# Absolute Value

## Key Questions

• Because it is a convenient way to make sure that a quantity is nonnegative; for example, you can define the distance between two real numbers $a$ and $b$ as $| a - b |$.

I hope that this was helpful.

• The absolute value of a number is simply the distance that number lies away from 0 on the number line. Absolute value eliminates the "direction" traveled to get there. It's like saying that you walked 3 meters frontward versus 3 meters backward. You walked 3 meters in different directions from where you started!
Some examples: $| - 3 | = 3$ and $| 3 | = 3$
$| - 9 | = 9$
$| 5 | = 5$
$| 3 - 11 | = | - 8 | = 8$

With a number line in front of you, you can point to any location and tell someone how far it is from 0 by just ignoring whether that point is to the left or right of 0. Think of that as "absolute value"!

• Absolute value is how far a number is away from zero |(insert number)| is the symbol for it. example: |-6| = 6, because -6 is 6 numbers away from zero. The same applies for positives. |6| = 6, because 6 is 6 numbers away from 0.