Topic: Absolute value

Levels Supported

Primary: no

Junior: yes

Intermediate: yes

Senior: yes

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Intermediate

The absolute value of a real number $a$ is written as $|a|$. It is defined as the distance from $a$ to $0$ on the number line. Formally, $|a| = \begin{cases} a, & \text{if } a \geq 0 \\ -a, & \text{if } a < 0 \end{cases}$

Important properties:

• $|a| \geq 0$ for any real number $a$ (absolute value is always non-negative)

• $|a| = 0$ if and only if $a = 0$

• $|a| = |-a|$ (absolute value ignores sign)

• $|ab| = |a||b|$ (multiplicative property)

• $\left|\frac{a}{b}\right| = \frac{|a|}{|b|}$ for $b \neq 0$

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Validation

Mathematical correctness: OK Age suitability: OK Progression between levels: OK