-9^2 = -81

[insufferablefury]

I need a help from maths teachers.

My dc says her teacher taught the children the answer is 81. And when she has done the work on online maths programme, it's wrong obviously.

I have explained, it's -81, since it's really - (92). And to get answer as 81, the question need to be (-9)2, not -9^2. But being not a maths specialist, cannot explain why in a logical way , and the child blatantly believes the teacher, which is a good thing, but not really if the teacher is wrong.

How do you maths teachers explain this to your students?

[StealthPolarBear]

(-9)^2 is 81

[StealthPolarBear]

Sorry I see you're agreeing. You wouldn't usually need to use brackets. The square of a negative is positive. Convention is that brackets are assumed.

[GuyFawkesDay]

-9 squared it 81. Squaring gets ride of the negative

[Teachermaths]

It depends on the question....

Is it substituting - 9 into an expression?

Or is it just - 9^2 as a standalone?

[Xiaoxiong]

The convention is that exponents take precedence over negation. So if I see -3^2, with no brackets, I do the square first, taking care of the exponent, then I make it negative.

-3^2=-9
(-3)^2=9

This is because in front of every - sign is an invisible zero. So the first sum above is "actually" 0-3^2, which hopefully is more obviously equal to -9 rather than 9.

[insufferablefury]

StealthPolarBear, I know we normally don't need to use brackets. The question we got stuck was -92, so I used brackets to show my dc the difference in -(92) and (-9)2. The rule of square of negative is positive. I know that. But it need to be (-9)2 or -9 x -9, instead of -92. to get 81. Seems to be very confusing when teacher says the answer for -92 is 81, but really, -9^2 = -81. And I can't explain well, the difference of having - in front of the number with powers.

[ItsGoingTibiaK]

It's a BODMAS (or PEDMAS or BIDMAS) thing. Squaring is an ORDER or EXPONENT, which means it is operated before the minus sign.

[Xiaoxiong]

Oh fucking hell. All my carats made italics.
-3 ^ 2 = - 9. Because there is an invisible 0 in front of the negative number.

[StealthPolarBear]

But thay is the convention. I don't understand why you're insisting it needs brackets.
A negative number squared is shown by -x2 where the 2 is superscript.

[insufferablefury]

Teachermaths, it's stand alone. So the answer is definitely -81.
-9^2 = ?

[insufferablefury]

ItsGoingTibiaK , that totally makes sense! Great. I think I got an answer how to explain. Thank you!

[insufferablefury]

And thank you, Xiaoxiong. It's too complicated to understand the thing about 0 for me, but now I got it, that exponents take precedence over negation. I think I can explain properly now why. Thank you.

[hiddenmnetter]

The answer is due to the order of operations. BODMAS- brackets, orders, divisions, multiplications, additions, subtractions.

The exponent is an order, so the 9 is raised to its square of 81, and then either subtracted or multiplied by -1, whichever you use. -9 x -9 = 81 though.

This is why the quadratic equation is +/- at the beginning, because both the positive and negative answer are right (and why quadratic formulae make parabolas)

[hiddenmnetter]

I see I've cross posted

[TryingAndFailing39]

It’s definitely -81 with no brackets. Brackets are needed to square the -9 and make the answer 81.

[insufferablefury]

Thank you hiddenmnetter.
And thanks, everyone. I explained Bodmas/Pedmas and I think(hope) dc understood. Says so. And I asked her to ask the teacher if still not sure.
Funnily enough, I am leaning maths myself, and have encountered this question asked by someone else recently, and being an adult, I just accepted this as a fact, that was an only reason I knew -9^2 was -81. But don't have enough knowledge to explain it to someone else.
It helped me understand too. So, thank you.

[myduckiscooked]

Constant issue with my students making a mistake on this one. You are absolutely correct.

(-9)^2 is in words - minus mine all to be squared.

-9^2 is simply minus nine squared

The addition of brackets means that everything within the bracket is squared. Omit the brackets and you are only squaring the nine.

[CharlieWork]

-9^2 is definitely 81. Not negative. You can check by plugging into a calculator.

It is just -9 x -9 = 81

If it was -(-9^2), then it would be -81

[Stillmuddlingthrough]

I wouldn’t assume a calculator works on the correct order of operations - many don’t especially non-scientific ones. It is definitely -81. Maths grad and post grad plus maths job but also the correct answer of -81 is exactly what my primary and secondary school children are taught.

[TeenPlusTwenties]

Charlie RTFT.

-9 x -9 = (-9)2 not -92

[insufferablefury]

CharlieWork, no you are wrong. It's not -9 x -9. It's - (9^2).= - 1 x 81
Try using scientific calculator. By typing in -92, and typing in (-9)2 , you get different answers.

[CharlieWork]

I have used a scientific calculator and have a maths degree! The square of a negative number is positive.

I have read the full thread, thank you

[CharlieWork]

Calculators are programmed to work using the BODMAS method

[EggysMom]

I did Maths many many many years ago, and we never had the "presume there is a zero at the start of the expression". So whilst I appreciate that BODMAS says the ordinal comes first, tome the '-' is not a minus sign (as in 0-9). I don't know the correct term but it's an indicator that the first number in the expression is -9 and not +9. It belongs to the 9, rather than standing alone. So to me, the equation is -9 squared which is +81.

[TeenPlusTwenties]

But Charlie

Say you have +10 - x^2

and x=9, that's 10-81 = -71. yes?

So -x2 + 10 has to come to -71 too. So -x2 means -(x2) not (-x)2