NUMBER PROPERTIES
Number properties describe rewrites that preserve value. They tell us when we may reorder, regroup, or distribute parts of an expression without changing what the expression means.
Commutative Property
Addition and multiplication of ordinary numbers allow us to swap the order of addends or factors without changing the result.
Associative Property
When we repeatedly add or repeatedly multiply, we may change the grouping without changing the result.
Identity Property
An identity element leaves a value unchanged under its operation: zero for addition and one for multiplication.
The Distributive Property
Multiplying a sum by a factor is equivalent to multiplying each term by that factor and then adding the products. The area model below shows the same total area partitioned in two equivalent ways.
Distributive Area Model
Reference & Check
Which property is demonstrated by this equation: 4 × (3 + 5) = (4 × 3) + (4 × 5)?
Connect Forward
These value-preserving rewrites will reappear whenever algebraic expressions are rearranged, expanded, or simplified.