Formulas & tables/Mathematics/Absolute value/Properties of absolute value
Properties of absolute value

Properties of absolute value

∣a⋅b∣=∣a∣∣b∣,∣ab∣=∣a∣∣b∣|a\cdot b|=|a||b|,\quad \left|\tfrac{a}{b}\right|=\tfrac{|a|}{|b|}

Result unit: — (liczba $\ge 0$)

What it describes

The absolute value of a product and a quotient equals the product and quotient of the absolute values.

Symbols

a,ba, b
real numbers (b≠0b\neq 0 for the quotient)

Where it comes from

The absolute value "distributes" over multiplication and division — the modulus of a product is the product of the moduli. Note: for a sum this does NOT hold.

When to use it

Simplifying expressions with absolute values.

Example

Compute ∣−3⋅4∣|-3\cdot4|.
Substitution∣−3∣⋅∣4∣|-3|\cdot|4|.
Result3⋅4=123\cdot4=12.

Related formulas

Definition of absolute value Inequalities with absolute value

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