Number Properties Practice

Name:

Date:

📖 Part 1: Definition Matching

Match each property with its correct definition by writing the letter in the blank:

Properties:

1. Commutative Property ____

2. Associative Property ____

3. Distributive Property ____

4. Identity Property ____

Definitions:

A. You can change the grouping of numbers without changing the result

B. You can change the order of numbers without changing the result

C. Adding zero or multiplying by one doesn't change the number

D. You can multiply a number by a sum by multiplying each addend separately

🔍 Part 2: Property Identification - Basic Level

1. Which property is shown in this example: 6 + 4 = 4 + 6?

Commutative Property

Associative Property

Distributive Property

2. Which property is shown: (3 × 2) × 5 = 3 × (2 × 5)?

Commutative Property

Associative Property

Distributive Property

3. Which property is shown: 4 × (5 + 3) = (4 × 5) + (4 × 3)?

Commutative Property

Associative Property

Distributive Property

4. Which property is shown: 17 + 0 = 17?

Commutative Property

Identity Property

Distributive Property

5. Which property is shown: 8 × 1 = 8?

Associative Property

Identity Property

Commutative Property

🎯 Part 3: Property Identification - Advanced Level

6. Check all examples that show the Commutative Property:

8 × 7 = 7 × 8

(2 + 9) + 1 = 2 + (9 + 1)

15 + 12 = 12 + 15

6 × (4 + 2) = (6 × 4) + (6 × 2)

7. Check all examples that show the Associative Property:

(5 + 3) + 7 = 5 + (3 + 7)

9 × 4 = 4 × 9

(2 × 6) × 3 = 2 × (6 × 3)

7 × (8 + 2) = (7 × 8) + (7 × 2)

8. Check all examples that show the Distributive Property:

3 × (4 + 5) = (3 × 4) + (3 × 5)

6 + 8 = 8 + 6

2 × (10 - 3) = (2 × 10) - (2 × 3)

(7 + 2) + 5 = 7 + (2 + 5)

✏️ Part 4: Apply the Properties - Basic

9. Use the Commutative Property to rewrite this expression: 9 + 16 = ___________

10. Use the Commutative Property to rewrite this expression: 7 × 12 = ___________

11. Use the Associative Property to rewrite this expression: (4 × 3) × 8 = ___________

12. Use the Associative Property to rewrite this expression: (15 + 6) + 4 = ___________

13. Use the Identity Property to complete: 23 + ____ = 23

14. Use the Identity Property to complete: 45 × ____ = 45

🔢 Part 5: Apply the Properties - Problem Solving

15. Use the Distributive Property to solve: 5 × (6 + 4)

16. Use the Distributive Property to solve: 8 × (10 - 2)

17. Solve using any property that makes it easier: 25 + 47 + 75

Which property did you use? _________________________

18. Solve using any property that makes it easier: 4 × 13 × 25

Which property did you use? _________________________

19. Use the Distributive Property to solve: 6 × 47

Hint: Think of 47 as (40 + 7)

20. Use the Distributive Property to solve: 9 × 98

Hint: Think of 98 as (100 - 2)

📝 Part 6: Fill in the Missing Numbers

21. Complete using the Commutative Property:

a) 14 + 8 = ____ + 14

b) 3 × ____ = 12 × 3

c) ____ + 27 = 27 + 19

22. Complete using the Associative Property:

a) (5 + 9) + 6 = 5 + (____ + ____)

b) 7 × (____ × 4) = (7 × 2) × ____

c) (____ + 11) + 3 = 8 + (11 + ____)

23. Complete using the Distributive Property:

a) 4 × (5 + 3) = (____ × 5) + (____ × 3)

b) 6 × (8 - 2) = (6 × ____) - (6 × ____)

c) ____ × (7 + 4) = (3 × 7) + (3 × 4)

🧠 Part 7: Explain Your Thinking

24. In your own words, explain what the Distributive Property means:

25. Explain why the Commutative Property works for addition and multiplication but not for subtraction or division. Give an example:

26. How can knowing these properties help you solve math problems faster? Give a specific example:

⭐ Part 8: Extension Challenges for Advanced Learners

27. Create Your Own: Write your own example showing the Associative Property of addition. Then explain why your example works:

My example: ___________________________________

28. Advanced Distributive Property: Use the distributive property to solve: 15 × 23

Hint: Break 23 into two numbers that are easier to work with

29. Multiple Properties: Solve this problem using at least two different properties: (2 × 5) × (18 + 2)

Show your work and name the properties you used:

30. Real-World Application: A bakery sells muffins in packs of 6. If they sell 8 packs of blueberry muffins and 8 packs of chocolate chip muffins, write an expression using the distributive property to find the total number of muffins sold:

Expression: _________________________________

Total muffins: _____________________________

31. Challenge Problem: Use properties to make this calculation easier: 37 + 28 + 13 + 22

Explain your strategy:

32. Property Detective: Look at this equation: a × (b + c) = (a × b) + (a × c). If a = 7, b = 9, and c = 1, prove that both sides are equal by calculating each side:

Left side: ________________________________

Right side: _______________________________

Are they equal? ___________________________