Commutative, Associative, Distributive Properties (Grade 3)

Videos, examples, solutions, and lessons to help Grade 3 students learn to apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Common Core: 3.OA.5

Suggested Learning Target

• I can explain the commutative, associative, and distributive property of multiplication.
• I can apply the commutative, associative, and distributive properties to decompose, regroup, and/or reorder factors to make it easier to multiply two or more factors.
• I can explain how the operation properties can and cannot apply to division and use those properties that can apply to make it easier to find the quotient.

Distributive Property

Commutative Property of Multiplication
The order of numbers does not matter when multiplying.

• Show Step-by-step Solutions

Associative Property of Multiplication
The sum or product stays the same when grouping of addends or factors is changed.

• Show Step-by-step Solutions

Distributive Property
When multiplying a factor and a sum, you can distribute the factor across the addition.

• Show Step-by-step Solutions

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