tries, it's on the student and parent to make sure the student understands it.
@@ThunderstruckGamesyou are wrong it's the teachers and the school that show the students how to do this properly this guy is dead wrong the first set of numbers numbers are-3 * -3 equals 9 + 30 is 39
How do you get 39 that's goofy!
@@robertlongwill8856It's -9 + 30
-3² means -(3²) not (-3)²
I entered the equation into Excel, and the result given is 39.
-3 ×-3 =9, I learned it that way and that's how I got 39 following exponents first. I feel better someone did the excel for clarity
@@msmith1wa Congratulations! You have found just about the only calculator or mathematics software out there that gets this wrong 🙂
It's a well known problem with Excel. I am sure Microsoft know about it (after all, Microsoft Math Solver doesn't say 39) but I'd be very surprised if they fix it in Excel. Existing spreadsheets all over the world would be at risk of breaking if they changed something like this.
@@peaceandlove809Excel doesn't give clarity here. It gives the wrong answer. This is a well known problem with Excel. It's baked in gy now though. I doubt they will fix it.
Microsoft do know how to solve this correctly though. Put this into Microsoft Math Solver and it will give the correct answer of 21.
This is a known gripe with Excel. You've found just about the only calculator that doesn't get this right.
Microsoft Math Solver will give the correct answer of 21 so Microsoft clearly know how to do this properly, but I doubt they're going to fix it in Excel.
@@peaceandlove809Excel has not added charity here. It's just an error in Excel. Put it in pretty much any other calculator on the planet if you want clarity - you'll get the answer 21.
-3² does not mean (-3)²
-3² means -(3²)
First rule in math is that we can never assume anything unless the information is explicitly provided. The first part of the equation is NOT "negative three" squared, but rather negative "three squared." Otherwise, it would be written as (-3)^2. This was explicitly taught in every math class I ever took. And the "-" operator is NOT a minus, but rather a negative sign which would then signify another multiplicative operation. So we can rewrite that entire first segment of the equation as (-1)(3)^2, which still yields the CORRECT result of -9 if we follow PEMDAS and complete the squaring operation first.
Nothing ambiguous or "gotcha" about this problem, in my humble opinion. But I suppose it might depend upon how well we were all taught math. But I immediately saw where the problem would be for most people watching this video lol.
Even if we interpret the negative as a minus sign, the rules still lead to the interpretation in the video.
@@jakemccoyThe two possible interpretations here are that the - symbol is either a character used to write a negative number, or it's a negation operator.
The first interpretation gives -3² = 9 and the second interpretation gives -3² = -9.
I think it's easy to see why this notation can be confusing. That's why teachers need to specifically teach it.
In order to interpret it correctly, you need to know that the convention is to treat the - symbol as a negation operator not a character in a negative number, AND you have to know that the negation operation has lower precedence than the exponentiation operation.
I made the same mistake.
HOWEVER, if the the problem would’ve been written as 6(4+1)-3^2, there’s no other answer than 21. So hat’s off to you.
Excel evaluates this expression exactly as written as 39.
Yep. That's a known gripe with Excel. Somebody at Microsoft understands it correctly though - Microsoft Math Solver gets 21 not 39.
As requested, I tried to input the expression as presented into my scientific calculator to be met with an "invalid expression" error. It seems that to be valid, you need to remove the ambiguity and either format that expression as "0-3^2 ..." or "(-3)^2 ..." before my calculator will accept it. That said, IMO you are incorrect as far as the convention I was taught, The initial minus sign is not an operation and the compound symbol "-3" represents the value under consideration and it is this value that is squared.
Casio or TI?
I concur! Even though I may be rusty these days, I don't think I have forgotten ALL the rules! --3 squared is -3 x -3 = + 9; then do inside the brackets 4+1 =5; then 6x5=30 +9 = 39. Simple.
Perhaps this "New math" that I hear about from my grandson offers a different process, but this is what I learned, and i would hope that mathematical calculations remain a constant ... or does the puzzling "new" way of doing mathematics offered by the person who posted this challenge explain why so many countries have trouble figuring out their annual budgets!
Did you use the +/- key or CHS key(CHS=(change sign). You type in 3 and then the latter key to change the sign
@@afre3398 There isn't a "+/-" or "change sign" key on modern Casio calculators.
