Absolute Value

Common Questions

What is absolute value?

Good question! Absolute value is the distance a number is from 0. So, for example, since both -5 and 5 are 5 away from 0, the absolute value of both -5 and 5 is 5! Read below to learn more.

Common Questions

Good question! Absolute value is the distance a number is from 0. So, for example, since both -5 and 5 are 5 away from 0, the absolute value of both -5 and 5 is 5! Read below to learn more.

Think of absolute value this way. You know how in video games, there are sometimes characters that can attack and characters that can heal?

Healing

Attacking

The healer adds 10 health points (+10), while the attacker subtracts 18 health points (-18). The healer has a positive effect on health, and the attacker has a negative effect.

But, if we just think about sheer power, we can compare them by saying that the healer has the power to change health by 10 and the attacker has the power to change health by 18.

This is just like absolute value. 3\textcolor{#FE4A49}{-3} is negative and 3\textcolor{#35CE8D}{3} is positive, but the change from 0 for both of them is 3. This change from 0 is called the absolute value.

Absolute Value

The absolute value of a number is its distance from 0. We write absolute value using two vertical bars like this:

5\mid 5\mid

Here are three important facts about absolute value:

  1. Absolute value is always positive or 0.
  2. 0 is the only number with absolute value 0.
  3. Every positive number is the absolute value of two different numbers:
12=12=12\Big| -\frac{1}{2}\Big| = \Big| \frac{1}{2} \Big| = \frac{1}{2}5=5=5|-5| = |5| = 5

Practice matching the equalities!