# Lesson: Operations with Signed Numbers - Part II

## Comment on Operations with Signed Numbers - Part II

### Are there some calculation

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

http://gre.myprepclub.com/forum/if-a-b-0-which-of-the-following-numbers-must-be-positive-1907.html 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.

Cheers,
Brent ### https://www

https://www.greenlighttestprep.com/module/gre-arithmetic/video/1059.html

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. ### Hi Abdul,

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?

Cheers,
Brent

### confused at this point. is it

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 ### -5² and (-5²) are equal.

-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

Does that help?

Cheers,
Brent

### Hi!,

Hi!,
what is the meaning of "yare number"?
Thank you ### Can you tell me where you saw

Can you tell me where you saw/heard "yare number"?
That will help me decipher :-)

### I read it in the following

https://gre.myprepclub.com/forum/if-x-and-yare-numbers-on-the-number-line-above-which-of-the-12496.html

Thank you ### Ahhhh! Looks like the

Ahhhh! Looks like the original poster didn't place a space between "y" and "are"
It should have read "If x and y are numbers..."
I have edited the question.

Cheers,
Brent

### where are the practice

where are the practice questions available? Is it the 3rd edition book? ### There's a lot of duplication

There's a lot of duplication between the 1st, 2nd and 3rd edition books. So, in the Reinforcement Activities box above, some linked questions listed as "GRE Official Guide" questions could be from just one edition or all 3. The important thing is that all of the Official questions are actual (retired) GRE questions.

Does that help?

Cheers,
Brent

### https://gre.myprepclub.com/forum

https://gre.myprepclub.com/forum/if-a-b-0-which-of-the-following-numbers-must-be-positive-1907.html ### At 4:26 mark, 2+3*4= 20. I

At 4:26 mark, 2+3*4= 20. I think this is wrong. Shouldn't it be 14?

Thanks! ### You're correct. If you watch

You're correct. If you watch the next 20 seconds, you'll see that I say 2 + 3 x 4 = 14
I used the expression 2 + 3 x 4 to set up orders of operations (i.e., PEMDAS and BEDMAS).

Cheers,
Brent

### https://gre.myprepclub.com/forum

https://gre.myprepclub.com/forum/x-x-14550.html

Hi Brent,

this question seems very easy, but I can't seem to understand it. In this question, we're told that x ≠ 0 and |x| = -x

------------------------------
ASIDE: Many students will assume that -x must be negative (since we have a negative symbol in front of the x).
However we can't make the conclusion that -x must be negative.
In actuality, -x can be either positive or negative (depending on the value of x)

For example, if x = 1, then -x = -1 (negative)
And, if x = 6.2, then -x = -6.2 (negative)

However, if x = -3, then -x = -(-3) = 3 (positive)
And, if x = -88, then -x = -(-88) = 88 (positive)
------------------------------

Okay back to the question.

Let's examine this part: |x| = -x
We know that |x| is POSITIVE for all nonzero values of x.
So, our equation becomes: some POSITIVE number = -x
This means -x is POSITIVE
In order for -x to be POSITIVE, it must be the case that x is negative (see my examples above)

Does that help?

### Sorry for the delayed answer.

Sorry for the delayed answer. Understood

### Hi Brent, I'm struggling at

https://gre.myprepclub.com/forum/gre-practice-question-if-b-0-and-a-b-563.html Given: a/b > 0 (the product ab is positive)

We know the following from the above video:
i) positive/positive = positive
ii) negative/positive = negative
iii) positive/negative = negative
iv) negative/negative = positive

So, a/b is positive, we know that EITHER a and b are both positive (property i) OR a and b are both negative (property iv).
In other words, we can be certain that a and b are the SAME SIGN

The three statements:
A. a > b
B. b > 0
C. ab > 0

We can see that A and B need not be true (be my solution for counter-examples)

However, if a and b are the SAME SIGN, then the product ab must be positive.
For example, if a and b are both positive, then the product ab is positive.
If a and b are both negative, then the product ab is positive.

So, statement C must be true.

Does that help?