My Casio calculator gives a result of 21, when inputting the equation exactly as written (including implied multiplication of the bracket by 6).
I disagree. -x^2≠(-x)^2
Or to put it another way, rearrange the formula to read 6(4+1) -3^2. Then it becomes clear.
Doesn't change anything. 6*5 +9. There is no subtraction there because subtraction does not exist. It is adding a negative. There is no negative because the exponent computes out to a 9.
-(3)^2+6*(4+1) comes up as 39 just as (-3)^2+6*(4+1) I am using excel formula. Not sure what the difference is but when I do it in VBA it comes out as 21: a = -3 ^ 2 + 6 * (4 + 1)
MsgBox a
In Excel you would need =-(3^2)+6*(4+1) to get the correct aswer.
@@quinnfamily5378 "In Excel you would need =-(3^2)+6*(4+1) to get the correct a[n]swer."
And that is exactly why these ambiguous expressions are so problematic: even though there are "rules"/guidelines on how to evaluate certain operators and functions, there is no real consensus across the board and different people as well as different "programming languages" (term used loosely) evaluate these expressions using various methods which can give different answers. Ambiguity is the problem here, and there are certain characters (people) who would like to impose their ideas and ideals without really explaining the reasoning behind it.
As I have mentioned before: brackets/parentheses are cheap! Use them!
Excel in this case takes a different approach on "evaluating" the expression and thus would require explicit brackets/parentheses to remove ambiguity, and precisely this is where this "math tutor" fails the community.
He writes ambiguous expressions and then tries to "educate" everyone that they fell into the same "trap". Well, I say (and repeat it ad nauseam) *quit writing ambiguous expressions!*
If you plug it into a TI the answer=21. ditto on my linux calculator. I don't see how one can get any other answer on this one the way its written...
The difference is because Excel is just about the only calculator or mathematics software out there which gets this wrong.
It's a known issue with Excel. Microsoft clearly understand it because Microsoft Math Solver gives the correct answer. I'd be very surprised if they ever changed it in Excel now because the error is long-established and people all over the world will have spreadsheets that rely on the correct behaviour.
Interestingly, I just tried "=-3^2+6*(4+1)" in the Numbers spreadsheet on my iPad, and it gave 39. But if I put "=0-3^2+6*(4+1)", which should give exactly the same result, then I get 21. An implementation of OpenOffice on iPad gives exactly the same result as Numbers. I agree that 21 is the correct answer, but this shows that it makes sense to add extra brackets when programming spreadsheet formulæ, to make it explicit to the program exactly what you mean.
My Casio calculator gives 21, as expected.
39 is in fact the correct answer. The presenter is incorrectly adding parenthesis to an integer. Whereas -1(3) does in fact = -3, that is NOT what the problem is stating originally. Changing an integer's representation is flawed. The answer is 39. Not 21 as demonstrated incorrectly in this video.
@@williamivanko7198
No, you're wrong. The integer is 3, the first operation is the power of 2, and addition and subtraction comes next. If the power was to be applied to -3, then it would be written (-3)^2.
@@jerry2357 - but it’s not subtraction, it’s a negative integer. Think of it like below 0° temperature… -10°. You’re not subtracting anything, it’s a representation of a number. You can’t just magically add parenthesis to make the equation what you want. IMO
@@michaelsanders2655
There is nothing to say it is a negative integer being raised to the power, so it's the square that is being subtracted. If the number being raised to the power was negative, then it would have to be in brackets, i.e. (-3)^2. -x^2≠(-x)^2.
@jerry2357 Subtraction is taking one value from another. The way this question is written, there is nothing to subtract from at the beginning, making the the number getting squared -3.
I think this equation needs to be more clearly stated. Are we are dealing with (-3^2) = 9 or are we are working with (-1)*(3^2) = -9.
Both of those equal -9. The parentheses need to be around -3 exclusively to get a positive result like this (-3)^2=9.
And yes, I agree. It needs to be expressed with less ambiguity.
In math writing, the unary minus is applied after exponentiation; however, in computer science, unary minus is evaluated before exponentiation. It's less a matter of clarity, and more one of knowing the context in which the expression was written.
