Directions: Use the properties of multiplication to solve each problem. Show your work where indicated.
Part A: Commutative Property (Order Doesn't Matter)
1. If 7 × 4 = 28, then 4 × 7 =
2. If 9 × 3 = 27, then 3 × 9 =
3. 5 × 8 = × 5
4. 6 × 9 = 9 ×
5. Fill in the blank: 3 × 7 = × 3
6. If 8 × 5 = 40, what is 5 × 8?
Part B: Identity Property (×1) and Zero Property (×0)
7. 9 × 1 =
8. 7 × 0 =
9. 1 × 15 =
10. 0 × 25 =
11. 42 × 1 =
12. 100 × 0 =
Part C: Associative Property (Group Differently)
13. Solve 2 × 3 × 5 two different ways:
(2 × 3) × 5 = × 5 =
2 × (3 × 5) = 2 × =
14. Solve 4 × 2 × 5 two different ways:
(4 × 2) × 5 = × 5 =
4 × (2 × 5) = 4 × =
15. (5 × 2) × 3 = 5 × ( × 3)
16. 2 × (4 × 3) = (2 × ) × 3
Part D: Distributive Property (Break Apart, Multiply, Add)
17. Use the distributive property to solve 4 × 13.
4 × 13 = 4 × (10 + 3) = (4 × ) + (4 × ) = + =
18. Use the distributive property to solve 6 × 12.
6 × 12 = 6 × (10 + 2) = (6 × ) + (6 × ) = + =
19. Use the distributive property to solve 5 × 14.
5 × 14 = 5 × (10 + ) = () + () =
20. Use the distributive property to solve 7 × 15.
7 × 15 = 7 × (10 + ) = () + () =
Part E: Name That Property!
Write which property is shown: Commutative, Associative, Distributive, Identity, or Zero
21. 8 × 1 = 8
Property:
22. 6 × 7 = 7 × 6
Property:
23. (2 × 4) × 5 = 2 × (4 × 5)
Property:
24. 9 × 0 = 0
Property:
25. 3 × 14 = (3 × 10) + (3 × 4)
Property:
26. 1 × 35 = 35
Property:
Part F: Word Problems Using Properties
27.
Maria knows that 6 × 8 = 48. She needs to find 8 × 6. What property can she use? What is the answer?
Property: Answer:
28.
Carlos wants to multiply 3 × 2 × 5. He groups (3 × 2) first to get 6, then multiplies 6 × 5 = 30. His friend groups differently and still gets 30. What property explains why both methods work?
Property:
29.
There are 7 rows of desks with 12 desks in each row. Use the distributive property to find the total number of desks. Show your work.
7 × 12 = desks
30.
A baker has 0 trays of cookies with 24 cookies on each tray. How many cookies does the baker have? What property does this show?