Absolute Value Property
The absolute value of a product equals the product of absolute values.
Formula
Variables
Example
|-3×4| = 12
How it works
The absolute value of a number measures its distance from 0, so it is always nonnegative. When you multiply two numbers, the sign of the product depends on the signs of the factors, but absolute value removes those signs and keeps only the magnitude. That is why taking the absolute value after multiplying gives the same result as multiplying the absolute values first.
When to use it
Use this rule whenever you need to simplify an expression with absolute values around a product, or when checking the size of a product without worrying about sign. It is also helpful in algebra, coordinate geometry, and physics when working with magnitudes.
Worked example, step by step
Evaluate |(-2)(5)|. Step 1: Multiply inside the absolute value: (-2)(5) = -10 Step 2: Take the absolute value: |-10| = 10 Step 3: Check with the property: |-2| × |5| = 2 × 5 = 10 Final answer: |(-2)(5)| = | -2 | |5| = 10
Common mistakes to avoid
- Forgetting that the absolute value applies to the entire product, not just one factor
- Thinking the rule works only when both numbers are positive
- Removing the absolute value bars before multiplying the numbers
Did You Know?
Absolute value measures distance from zero, so it is always positive — the number line has no negative distances.
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