A negative multiplied by a negative is a positive, so -3 × -3 = +9 add 5 × 6 = 30 , answer 39.
@@howarddavies8937apparently not. But I agree
To make a long story short, when you want a negative to be your base you absolutely need parentheses. Right?
(-3)powers 2 = 9. If there are no ( ) then the negative sign must be put on hold until you deal with the base and the exponent i.e. in this case 3 powers 2 = 9 and you add the negative sign afterwards.
That was a tricky problem for sure.
I agree that this is what is expected. Personally, I feel that negation is a property of the number itself and implies parentheses are placed around it. But... it seems I am mistaken.
@@laurendoe168 Obviously I made the same mistake. I was thinking like you and I got 39 instead of 21 before finding out where I missed. ;)
I got it right because I knew the convention you use on -3 squared. I still don’t like the convention you use. I have always assumed it is a -3 squared when written like this. Not -(3 squared)
You are absolutely correct. This mathematical expression is written wrongly. The minus should be in parentheses or I would think that the minus calls for changing the sign of +6 to -6.
My sister is a literal math genius. I, however, am not. She said that a lot of these problems are printed in a way they wouldn't be in the 'real world'.
Parentheses first (4+1)=5, then exponential (-3 sq) =9, then multiplication (6x5)=30, then addition (9+30)= 39
At 0:22 you say "negative three squared" which would, by your definition, be "negative three squared" as opposed to "minus three squared".
So, to "square" the value you spoke as "negative three" would evaluate to the number "9" which would be a positive integer. To clarify that you intend the (poorly implied) -1 to be distributed after squaring, it would need to be isolated via parenthesis. Otherwise... -3^2 = 9
A lot of these algebra videos have been popping up to me lately. I am pretty sure I can find one that says the opposite. That the first minus sign indicates that the 3 is a negative number not an operator. I worked as a draftsman in mechanical engineering. Our equations were real world problems not just playing games with numbers using confusing sometimes obscure rules. Any equations we used had to be written using enough parentheses so there could be zero misinterpretation.
Please, go ahead and find one which says the opposite then. I challenge you, because to really say the opposite, you would have to be ignorant enough to say the expression -x² + x² was 2x² instead of simply zero, if the exponent applies to the implied negative 1 coefficient.
Graph out y = -x² on desmos, and notice it is a downward pointing parabola, with all values less than or equal to zero. When you substitute x as 3, it is - 3² and notice on the graph, how that is negative 9, and not positive 9
Greetings. The answer is definitely 21. Determined as follows -3^2 is not the same as (-3)^2. Now, we can move on. -9 +6(4+1)= -9 +6(5)=
-9+30=21. Lovely.
I'm not doing that, that is bullshit, that isn't the way I was taught, -3 squared is=9 period
There are two legitimate interpretations of what he wrote. What he says is (-3)^2. What he does is -1(3^2). Order of Operations #1: Write Clearly. Once we get a clearly written problem, then we can move on to solving!
@@padraicbrown6718 To get the answer this guy wants the 3^2 must be in parenthesis as in -(3^2) because -3^2 is 9. I do not see any other way to look at it. I asked a friend with a Masters and he agrees with me.
@@tomjackson4374 --- Exactly. I expressed it as -1(3^2), which amounts to the same thing.
To help reduce any confusion would be to juxtapose the two steps[6(4+1)-3(squared)]. This helps explain the use of the subtraction/negative sign.
Most helpful comment I've seen posted. Thanks. I've been trying to explain a few math concepts to a friend's child who is behind. Most things are clicking, but some I just inherently understand but can't explain why. Your example is perfect. I appreciate it. Thank you.
Better yet, just learn it properly.
Right. Since the numbers are added it is commutative and can be swapped as in 6(4+1)+ -3^2. But the way it is written, it would be 30 + -3*-3. It is not 30-3*3 and it is not 30+ - (3*3). It is 30+ -3*-3 which would resolve to 30+9 Squaring something can never end up as a negative.
@@steveklemetti8035 If you square a negative # the results is gonna be negative as well. You're not multiplying the # your raising it to the power of 2. doesn't matter what the power is either the result will always be negative if the base is negative. thus -3*-3=9 BUT -3 squared = -9.
