---
title: "Absolute value as distance from zero"
description: "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 fr"
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# 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

Subject: Mathematics · Area: Number Representation & Place Value · Ages 11 to 12
Page: https://lightmysky.com/learn/mathematics/absolute-value-as-distance-from-zero-mt_RWUY7_IXvw

## Ready when they can

- 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

## Lesson: Absolute value as distance from zero

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.

*(drawing: -7 is 7 steps away from zero, so its absolute value is 7.)*

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.

**Example.** 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.

**Recap.** Absolute value is the distance from zero, so it is never negative. Comparing distances is a different question from comparing the signed numbers themselves.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Positive and Negative Numbers](https://lightmysky.com/learn/mathematics/positive-and-negative-numbers-mt_9QzSnn8m80)