Math question- What is a negative number squared?

[NikkiLovesWDW!]

I think I understand the teacher's reasoning. Remember "please excuse my dear aunt sally?" Used to remember order of operations - parenthesis, exponents (which would be the squared), multiplication and division, addition and subtraction.

Technically a negative number is a subtraction so the exponent operation on the 7 takes precedence. So the 7 is squared and then the negative is on that result. Because parenthesis takes precedence over everything, that is the only way it would result in a positive number.

 

[RitaZ.]

Is it any wonder our children are failing the standardized math tests when even the adults disagree on the answer?

 

[mrsklamc]

Technically a negative number is a subtraction

No, it's an integer.

 

[NikkiLovesWDW!]

No, it's an integer.

So where do integers fall in the order of operations?

Sent from my iPhone using DISBoards

 

[BCDisneyFanatic]

High school math teacher here.

-7^2 can actually be visualized as -1 x 7^2; the negative is MULTIPLIED with the 7 to make it negative. However, according to BEDMAS (or PEMDAS for you Americans), you do exponents before multiplication.

Therefore, -7^2 = -1 x (7)^2 = -1 x (7x7) = -1 x 49 = -49

However, if there are brackets, then everything in the brackets is squared since brackets come before exponents in the order of operations:

(-7)^2 = (-7) x (-7) = +49

Absolutely, positively, hundred-percent sure on this, having taught it to both 9th and 10th graders in the last three weeks!!!

 

[Planogirl]

This isn't how I was taught but maybe this is the new math. It was always a negative number squared was a positive number.

 

[BCDisneyFanatic]

So where do integers fall in the order of operations?

Sent from my iPhone using DISBoards

You question doesn't make sense mathematically.

The order of operations is a set of rules. Integers are a set of numbers. When mathematical operations are applied to integers, you follow the order of operations.

 

[Planogirl]

These are the rules per two math websites. It looks like it depends on context:

http://www.mathsisfun.com/square-root.html

http://mathforum.org/library/drmath/view/55709.html

 

[abdmom]

HS Chem teacher here

BC is exactly correct. It's negative.

To think of it another way, and at the risk of confusing everyone, lol

The expression -x^2 is

negative one times x times x which will give a negative number

 

[cassandrap83]

 

[mhsjax]

I feel like an idiot for asking this question but I don't know if I was taught wrong in school. However, if I was taught incorrectly several of my friends were as well because they agree with me.

I have always thought a negative number squared is a positive number such as a -7 squared (I don't know how to make the little two on my ipad) is 49. However, my son's teacher is saying that the answer is -49 as you do the exponent portion first (7x7) then you add back the negative sign after. What?? She states the only way it is positive is if the -7 is in parentheis.

Are there any math wizards out there that can help me?

She is correct. The negative is only "attached" to the seven if it is in parenthesis. so - 7 squared in -49, (-7) squared is 49.

 

[pumpkinmomma]

High school math teacher here.

-7^2 can actually be visualized as -1 x 7^2; the negative is MULTIPLIED with the 7 to make it negative. However, according to BEDMAS (or PEMDAS for you Americans), you do exponents before multiplication.

Therefore, -7^2 = -1 x (7)^2 = -1 x (7x7) = -1 x 49 = -49

However, if there are brackets, then everything in the brackets is squared since brackets come before exponents in the order of operations:

(-7)^2 = (-7) x (-7) = +49

Absolutely, positively, hundred-percent sure on this, having taught it to both 9th and 10th graders in the last three weeks!!!

This! 100% this. Math teacher here who teaches college level classes.
There is a whole bunch of incorrect information on this thread. Please do not rely on Siri for math help.

 

[SandrA9810]

Always think of a negative sign as multiplying by -1. It will help greatly in rembering to multiply it the proper way or else you're likely to leave it off and not include the negative sign properly.

 

[theworldneedscolor]

That is how I was taught in elementary school. But I am in Calculus this year, and my teacher is really stressing that the negative is only attached if it is inside the parentheses.

ETA: Negative seven squared is positive forty nine. But negative seven is written as (-7). -7 means -1 X 7.

 

[BCDisneyFanatic]

ETA: Negative seven squared is positive forty nine. But negative seven is written as (-7). -7 means -1 X 7.

Mmmmmm... in my opinion, "negative seven squared" is -49.

However, the "square of negative seven" is +49. Or, "negative seven all squared" is +49.

Ahhhh, if only my students loved the language of math as much as I do .

 

[mrsklamc]

What I find interesting is that apparently a lot of us were taught incorrectly, and in the 20 years since algebra it has not mattered in my life once.

 

[ready123go]

What I find interesting is that apparently a lot of us were taught incorrectly, and in the 20 years since algebra it has not mattered in my life once.

That is, until this thread! Lol...

 

[sam_gordon]

Always think of a negative sign as multiplying by -1. It will help greatly in rembering to multiply it the proper way or else you're likely to leave it off and not include the negative sign properly.

But 'squaring' a number means multiplying it by itself, right?

So 7^2 is the same as 7 * 7, right?

So if -7 is squared, -7 multiplied by itself, so -7 * -7.

For those who say the negative sign just indicates multiplying by -1, then why isn't -7^2 also written as (-1 * 7) * (-1 * 7)?

Is -7 (not squared, just the number) an integer or a calculation?

I really think the problem with this problem is using the spoken word to determine an equation.

 

[mnrose]

If you think that is interesting, try the discussion my husband and my son (a math geek) had. One of the problems my son had in his math homework was "what is 8 divided by zero? Justify your answer."

Now, I know we all learned that 8/0 is "undefined" (which is the "correct" math answer), but why? As my husband said, in the real world, if you have 8 things and divide by nothing, you still have 8 things.

And, it turns out, the reason that the answer is "undefined" is that mathmaticians really don't have a good answer for what happens when you divide by zero. It violates other "core" principles of math, and makes no sense. For example, if you divide 8 by a positive number that is very, very close to zero (for example, .000000000000000000000000000000001), you get a very large positive number. As this number gets smaller and smaller, it approaches positive infinity. On the other hand, if you divide 8 by a negative number that is very very close to zero, you get a very very large NEGATIVE number. The two numbers you divided by are minutely different, yet, using normal principals of math, the answer is infinitely different. Makes no sense. So, what do you get when you divide by the "real" zero?

Undefined.

Love that. Can't figure it out? Makes no sense with other math rules? Simply call it undefined.

Kahn Academy has some excellent videos on this one if you are interested. As my son was.....

 

[disneyfanforever]

Thanks for all of the explanations! I understand more what the teacher is saying now. I really don't think that is how I was taught so it is going to take some adjustment in my thinking when helping him.