@@leecowell8165 No. If you square a negative number it will always result in a positive product. -3*-3 is the same as -3^2 or -3 squared giving the product of 9. Doing a search of squaring a negative will state this on many websites. However -3*-3*-3 is a -27 because -3*-3 is positive 9 and then multiplying that by a -3 results in a -27.
As math students have always been taught that any "number" raised to the power of "2" means to multiply said number by itself, this then becomes a very ambiguous question.
If the "-3" is expressed on its own, it is accepted as a single entity of one singular number, expressly "-3".
When you arbitrarily decide this is a positive number with respect to it being raised to a power, you have completely altered the given equation.
Imho, you cannot refer to a unique number in two seperate and distinct ways. It is EITHER "-3" OR "3" squared, the square must use the entire number not just a portion of said number
The entire number being raised to the power of two is simply three, though. Not (minus three). Had the expression wished to indicate that it was minus three being raised to the power two, then it would have needed to be written as (-3)². Without the parenthesis it's just minus an expression term, where the expression term is 3².
At about 25 seconds into reading the problem you say negative 3 squared! If you want the negative not to be in the power you need to read the problem DIFFERENTLY. LIKE the opposite of three squared. So how do you read it if you wanted (-3)^2, if not the way you said it at about 25 seconds in?
It's all about the USE of grouping symbols so this problem is either poorly stated, misread at 25 seconds in, poorly grouped or ambiguous.
Hmm, the answer from windows calculator depends completely on how you read the equation. Is it '3' '±' 'x²' or '-' '3' 'x²' as one is not equal to the other. This is a failing of PEMDAS as it's completely unclear which is meant. Excel and others requires a complete reformat of the problem so doesn't count as in the reformat you decide which is meant as you do the reformat. "=power(-3,2)" or "-power(3,2)". Again, what prompted the equation? What is the reason the math problem exists and thus what is the context? In the real world, *why* the equation is being performed would tell you if it's -(3²) or (-3)².
Also, you keep saying "Negative 3 squared". Negative 3 squared is 3 lower than zero, squared. Minus 3 squared is what you mean but never actually say (although maybe some regions would think that's the same as 'negative 3' so "subtract 3 squared" would be more accurate).
I think I can see the problem here .. but I'll check your solution later
Is -3 squared 9 or -9 ?
I'm going to say that it's -9 because it's -(3 x 3) and not -3 x -3
-3 squared + 6(4 + 1)
-3 squared + 6 x 5
-9 + 6 x 5
-9 + 30
21
A lot of folks on here are super upset they got it wrong and, being the know-it-alls they probably are to all their friends as well, are incessantly trying to justify their incorrect answer. 😂
I was taught that this is an "irrational" problem.
-3^2 is the number -3 squared, not the negative value of 3 squared. The answer is 39, not 21. Not the first video I've seen from this page, and I've yet to see one where they actually got the math right.
It's 39. -3 squared is 9. To get -9, the notation would be -(3^2).
This isn't a negative number times a negative number, though. That would be (-3)^2. This is a positive number, three, squared, with a negative symbol in front of it.
Think of it as an expression "-a+b" where a is 3^2 and b is 6(4+1). -a+b = b-a.
So -3^2+6(4+1) = 6(4+1)-3^2 = 21
is an old school answer (30) automatically wrong?
Do I need to relearn algebra?
I last took algebra 60 years ago. My teacher is spinning in his grave.
The problem I have with this is that I was taught if something is squared, it's multiplied by itself. There is inconsistency in this it seems because as it's written -3^2 should be -3 x -3, not 3 x 3 with negative symbol being tacked on later like a seperate entity.
a negative times a negative is a positive -3 times -3 is 9 I don't agree with him
@@whatsup3270 I think he is wrong, just trolling us. I never seen a negative number being given a parenthesis. my answer was the big number (-3) x (-3).
@@whatsup3270 - you are correct - he is wrong to add parenthesis where there is none.
