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Name: _____________________________________________________________________ Date: ___________________ Student Accessible – studentaccessible.com – Maya Khalil Properties of Addition and Multiplication 1. Commutative property of addition: Switching around the numbers you are adding does not change the answer (sum) to an addition problem. Example: 5 + 9 = 9 + 5 14 = 14 2. Commutative property of multiplication: Switching the order of the numbers you are multiplying does not change the answer (product) to a multiplication problem. Example: 1 • 4 = 4 • 1 3. Associative property of addition: When adding three or more numbers, it does not matter which two numbers you add first. Parentheses are used to show which numbers are added first. Example: (8 + 5) + 7 = 8 + (5 + 7) 13 + 7 = 8 + 12 20 = 20 4. Associative property of multiplication: When multiplying three or more numbers, it does not matter which two numbers you multiply first. Example: (1 • 4) • 2 = 1• (4 • 2) 40 • 2 = 1: • 8 80 = 80 5. Is subtraction commutative?____ give an example to explain your answer. ______________________________________________________________________ 6. Is division commutative?____ give an example_____________________________ 7. Ryan says that he uses the distributive property to simplify multiplication problems. For example, when asked to multiply 4 • 23, Ryan rethinks the problem as 4 • (20 + 3), then he performs: 4 • 20 + 4 • 3 80 + 12 = 92 Use the distributive property to solve the following problems: 8. 9. 10. 11. 12. 13. 8 • (10 + 5) = __________________________ 7(6 + 9) = _____________________________ 9(11 – 4) = ____________________________ -11(2 + 10) =___________________________ 4(8 + (-5)) = ___________________________ 7(x + 8) = _____________________________ Match each of the following equations with the correct property. 14. 15. 16. 17. 18. 19. 20. 21. 22. (5 + 9) + 11 = 5 + (9 + 11) __ 16(10 + 2) = 16 • 1: + 16 • 2 __ 123 + 56 = 56 + 123 __ (24 • 9) • 6 = 24 • (9 • 6) __ 18 • 7 = 7 • 18 __ xy = yx __ n(m + 7) = nm + 7n __ x + (y + z) = (x + y) + z __ 9(5x – 3y) = 45x – 27y __ a. Distributive property b. Commutative property (addition) c. Commutative property (multipl.) d. Associative property (addition) e. Associative property (multipli.)