Commutative, Associative, and Distributive Properties Worksheets

What are Commutative, Associative, Distributive Properties? Commutative, associative, and distributive properties are the three properties underpinning the fundamentals of algebra. Students are first introduced with these properties in broader terms in the early years. However, as the students learn advance concepts, the understanding of these properties become essential. Commutative Property - Commutative is derived from the word commute, which means to move around. As the name implies, the commutative property refers to moving the numbers around. The commutative rule states that if we move the numbers around, we will still get the same answer. The equation of commutative property of addition is written as: a + b = b + a. The equation of commutative property of multiplication is written as: a x b = b x a. Associative Property - The word associative is derived from the word 'associate' which means to 'group'. And as the name implies, associative property refers to associating or grouping number. The associative property also states that grouping and regrouping of numbers don't affect the result. The equation of associative property of addition is written as: (a + b) + c = a + (b + c) The equation of associative property of multiplication is written as: a x (b x c) = (a x b) x c Distributive Property - Distributive property states that multiplication distributes over addition. The equation of this property is written as: a x (b + c) = a x b + a x c.