@@whatsup3270 Okay but you would agree with him if we rewrote the exact same equation as 6(4+1) - 3²=21
@@aebalc excellent, and yes of course, so what is the difference? If we look at -3 what do we see a noun? adjective and noun pairing? or a verb and noun pairing? In classic teaching we see a noun. Why? will that is simple since -3 has no reference point before it it can not transition thus it is viewed as a noun. -3 is a place, while x-3 is a movement(verb) of 3 units(noun) from an origin of x
My scientific calculator gives:
I typed:
3 [change sign key: +/-] x^2 [x squared key] + (6 * (4 + 1)) =
Answer:
squared(-3) + (6 * (4 + 1)) = 39
In order to get your answer, I have to type:
0 - 3 x^2 [x squared key] + (6 * (4 + 1)) =
Answer:
0 - squared(3) + (6 * (4 + 1)) = 21
39
Just talked to a guy with a Masters working on a Doctors in math, the answer is 39.
@@tomjackson4374
thats my conc.
Order of operations is the crux of algebra. The main problem with "order" is that if you do calculations in the wrong order, you get the wrong answer.
Sooooo.....just download an "order of operations" structure and you will get the right answer. It's not rocket science.
Sanjosemike (no longer in CA)
I had both 39 and 21 due to the potential of the - in front of the 3².
21 I got
-3*-3 is a positive 9
I now seem to recall a math rule that supports the answer of 21. I remember hesitating when I saw -3 squared wondering if the value changed?
I though multiplying two negative number made the result positive. No wonder I didn't do well in algebra.
The formula isn't multiplying two negative numbers, though. That would be (-3)². This is subtracting the square of a positive number, -3² = -(3²) = -9.
Like how, if the expression terms had been reversed, you would say 6(4+1)-3² = 30-9 = 21. This is the same as simply reversing the terms of -x+y to be y-x.
@@RichSmith77 But it IS multiplying two negative numbers. it IS (-3)^2 because the value the exponent is applied to IS -3. The '-' isn't a subtraction symbol, but part of the number itself. IF the intended use is to square the 3 and then make it negative then it should be expressed as -(3^2), but it isn't. Therefor, it IS (-3)^2.
@@the-dave-house-project Have you heard of WolframAlpha? It's a well respected maths website. I invite you to visit that site, enter -3^2 into it's formula bar, and see whether it thinks you're right that that equals 9 or not. Then try the equation from the video, -3^2+6(4+1), and see what it thinks the answer for that is.
Without brackets around -3 you're not squaring -3.
@@the-dave-house-projectno the exponent must be completed before the subtraction is applied.
Please compare und consider the difference:
A) -3^2 as it is given here
B) (-3)^2
A) -3^2 = -(3x3) = -9
B) (-3)^2 = (-3) x (-3) = 9
So:
-3^2 +6 (4+1) = -9 + 30 = 21
My Distraction error
-{3}^2 is of course -9
John I enjoy this. Many people arguing about pemdas but applying it correctly and it work out
Funny in lack of any scientific calculator I used excel and wrote in this =-3^2+6*(4+1) And got 39 the same in google sheet. But asking Google =-3^2+6*(4+1) I got 21. But google added parentheses and "corrected" it to =(-(3^2))+(6*(4+1)) but rally that was not what I meant. It is mess out there. For my own part I would say 39 is the correct answer. And no Mr Math teacher it will depend on what scientific calculator brand you use. Different brands may give different answers, either 21 or 39. This is really nothing new. You have always needed to take care on how you use your parentheses when programming math expression.
Plug into an RPM (HP) calculator and you get 39 but plug it into TI programmable and you get 21. Also a linux calculator also yields 21. Micropuke can't get anything right.
The bottom line though is that this is a very poorly worded problem with the way that first minus sign is dangling out there. If I was a math teacher and saw students answer either 21 or 39 I would give them full credit as long as they show their work so I understand whether they interpreted that as -9 or +9. I would also try to avoid wording problems like that, because it’s too confusing.
Love your class! At 66 I am actually "getting" Algebra. Thank you. And yes, I got 21!!
I got '21' too.
Apparently PEMDAS doesn't recognize negative integers? Never had to deal with this nonsense in college level math and physics. I did get 21 for the answer because I assumed this would be treated as -(3^2)+(5+1) which would be the correct, nonambiguous, expression yielding the answer given as 21.
got it in 4 seconds. I'm 62.
