NUMBER PROPERTIES
If PEMDAS is the grammar of math, Properties are the physical laws. They tell us exactly how we can stretch, swap, and reshape an equation without breaking it.
Commutative Property
The word "commute" means to move around. This property says you can swap the order of numbers and get the same answer.
Associative Property
Who you "associate" with means who you group with. This property lets you move the parentheses to group numbers differently.
Identity Property
Every number wants to protect its identity! These rules tell us what we can add or multiply to leave a number completely unchanged.
The Distributive Property
This is arguably the most powerful tool in Algebra. To multiply a number by a group, you must "distribute" that multiplier to every single item inside the parentheses. Use the Area Model below to prove why this works!
Distributive Area Model
Verification Protocol
Which property is demonstrated by this equation: 4 × (3 + 5) = (4 × 3) + (4 × 5)?
Rule Mastery
You know the laws of mathematical motion.