Absolute values??

Question

Okay.. My algebra book says this:

Explain why the |absolute value of A over B| = A over B is NOT always true. I DONT KNOW! Please helppp!

Answer 1

Here's an example why it's not always true.

A = -4
B = 4

ABS (-4/4) = 1

A/B = -4/4 = -1

This occurs because if A OR B is negative than this result will be negative.

Hope that helps!

Answer 2

The absolute value of a number is its numerical value without regard to its sign. In the case you mention, if A or B is negative (not both), the statement is false.

For example, If A=6 and B=(-2), A/B is equal to (-3), but the absolute value is equal to 3.

Answer 3

If A = -1 and B = 1, then A/B = -1/1 = -1.

However, |A/B| = 1.

Thus A/B <> |A/B|

Answer 4

Let a=-1 and b=1. Then

a/b=-1 and |a/b|=1. 1≠-1. Therefore, |a/b| is not always equal to a/b. Q.E.D.

Basically, the difference shows up whenever the expression inside the absolute value sign is negative - in such a case, the expression will not be equal to its absolute value, because absolute value is always nonnegative.

Answer 5

For example, A=-4, B=2:

|-4/2|=2
-4/2=(-2)

Absolute value is positive, same division without absolute value is -2.

Answer 6

A over B can be positive or negative (positive if signs are same; negative if signs are different).

The absolute value of A over B is always positive (or zero if A=0).

Answer 7

here is an example that is not true

a=-3
b=3

absolue value of a/b=|-3/3|=1 (thats what absolute value means, if its negative, it makes it positive)

whereas -3/3 = -1

1 does not equal -1

Answer 8

absolute value is always positive, so if you have |(-1)/2| it will equal 1/2, always positive, not (-1)/2, the original problem

Answer 9

Very simple: |absolute value of A over B| is always greater than or equal to zero, but A over B isn't.

eg. |3/(-5)|=0.6, 3/(-5)=-0.6

Answer 10

if at anytime A or B is negative, then the |A/B| cannot equal A/B since you can't have a negative absolute value.