I got 21. First I find the square root of minus three which is minus nine following the rule of exponent first. Second I applied the BOMDAS approach which is adding the variable or numbers in the bracket and then multiplying the total to six. Having arrived at 30 I then subtract minus nine from thirty giving me 21.
Got it and I appreciate your clarity!
The correct interpretation has to be like described in the video. Here is why…
Write a number right before that term. For example…
17-3^2
The negative is then a subtraction operation, and subtraction is lower priority in the rules. Well, in the video imagine that number is zero instead of 17. So you have
0-3^2
Thus, the answer is -9.
I get 39.
So does my scientific calculator 🤷🏼♀️
Similar issues of operation order arise in computer programming. I always made the operation order clear by including parentheses in my program code. The lack of this when presenting arithmetic problems does seem like a "gotcha" instruction technique, as mentioned by someone else in this comment section.
It is confusing, but it's not uncommon. If you work with math you will encounter it many times, and so you should recognize what it means.
@@peterwilson8039Exactly. Teachers NEED to teach what this notation means because it is used ubiquitously.
It's as CLEAR and SIMPLE as it gets. GREAT job explaining the rules of operations. You make math fun to learn. 😊
Even though he is dead wrong the -3 is one number not two operations
Don't learn from this guy. His math is wrong in every video I've seen him release so far.
Hm i tried it with my scientific setting of the Windows calculator and if i enter 3 then press +/- to change the sign to negative and then press x^y and enter 2 next it immediately returns 9 and if i enter the rest i end up with 39. Not sure how to enter that into the calculator to get to 21 without using additional parenthesis.EDIT: I get to 21 if i use the - button first which the calculator turns into 0 - 3 and so on.
try putting it in wolfram alpha too - Would you say the expression -x² + x² was 2x instead of simply zero, if the exponent applied to the implied negative 1 coefficient then, as you want us to believe?
Graph out y = -x² on desmos, and notice it is a downward pointing parabola, with all values less than or equal to zero. When you substitute x as 3, it is - 3² and notice on the graph, how that is negative 9, and not positive 9
Okay that was confusing. I have always misunderstood when to and when not to implement the - in the final answer. Thanks for clearing that up.
If it is confusing then the person who wrote the formula failed.
I look at 9-2 squared as 9-4 but -2 squared + 9 I am not sure. The person writing the equation in the real world has to take things like that into consideration.
The key is to think about the first term as (-1)(3)^2
Many confused about difference of (-3)^2 and -3^2.
(-3)^=9. -3^2=-9
😊 Brother , you are a great math teacher . I'm a 68 yr.old guy who learned high math with a pencil and paper, no calculator. A computer was the size of a small car..
39! BODMAS Do brackets and exponents first 9 and 5. Then multiplication : multiply 5 by 5= 30. Addition 9 + 30 =39
You mean 6 x 5 = 30
21 I DON'T HAVE GREAT MATH SKILLS, QUIT POINTING OUT THAT MANY OF US WILL GET YOUR PROBLEMS WRONG. I DON'T KNOW ABOUT OTHERS, BUT THAT DEFEATS ME BEFORE I EVEN TRY!!! Holy hell....I got it right. I did the problem before you made a peep, did it in my head, and I got it right. However, I still wish you would stop telling people they are probably going to fail. That was all I ever needed to fail..........was to be told I would. I just remembered for the first time that the 'E' stands for is exponents. Powers beyond being squared will take me some time to understand though. Sorry I yelled, it's just that I remember how I struggled with math back in the 70's.
As it is redacted, including in the description : " -3 squared ...", as you redacted it, the answer is 39.
If you meant -(3²) = -9, and then you improperly redacted your problem, the answer would be 21.
But "as is", it's 39.
The answer is 21, plain and simple. Don't know what "redaction" you are referring to, and what is in the title or description is not the expression to be evaluated.
@@donmoore7785 --- Okay. English grammar time! Redaction here refers to an obfuscation in a document, specifically, how Mr Math Man reads the problem orally vs how he writes it. What he says is a normal English sentence, and can be easily diagrammed to reveal what he actually means: "Negative three squared":
1. "square" is a verb and means multiply the specified number by itself, or raise it to the second power
2. "squared" here is the past participle form
3. "negative three" is a noun phrase consisting of a numeral, three, and its adjective, negative; as an object, it is the patient of the verb, which means that it is the thing being done to
4. although it is not spoken, the agent of the verb is "you"; the agent is the one who does the operation of squaring upon the patient, which is the numeral negative three
We have to translate this normal English sentence into mathematical symbols.
