Properties of Operations
Explore and apply the commutative, associative, and distributive properties to simplify expressions and solve problems at a Grade 6 level.
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Properties of Operations
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Read each question carefully and answer to the best of your ability. Show your work where necessary.
1. Which property states that the order of numbers does not change the sum or product?
Associative Property
Commutative Property
Distributive Property
Identity Property
2. Which expression demonstrates the Distributive Property?
5 × (2 + 3) = (5 × 2) + 3
5 × (2 + 3) = (5 × 2) + (5 × 3)
5 + (2 + 3) = (5 + 2) + 3
5 × 2 = 2 × 5
3. The Property of Addition states that changing the grouping of addends does not change the sum.
4. According to the Commutative Property of Multiplication, 7 × 9 is equal to .
5. Use the Distributive Property to rewrite and solve the expression: 6 × (10 + 4).
6. The expression (3 + 5) + 2 = 3 + (5 + 2) demonstrates the Commutative Property of Addition.
True
False
7. The Identity Property of Multiplication states that any number multiplied by zero equals zero.
True
False
Match each property with its example.
8. Commutative Property
a. 4 × (2 + 5) = (4 × 2) + (4 × 5)
9. Associative Property
b. 9 + 3 = 3 + 9
10. Distributive Property
c. (2 × 3) × 4 = 2 × (3 × 4)