lesson
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If you take 5 steps forward, you walked 5 steps. If you take 5 steps backward, your fitness tracker still counts 5 steps — not negative 5!
In math, when we only care about how far a number is from zero, we use absolute value.
Distance on the Number Line
The absolute value of an integer is its distance from zero on a number line.
📊An interactive-style clean visual diagram showing a horizontal number line from -5 to +5 with zero at the center. Two curved jump arrows start from 0: one arcs right to +4 labeled '4 units', and one arcs left to -4 labeled '4 units'. Below the number line, two highlighted cards show: '|4| = 4' in blue and '|-4| = 4' in teal. A small footprint icon is near both endpoints to emphasize physical steps.
We write absolute value by putting straight vertical bars around the number, such as ∣−4∣ or ∣4∣.
Because distance can never be negative, the absolute value of any number is always non-negative (either positive or zero).
What about zero itself? Since 0 is already at the starting point, its distance from zero is 0, so ∣0∣=0.
How do we calculate absolute value for any integer quickly? Let's look at three quick examples.
Calculating Absolute Value
To find ∣−9∣, ask: How many units away from 0 is −9? It is 9 units to the left, so ∣−9∣=9.
To find ∣15∣, ask: How many units away from 0 is 15? It is 15 units to the right, so ∣15∣=15.
📊A 3-card comparison display side-by-side. Card 1 (Negative Integer): '|-9|' with an arrow pointing to '9' with subtitle '9 steps from 0'. Card 2 (Zero): '|0|' with an arrow pointing to '0' with subtitle '0 steps from 0'. Card 3 (Positive Integer): '|15|' with an arrow pointing to '15' with subtitle '15 steps from 0'. Each card has a distinct border accent (orange, gray, green).