The Number System
GradesGrade 7The Number SystemAbsolute Value & the Number Line

Absolute Value & the Number Line

🔢 The Number System
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Absolute Value & the Number Line

Absolute value is a number's distance from zero — always non-negative.

The absolute value of a number is its distance from 0 on the number line, regardless of direction. Absolute value is never negative. It is written with vertical bars: |x|.

∣−7∣=7∣7∣=7∣0∣=0|{-7}| = 7 \qquad |7| = 7 \qquad |0| = 0
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|x| = x if x ≥ 0, and |x| = −x if x < 0

🌡️Temperature difference
City A is −12°F. City B is 5°F.

How much warmer is City B?
Difference = 5 − (−12) = 5 + 12 = 17°F

Or: |−12 − 5| = |−17| = 17°F
∣a−b∣=distance between a and b on the number line|a - b| = \text{distance between } a \text{ and } b \text{ on the number line}

Ordering rational numbers with negatives:

1Plot all numbers on a number line
2Numbers further left are smaller (more negative)
3Numbers further right are larger
4Remember: −1/2 > −3/4 because −1/2 is closer to 0 (to the right)
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Remember This!

When comparing two negative numbers, the one with the greater absolute value is actually the smaller number. −100 < −1 because −100 is farther left on the number line.

✏️ Try It!

Evaluate |−3.5 − 2|.

Practice with CalcVerse
📍Number Line Plotter| |Absolute Value Solver
Take Quiz 📝 — 25 Questions