The only clear translation of what he actually says is (-3)^2. This results in 39, plain and simple.
If Mr Math Man wants the answer to be 21, then he needs to say "negative one times the product of three squared" or "negative one parentheses three squared close parentheses".
His imprecise writing is invalidated by his own spoken words.
I never thought I'd have to diagram a bloody math problem to figure out what Mr Math Man actually means! All he had to was write clearly in the first place!
I like the idea of taking your online classes. I feel like I have forgotten more than I have ever learned! 😉 I am not sure exactly where to start but I suspect that it wouldn't hurt just to start with the foundations.
If people are interested in this channel, they will subscribe without you constantly telling them to. It is extremely irritating for you to continue to ramble on before solving the problem
I can't even believe I got this problem right. In record time ! I'm so proud of myself. Thank you
Thanks for the clarification!
BODMAS.
Brackets. 4+1 =5.
OPPERATIONS. Including powers. -3 squared is -3 × -3. Two negatives make a positive so, 9.
MULTIPLICATION.
6×5 =30.
ADDITION. 9 +30 =39.
QED.
I remembered that there is an order of operations in mathematics, but I didn't remember the order. Sooooo, the first problem I did on your channel I got wrong (2 instead of 17 and other wrong choice was 15). This one I got right. Thank you for the acronym PEMDAS and I made use of your breakdown notes to further explain things.😊😊😊😊
Following your regime, how do you solve say the quadratic formula. and how do you write it out to get a number. Beacuse in the quadratic formula you have the √(b^2-4ac) part. If b was -2 i would simply write this as -2^2
Exactly
If b was -2 you would write (-2)²
If b = -2 then b² is 4, not -4.
At 69 I really enjoy these problems; as a UK citizen I last did maths at 'O-level' (16-ish) before moving into the 'Literary stream' and finishing up doing law. I know your articles are aimed at youngsters but you have no idea how satisfying it is to smash a problem and think-'well I'm not quite ready for the rubber room yet' !
So, if you remove the ^2 from the equation, you have:
-3 + 6(4+1)
You read this as “negative 3” + 6 times (4 + 1).
Adding the ^2 changes this to negative 3^2, because of PEMDAS. It’s been too long since I was in a math class, so I’m unsure of the answer. I initially read this as (-3)^2, associating (implied relationship) the “-“ with the three. If you don’t associate the “-“ with the three, then it’s like saying
(-1)* 3^2. This would be wrong because there is no implied multiplication.
No the implication would be that it is 0-3^2+6(4+1). The exponent would be completed before the subtraction, making it -9+30=21
Excel says 39. That's what I got as well. formula: =-3^2+6*(4+1) result: 39.
-3^2 + 6(4+1) = -3^2 + 6*5 = -3^2 + 30. Now we get to the tricky bit. "-3" looks like an expression, but it isn't "-3" is just the representation of negative 3, so -3^2 should be read as (0-3)^2, i.e. 9, _not_ 0 -(3^2), i.e. -9, so the answer is 39.
No, -3² should not be read as (0-3)². If that were the case, 30-3² would be read as 30(0-3)²=270
-3² should be read as -(3²)
The answer is 21.
My biggest quibble with the way you explain PEMDAS is when you say "We're going to follow it from left to right." This is the basis for so many people not understanding that multiplication and division carry equal weight as do addition and subtraction. When they hear people like you say that, they then think in strict literal and linear terms, not mathematical terms and they invariably will do multiplication first, then division, then addition, and finally subtraction. This is of course NOT the right way to interpret PEMDAS at all since we know that you do multiplication and division in the order in which they appear in the equation, followed by doing addition and subtraction in the order in which they appear.
It is far better to switch over to the alternative anagram, GEMA (grouping symbols, exponents, multiplication & division, addition and subtraction). Even though there really isn't a cute mnemonic to go along with GEMA, it is a far superior anagram to use due to it's simplicity and ease of learning, not to mention its more accurate meaning.
