Follow up question for |3-9| / 3-9. Confused. Positive or negative?

Question

Question:

|3-9| the answer I get is -6/-6 which I would think is 1. according to my book, the answer is -1.
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3-9

Now, if this was a fraction being simplified, I get that the answer would be -1. But, being that this is division, shouldn't a negative 6 divided by a negative 6 be a positive 1?

 

Answer

Chaya,

The numerator is l3-9l which is l-6l which is 6, you have to take the absolute value so the numerator is +ve.

Denominator is -6, hence 6/-6 = -1

 

Follow up

Thank Sanjay for the answer,
I'm confused though. what does | | represent, and what is absolute value?

Answer 1

Absolute value is how far the number is from 0, no matter what direction.  It's always positive, because the distance is a positive number.

 

If the number is positive, then the distance from 0 is equal to the number.

 

But if the number is negative, then the distance from 0 has to be the negative of the number. 

 

For example, 6 is 6 away from 0.  But -6 is also 6 away from 0, just going in the other direction.  So the absolute value of both 6 and -6 is 6.

 

So just remember:

 

If x ≥ 0, then |x| = x.

 

But if x < 0, then |x| = -x