Lesson: Operations with Signed Numbers - Part II

Comment on Operations with Signed Numbers - Part II

Are there some calculation mistakes in the way in which this problem has been solved?


greenlight-admin's picture

Question link: http://greprepclub.com/forum/if-a-b-0-which-of-the-following-numbers-mus...

Yes, there were several calculation errors in his response.
I have admin privileges on that site, so I was able to edit the mistakes.
It should be good now.


Abdul Hannan's picture


I have a problem in this question Mr Hanneson. the thing is when you square a negative number you get a negative answer e.g. -3^2=-9.

but when you put a bracket around a negative number and square it we get a positive number e.g. (-3)^2=9

now there is no mention of any bracket so how should i solve it, I am confused. please reply.
greenlight-admin's picture

Hi Abdul,

We can think of this in terms of order of operations (BEDMAS aka PEMDAS)

In both cases, (-5)² and -5², we can think of expressions as having two operations: subtraction and an exponent.

In the case of (-5)², we must first deal with what's happening inside the brackets. So, we have -5 in the brackets.
Then we'll deal with exponent (the power of 2) to get: (-5)² = (-5)(-5) = 25

Conversely, the expression -5² has no brackets. So, according to BEDMAS/PEMDAS, we must deal with the exponent before we deal with the subtraction.
So, -5² = -(5²) = -(25) = -25

Does that help?


confused at this point. is it that -5^2 and (-5^2) are not the same, as such we can't get the same answer
greenlight-admin's picture

-5² and (-5²) are equal.
-5² = -25 and (-5²) = -25
We can say that -5² = -(5²) = -(25) = -25

On the other hand,(-5)² = (-5)(-5) = 25

It's all about notation.

Does that help?


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