Absolute Values: N00b Lesson for Beginners

[vincentm]

Can someone give me a n00b lesson in absolute values, i though i remembered, but i don't.

I got stuck on a

$$-|-8|$$

 

[Chi Meson]

Read this as "negative one times the absolute value of negative eight."

zat help?

 

[HallsofIvy]

What is |-8|?

What is the negative of that?

 

[vincentm]

Read this as "negative one times the absolute value of negative eight."

zat help?

this is integers right?

so uhm..
$$-1|-8| = 7$$ ?

 

[TD]

No, the absolute value means that you "make the number positive", if it's negative.

It can be defined by saying:
|x| = x if x ≥ 0
|x| = -x if x < 0

Which is just a more mathematical way of saying that positives stay positive and negatives become positives.

A few examples may help:
|2| = 2
|-3| = 3
|0| = 0
|-5/3| = 5/3

Now, you can solve yours?

 

[vincentm]

-|-8|= 8

right?

 

[TD]

What is |-8| ? And then again a -, since it say - (|-8|)

 

[vincentm]

What is |-8| ? And then again a -, since it say - (|-8|)

So the answer is -8

 

[Chi Meson]

that's right.

 

[vincentm]

Thank you ^.^ so can i get a laymens explanation(if that is possible) on how this answer is achieved?

 

[EnumaElish]

-(|-8|) is two functions nested: g(f(-8)) where f(x) = |x| and g(y) = -y. With nested functions you begin to peel the onion from the inside, as it were. So you first figure f(-8) is |-8| which is 8 (why?). Then you substitute this answer for y = f(x), inside g and now you have g(8) = -8. Make sense?

 

[HallsofIvy]

Do you see where you went wrong with the first one?
$$-1|-8| = 7$$

I think you recognized that |-8|= 8 but then you subtracted 1

-|-8| or -1|-8| does not mean subtract the two numbers- it means multiply!

 

[vincentm]

Do you see where you went wrong with the first one?
$$-1|-8| = 7$$

I think you recognized that |-8|= 8 but then you subtracted 1

-|-8| or -1|-8| does not mean subtract the two numbers- it means multiply!

thank you.