Love this channel. I need the refresher in order to help my middle school granddaughter with her homework ❤.
Amazingly I got it right. But only because I watched another one of your challenges yesterday and remembered just enough to figure out this one. Thanks!
Except that the video is incorrect and flawed.
Should every negative number in every calculation be represented with parenthesis; -3 to be automatically considered -(3) or -1(3) thus making -3 some kind of mathematical shorthand? Or are there rules in math like there are in English such as 'i before e except after c' that contains numerous exceptions? Why should -3² be considered -(3²) when it is taught that when you have an exponent, you multiply the number the exponent is attached to, by itself based on the exponent number so -3² would read as, "Negative three times negative three"? Why would you consider the - just free floating like a -1 multiplied by whatever the outcome of the exponent calculation. It just seems arbitrary and entirely counterintuitive.
That one was so easy I got it just watching the clip nail. I’m 70 years old. I went to school in the south when they made you learn. Thanks to all my teachers except one.
wow what a very long winded answer that have been addressed in 3 min
Super easy
the negative sign does NOT effect the number being squared. So it is -9 + 30 which equals 21.
Simple solve with in the brackets 5 x 6 = 30 3 square= 9 but it's a Minus-9 = 21
The answer is not 21
The answer is 39
As per follows:
-3 squared which is -3 x -3 = 9
6 times the sum of 4 and 1 which is 6 x 5 = 30
9 + 30 = 39
The way it is written the answer is 21. The negative sign is the opposite of 3*3, nor lt negative 3 squared.
If you want 21 as the answer then should present as -(3^2). This is according to Excel...and Microsoft is never wrong.
Hehehe yes in this case it is wrong.
what happens if you move the -3 to the other side of the equation and the solve? in other words, add +3^2 to both sides.
And yet again, "Flexi Says:
The sets of rational and irrational numbers constitute the set of real numbers. The set of real numbers is denoted by
Similar to integers, real numbers can be divided into three subsets: negative real numbers, zero and positive real numbers. Zero is considered neither positive nor negative." If n
is a positive integer and x
is any real number, then xn
corresponds to repeated multiplication
xn=x×x×⋯×xn times. -3 raised to the 3 power would be -27.
21 is the correct answer.
The problem is the way that this guy states the equation. He constantly states negative 3 squared.
As he shows, a minus 3 in parentheses with an exponent of 2 actually means negative 3 squared.
The way the equation is written actually means subtract 3 squared.
He misstated the actual equation. I have dealt with multiple teachers and professors who misstate something and then don't understand why most of the students get the answers wrong.
There are a few ways to make this more understandable.
1. Put a 0 at the beginning of the equation.
2. State subtract 3 squared.
Putting a 0 at the beginning helps you understand that it is subtract 3 squared rather than negative 3 squared.
His stating negative 3 squared is the biggest problem. Making that statement makes the answer 39.
His explanation later on is correct. The negative 3 in parentheses would actually be negative 3 squared. As the equation is written, it means subtract 3 squared.
If his wording was correct the entire time, the whole thing would be more understandable.
Parentheses - 4+1=5
Exponent - -3x-3 = 9
Multiplication - 6 x 5= 30
Addition - 9+30=39
-3² is not (-3)², it's -(3²). So the answer is 21.
Yay! I got it right. I’m awful at math. I cried through my college math classes.
So you are also saying 3 to the 3rd power is 27 not -27? Another from Google search "So if they give you an exercise containing something slightly ridiculous like (−1)1001, you know that the answer will either be +1 or −1, and, since 1001 is odd, then the answer will have to be −1." Another "Can you square anything and have it come up negative? No!"
The best way to solve this is to add a zero at the start .
0-3^2 + 6(4+1) .
Duh! Without parens it’s minus three square = -9 ! So correct answer is -9 + 30 = 21
it's easy if you know PEMDES operation
1. parentheses
6*(4+1) >>> 6*5 = 30
2. exponent
-3^2 >>> -9
watch out this is NOT (-3)^2
3. put them together
-9+30 or 30-9 = 21
Answer is 21
Unfortunately, he didn't write it clearly, leaving it open for interpretation. This was his mistake.