Negative numbers

A

Andrius

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Jan 22, 2021
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Hi all,

I always thought that my maths is pretty good but turns out not. Basically I was helping my son with his maths homework and got confused. We've tried scientific calculator, Google calculator, calculator on mobile phones and we've got the same answers. Here is my question - why -2 squared equal -4 but -2 × -2 is 4? Can anyone please explain me what am I missing here?
 
It may be a semantic problem:

[math](-2)^{2} = (-2)\cdot(-2) = 4[/math][math]-2^{2}[/math] MAY be interpreted differently as [math]-(2^{2}) = -4[/math]
If you are programming, you need to be familiar the the strict precedence of operators.
 
order of operations ...

[MATH]-2^2 = -1 \cdot 2^2 = -1 \cdot 4 = -4[/MATH]
[MATH](-2)^2 = (-2) \cdot (-2) = 4[/MATH]
 
So basically there is no correct answer? The question in my sons homework was - x squared + y squared(no brackets) , x=-5 and y=4. We got answer as -9 and it turned out to be incorrect. What is the correct answer then?
 
Andrius said:
Hi all,

I always thought that my maths is pretty good but turns out not. Basically I was helping my son with his maths homework and got confused. We've tried scientific calculator, Google calculator, calculator on mobile phones and we've got the same answers. Here is my question - why -2 squared equal -4 but -2 × -2 is 4? Can anyone please explain me what am I missing here?
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The trouble probably is in how you are reading the symbols. When you write \(-2^2\), it doesn't mean "-2 squared"; it means " the negative of (2 squared)".

Which answer, -4 or 4, are you thinking is right, and which is wrong? Which is technology giving you, and what are you entering? (Different calculators have given different results for such an expression in the past, but I think most currently follow the rules taught in school and will say \(-2^2=-4\) and \((-2)^2=4\).)
 
I like to think of it this way. How would you compute 10-22? I suspect that you would say 10-4 =6. That is, you replaced -22with -4. End of discussion, ok?
 
I often refer to my primary programming language. It does very, VERY little that is NOT strictly right-to-left.

-2^2 is definitely interpreted 2^2 = 4, then -4.
There is a funny little symbol, called "high minus" which forces the sign to be interpreted with the trailing number. -2^2 = 4

No substitute for knowing EXACTLY what one is doing.
 
Andrius said:
So basically there is no correct answer? The question in my sons homework was - x squared + y squared(no brackets) , x=-5 and y=4. We got answer as -9 and it turned out to be incorrect. What is the correct answer then?
Click to expand...
Absolutely NOT! Was it this? [math]-x^{2} + y^{2} = y^{2} - x^{2}[/math], and there is no ambiguity in either condition.
 
Andrius said:
So basically there is no correct answer? The question in my sons homework was - x squared + y squared(no brackets) , x=-5 and y=4. We got answer as -9 and it turned out to be incorrect. What is the correct answer then?
Click to expand...
You seem to be saying that the problem was to evaluate -x2 + y2 when x=-5 and y=4.

This becomes -(-5)2 + (4)2 = -25 + 16 = -9. Who said that -9 is wrong?
 
Some of the homework my son has to do online, some website, and that's where we've been told that the answer is incorrect. Annoyingly his math teacher,when challenged on this, told my son to follow wrong rules as she can't be bothered to investigate why website is giving wrong results. So basically, she is telling all class to do it wrong way so it is easier for her.

Thank you all for your responses, this helps me a lot and it confirms to me that my maths isn't that bad :)
Once again,thank you all for your help
 
Is the teacher telling the students that -9 is correct but to put in some other answer because the online system thinks that is the correct answer? Or is the teacher teaching the students the wrong way is the correct way to do these type problems?

As long as the teacher shows the students the correct way, gives them the correct answer or whatever way she communicates to the students these days that the correct answer is -9 but if you want credit please choose 41 (or whatever number) as the right choice does that really matter to the students? In my opinion all that matters is that she teaches her students well.

On the other hand if the teacher is teaching the material the wrong way just so her students get the correct answer that is totally unacceptable. Given my history for speaking poorly of 8-12 math teachers I prefer that someone else addresses this case, if in fact it is true.
 
skeeter said:
I do appreciate the “heads up”
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I can really attack them. This time however I do not know if the teacher did anything wrong--at least mathematically.

I take it you haven't read any of my comments regarding poor teachers?
 
skeeter said:
Haven’t had the pleasure ... yet.
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You really missed out on some amazing post. I actually try to be somewhat calm as one helper here really doesn't like my bashing, so out of respect I try to be less rude.

I went to school in Brooklyn, NY and I can certainly say that I learned next to no math until I started going to City College (one of the campuses of the City University of New York). They trained me well.
Then I started teaching full-time and I got to meet the average adjunct. Of my is all I'll say now. What are your experience with high school math tutors?
 
No direct experience ... mostly word of mouth from my former students on their expertise or lack thereof. Most had good things to say about retired math/science teachers who tutor on the side.
 
Adding my two cents which isnt much different than what others posted above.

When the exponent is 2 and is next to a number like -3, the answer will be -9, because the exponent does not touch, does not affect the negative sign.

however, when you substitute -3 for a variable that has an exponent 2, b becomes -32 because b is -3.

think of the sign — as a subtraction sign but when subsituting it becomes a negative sign, part of the number.
always remember it can mean negative, not just to subtract
 
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