-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?

Confuddled in every other case the negative in front of the 9 would make it a negative number, but not in this particular case where there is an exponent. That's why you have to use brackets if you want to show that you in fact want to square the number -9, rather than produce the negative of the square of 9.

If no brackets, you start with the exponent, then negate what is produced.

If brackets, you apply the exponent to what is inside the brackets.

The "imaginary" zero in front is just to demonstrate this convention, because everyone on this thread would correctly answer -81 if the question was 0 - 9 ^ 2 = ?

(Sorry for the spaces, trying to avoid it all becoming italicised)

@Fabuleuse me too. I can’t look at the question and see anything other than -81 as the answer. I am baffled!

Explain to her that if the teacher says ‘minus 9, squared, is 81’, that’s correct. People don’t speak brackets, instead they make it obvious it’s a negative number by how they say it.

That calculators need brackets to be told it’s -9 squared.

That the online maths program is a calculator.

That she won’t be asked this without brackets in a maths exam and the online program is a bit rubbish for asking her it without brackets.

DD is doing A level maths.
She has just taken an exam.
She says it stands as 81.
-9*-9
If they wanted -81.
-(92). Or -(9)2
They will show the brackets.
You need to let your child got with how the teacher says, as that is how it will be marked in the exams.

For the context, she can figure out 9 1/2 is square root of 9. Or 9 3/5 is same as fifth root of 9^3.

It's a badly written question I'm guessing. The teacher wanted to combine squaring with multiplying negative numbers, and wanted them to do (-9)^2 = 81.

It is however -81, OP is correct. I like the 0-92 explanation, I'd also think of it in terms of x2 and -x^2 not being the same expression (I find these things easier with algebra than numbers).

Those saying you can't stick a zero in front because the expression doesn't mean 0 less blah blah blah, it means the 9 is negative are wrong. Those expressions are the same: 0-5 and -5 are the same number.

(Lecturer in a mathematical subject, apologies for the clumsy explanation. It's a poorly written question, done quickly when the teacher was trying to quickly put together a range of exercises testing different algebraic skills - easily done, we've all been there.)

So Noble, do you think it's better for her to think -92 = 81? I am truly confused. For exam purpose for secondary, -9 squared is 81, and I know it's correct. But truly mathematically, -92 is different from (-9)^2 but ignore it? I thought I could explain to her the difference, it would be good for her, since most of her understanding is very intuitive.

MindyStClaire can you explain why the A level teachers are teaching it as 81 then.
DD got all the algebraic questions right.

I think most people would glance at it and say 81 at first in truth, I did too.

Very technically, the answer is -81.

I don't know why teachers would teach that it's 81, other than lazy shorthand.

Explaining why it's -81 but telling the DD to do what the exam board says is probably good advice.

Most of the time in school the brackets are missed out due to sloppy practise!

If this was on a GCSE paper it would be very clearly either (-9)2 or - (92).

With A level, it would depend on where the skill is being used in the question. There wouldn't be a standalone question like this at A level. Instead it would probably be part of a substitution question. If x=-9 then x^2 is 81 because it is - 9 multiplied by - 9.

The OPs question is subtly different.

Teachermaths, she knows √ 9 = +/- 3. There is no confusion. This was very new thing happened today, and dd was so confused and unhappy that the answer was wrong and asked me, and luckily, I did know the right answer by true coincidence. But start to think it may have been better if I didn't.
So am I safe to think something like -9^2 won't come up, unless clearly marked with brackets?

Some textbooks obsessively put brackets around every instance of a negative number so would have the question 3-(-3) and the kids get totally confused about what the brackets mean.

Exam questions would usually be written -2 x -3 without brackets, (-2)^2 with brackets and if they wanted to test subtracting a negative they’d avoid the bracket issue by doing it as substitution into an expression or a difference of temperatures.

So you could anticipate the issue of saying ‘minus 9 squared’ but having to write (-9)^2 by bracketing every negative number to get in the habit, but we generally don’t. Kids don’t realise the importance, except when we tell them ‘be careful when squaring a negative with your calculator, it needs brackets’.

So am I safe to think something like -92 won't come up, unless clearly marked with brackets?^

Yes. In a proper exam anyway.

Thank you. I think it hasn't fundamentally solved my ultimate question of understanding difference between -92 and (-9)2, as far as secondary maths is concerned, it's doesn't seems to be a big deal. Especially so many people seems to have totally opposite view, even though they all claims to have degree in maths.

I guess she needs to find out the truth for her herself, if she decided to pursue maths.

Thank you for all your help.

The truth is if knowledge of the difference between -92 (=-81) and (-9)2 (=81) were examined at GCSE, we’d be all over it at secondary school, but it’s not, so we aren’t.

Noble, yes, I realised that. I never thought this was so controversial until today. I just simply took it as a fact and never questioned, it was negative of 92 for me, not (negative 9)2. And many people said I was wrong, but I never doubted I was wrong, for some unknown reason.
But I just wonder, if the child loves maths, and asked you why she was wrong to say 81, do you just tell her to ignore it because it's not examined at GCSE ? Or like me, try to get some answers, even though many people seemed to laugh at me for saying it's -81, because I simply believe it is?

I've got perfect explanation, a very logical and a simple one, thanks to people here. So I am glad that I started this thread, even though this seems to be of no importance in the secondary maths.

No, obviously I’d explain to her why she was marked wrong for 81.

When I’m teaching it, I’d always point out they need brackets for the calculator, and explain that it was because of BIDMAS.

But if they wrote -9^2 = 81 in their book without brackets would it be something I would insist they corrected to have brackets? Possibly not.

It’s like unequals equals. If a kid is asked to work out the area of a triangle with base 4 and height 6 and wrote
4 x 6 = 24 / 2 = 12 cm^2 would I kick up a fuss? Top set, yes, bottom set I’d be bloody delighted they remembered to divide by 2.

Very technically, the answer is -81.

The answer is -81, but it's just by the normal rules of algebraic notation. Nothing too technical about that. See picture.

(Credentials: Maths degree, ex-Maths teacher, use exactly this kind of calculation in my job)

(But incapable of rotating a picture it would appear - try again).

4 x 6 = 24 / 2 = 12 cm^2 would I kick up a fuss? Top set, yes, bottom set I’d be bloody delighted they remembered to divide by 2.

...and pretty impressed that they'd shown the cm^2 as well, I bet!

I know that DadDadDad (we have the same professional qualification as well as similar degrees), but we also all know that that's not what the teacher was getting at.

Most people (including mathematicians) would glance and say 81 before thinking again I think.

I texted it to DH (PhD physics, works with more complicated mathematical models than I do) and he said 81, and only changed his mind when I pointed out x2+5 Vs -x2+5, and what putting a zero in front does etc.

I'm sorry op. I wasn't calling you stupid I was equivalencing stupid equations. But I can see I was rude and I didn't mean to be.

x2+5 Vs -x2+5
What do you get where x is +9 and when x is -9?
Its not clear from the original question which it is.

x=9 you get 86 Vs -76
x=-9 you get 86 Vs -76
The same for both so the answer is still 81 or -81 depending on whether its the a positive or negative 9. I appreciate that many expect negative numbers to be in brackets when shown on there own but we don't show the + for positive numbers. I can see it being -81 but I still would by default have said -9 squared on seeing that equation.

I love a good maths thread. Cheers me up no end.

Me too, Teen, thanks for the @ summons last night.