Absolute value as distance from zero
Understand the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as magnitude in real-world contexts; distinguish absolute value comparisons from ordering statements
What a learner can do afterwards
- Define absolute value as distance from zero on a number line
- Calculate the absolute value of positive and negative rational numbers
- Distinguish between comparing absolute values and comparing signed numbers in real-world contexts
1 · Read
Every number has a distance from zero on the number line. That distance is called the absolute value. It is always zero or positive, no matter which side of zero the number sits on.
You already know -7 and 7 sit on opposite sides of zero. Absolute value ignores which side and only counts the steps. So the absolute value of -7 is 7, and the absolute value of 7 is also 7.
A diver is 18 meters below the surface, written as -18. The absolute value of -18 is 18, because the diver is 18 meters from the surface, whether that distance goes up or down.
Comparing absolute values is a different question from comparing the numbers themselves. -9 is less than -2, because -9 sits further left on the line. But |-9| = 9 is greater than |-2| = 2, because -9 is further from zero. When a question asks which is farther, deeper, or bigger in size, compare absolute values. When it asks which is lower or colder, compare the signed numbers.
Absolute value is the distance from zero, so it is never negative. Comparing distances is a different question from comparing the signed numbers themselves.
2 · Watch
Take it off screen
Where it sits
Learn first
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.