The Fancy Way to Say: “Find the Distance” Absolute Value The Fancy Way to Say: “Find the Distance”

Absolute Value |x| or |-x| The distance from zero on the number line, or the distance from the ‘starting point’ in the real world. Represented by straight up and down bars before and after the number’s position. |-5| Whatever is inside the absolute value bars is considered positive.

Remember… The signs of a number just tell which way to go on the number line/axis, like a GPS gives directions! means turn Left or turn Down on the number line/axis. means turn Right or Up on the number line/axis.

How Absolute Value Works The number 5 is at +5 on the number line. Its distance is five spaces from zero to the right. The absolute value of +5 is written |5|. This means that +5 is a distance of 5 units from zero.

How Absolute Value Works The number -5 is at -5 on the number line. Its distance is five spaces from zero to the left. The absolute value of -5 is written |-5|. This means that -5 is a distance of 5 units from zero. It does not mean it is -5 units from zero.

THERE IS NO NEGATIVE DISTANCE! Never Forget THERE IS NO NEGATIVE DISTANCE! Even if you move backward or downward, you are still moving a positive amount. You are not moving a negative amount. You cannot move -3 spaces. You can only move 3 spaces in the backward direction.

Let’s Delve Deeper! Let’s examine: |-9| Since there are absolute value bars, I know I am looking to solve for distance. Since there is a negative in front of the 9, I know the number is located behind the zero on the number line. Though -9 is located behind the zero, it is still positive 9 spaces behind the zero. |-9| = 9

Review What does absolute value mean? Solve |-9|. Where is |-9| on the number line? How far from 0 is |-9|? Is 9 = -9? Is |9|= |-9|?

Classroom Handouts

Let’s Delve Deeper! Let’s examine: |-9| Since there are absolute value bars, I know I am looking to solve for _____________. Since there is a negative in front of the 9, I know the number is _________ _____the zero on the number line. Though -9 is located behind the zero, it is still _________9 spaces behind the zero. |-9| = ___

Real World Application Submarine A is at -13ft. But it’s distance from 0 is positive13 feet below sea level. The absolute value of submarine A is |-13|ft. Submarine B is at _____ft. But it’s _________ from 0 is 6 feet below sea level. The absolute value of submarine A is _____ ft.

Review What does absolute value mean? Solve |-9|. Where is |-9| on the number line? How far from 0 is |-9|? Is 9 = -9? Is |9|= |-9|?