Math question- What is a negative number squared?

[disneyfanforever]

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?

 

[emjester1]

Ok, I just re-read your post. So, if the problem is -(7 squared) I.e. the number inside of the parentheses is squared, and the negative sign is outside of those parentheses, then the teacher is correct.

 

[eduk8r26]

I still remember Edward James Olmos as Jaime Escalante in "Stand and Deliver" telling his math classes "A negative times a negative equals a positive". He made them memorize that.

 

[BillSears]

I think the problem is how it is written.

For example:

100 - 7squared = 100 - 49 due to order of operations. You would do the squared first before the minus.

But to me negative 7 squared implies that the negative is first. -7 X -7 = 49

So is it minus seven squared or is it negative seven squared?

 

[Kitty 34]

it would be a positive number

 

[disneyfanforever]

Ok, I just re-read your post. So, if the problem is -(7 squared) I.e. the number inside of the parentheses is squared, and the negative sign is outside of those parentheses, then the teacher is correct.

The teacher is saying that -7 squared is -49 if there are no parenthesis at all. She said the only time it is positive is if it is (-7) squared.

I am so confused. As a side note, Siri agrees with me.

 

[joanne312]

I think the teacher is incorrect. -7 x -7 = 49

 

[disneyfanforever]

I think the problem is how it is written.

For example:

100 - 7squared = 100 - 49 due to order of operations. You would do the squared first before the minus.

But to me negative 7 squared implies that the negative is first. -7 X -7 = 49

So is it minus seven squared or is it negative seven squared?

You make a good point. I agree with what you are saying. I thought I understood all of this but now I am completely doubting myself.

 

[sam_gordon]

I think the teacher is incorrect. -7 x -7 = 49

This.

-7^2 = -7 * -7 = 49
-(7^2) = -(7 * 7) = -49
(-7)^2 = -7 * -7 = 49

NOTE: ^ is 'to the power of' & * is multiply.

I don't know any other way this can possibly be written.

 

[castleview]

I still remember Edward James Olmos as Jaime Escalante in "Stand and Deliver" telling his math classes "A negative times a negative equals a positive". He made them memorize that.

That's a foreign concept. I suck at math and knew that easily. I guess my public school education was a lot better than I thought.

 

[ready123go]

Correct: -7 sq = (-7 x -7) = +49 because the -7 is taken in its entirety* and would be said "negative seven squared".


Correct: It is the same as (-7 sq) = -7 x -7 = +49: Said "negative seven squared"


Also correct: -(7 sq) = -(7 x 7) = -1(7 x 7) = -49: Said "the negative square of seven"


(in college I used to tutor geometry, trig & calculus 1-3. Been a long time, but not that long...)


*Negative seven is, by convention, taken in its entirety. The reason is that a negative number cannot, logically, have a square root. In order to get around this conundrum, and imaginary number (i) is used.

 

[mrsklamc]

If someone is saying "negative seven squared" no parenthesis are implied, it's just -7 x -7 and the teacher is incorrect.

 

[mcraige]

The answer is -49. Negation is an operator on the same level as multiplication and division, which is evaluated after the exponent.

Some calculators (and even Excel) use an order of calculation rather than an order of operation, so they get it wrong. Microsoft documents that to solve the problem accurately, it should be entered -(7^2).

 

[sam_gordon]

The answer is -49. Negation is an operator on the same level as multiplication and division, which is evaluated after the exponent.

Some calculators (and even Excel) use an order of calculation rather than an order of operation, so they get it wrong. Microsoft documents that to solve the problem accurately, it should be entered -(7^2).

Disagree.

To me, "negative seven squared" should be written as -7^2. That equates to -7 * -7. That means 49. Another way to write it would be (-7)^2.

Or do you equate "negative seven squared" to -(7^2)?

ETA: I see what you're saying. I still disagree. -7 is a number, not an equation. IMO.

 

[LisaR]

OP'er, do you actually have the problem written out in front of you on a piece of paper? Are these examples that have been written down with the answers? You say that "the teacher states......" Where does she state this? I'm curious what her exact examples look like.

 

[mrsklamc]

Disagree.

To me, "negative seven squared" should be written as -7^2. That equates to -7 * -7. That means 49. Another way to write it would be (-7)^2.

Or do you equate "negative seven squared" to -(7^2)?

ETA: I see what you're saying. I still disagree. -7 is a number, not an equation. IMO.

This is the issue. (And I agree with you.)

 

[Wdog999]

Here are the rules regarding negative numbers and squaring:
NOTE: ^ should be read as "to the power of," with ^2 meaning "squared."

(-7)^2: This should be read as "the quantity of -7 squared," which is -7x-7=49

-7^2: This should be read as "7^2 negated," which would be -(7x7), which simplifies to -(49), which is the same as -49.

-(7^2) is read exactly the same as -7^2.

-(7)^2: This is read as "the quantity of 7 squared and then negated." This becomes -(7x7), which, as shown in the second example, becomes -49.

Just to clarify the second and fourth definitions, to negate a number is to reverse its sign. For example, taking 1 and turning into -1, thus reversing it from a positive number to a negative number, would be considered negating 1.

Hope this helps you.

 

[leebee]

Here are the rules regarding negative numbers and squaring:
NOTE: ^ should be read as "to the power of," with ^2 meaning "squared."

(-7)^2: This should be read as "the quantity of -7 squared," which is -7x-7=49

-7^2: This should be read as "7^2 negated," which would be -(7x7), which simplifies to -(49), which is the same as -49.

-(7^2) is read exactly the same as -7^2.

-(7)^2: This is read as "the quantity of 7 squared and then negated." This becomes -(7x7), which, as shown in the second example, becomes -49.

Just to clarify the second and fourth definitions, to negate a number is to reverse its sign. For example, taking 1 and turning into -1, thus reversing it from a positive number to a negative number, would be considered negating 1.

Hope this helps you.

Only if you are punching numbers into a calculator or computer, because then you need to use parenthesis so the technology can understand the question. I prefer to teach my middle schoolers standard math. Basic, standard, paper-n-pencil math says that negative seven squared is positive 49: Seven times seven is 49, a negative times a negative is a positive.

Of course, the answer really IS negative 49 because the teacher says so.

 

[Pig Pen]

and this is why I hated math.

 

[LisaR]

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