Properties of Numbers interactive worksheet - Free Printable

Let's solve this step by step. The task is to identify which property of numbers each equation demonstrates. The four properties we're working with are:

- Commutative: Changing the order of numbers does not change the result.
- Addition: $ a + b = b + a $
- Multiplication: $ a \times b = b \times a $

- Associative: Changing the grouping of numbers does not change the result.
- Addition: $ (a + b) + c = a + (b + c) $
- Multiplication: $ (a \times b) \times c = a \times (b \times c) $

- Distributive: Multiplication distributes over addition or subtraction.
- $ a \times (b + c) = (a \times b) + (a \times c) $

- Identity:
- Additive Identity: $ a + 0 = a $
- Multiplicative Identity: $ a \times 1 = a $

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Now, let’s go through each problem and determine the correct property.

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1) $ 5 + 2 = 2 + 5 $
→ Order changed in addition → Commutative

2) $ 2 \times 8 = 8 \times 2 $
→ Order changed in multiplication → Commutative

3) $ 13 \times 2 = 2 \times 13 $
→ Same as above → Commutative

4) $ 8 \times 1 = 8 $
→ Multiplying by 1 gives same number → Identity (Multiplicative)

5) $ 1 \times 6 = 6 $
→ Same as above → Identity (Multiplicative)

6) $ 12 \times (3 \times 4) = (12 \times 3) \times 4 $
→ Grouping changed in multiplication → Associative

7) $ 8 \times (2 \times 4) = (8 \times 2) \times 4 $
→ Grouping changed → Associative

8) $ (2 \times 4) + (2 \times 3) = 2 \times (4 + 3) $
→ Factoring out 2 from both terms → Distributive

9) $ (12 \times 8) + (12 \times 1) = 12 \times (8 + 1) $
→ Factoring out 12 → Distributive

10) $ 6 \times 7 = 7 \times 6 $
→ Order changed → Commutative

11) $ (7 \times 5) - (7 \times 4) = 7 \times (5 - 4) $
→ Distributing multiplication over subtraction → Distributive

12) $ 5 \times (4 \times 9) = (5 \times 4) \times 9 $
→ Grouping changed → Associative

13) $ 7 \times (15 \times 10) = (7 \times 15) \times 10 $
→ Grouping changed → Associative

14) $ 2 \times (13 \times 14) = (2 \times 13) \times 14 $
→ Grouping changed → Associative

15) $ 1 \times 64 = 64 $
→ Multiplying by 1 → Identity (Multiplicative)

16) $ 18 \times (2 + 9) = (18 \times 2) + (18 \times 9) $
→ Distributing 18 over addition → Distributive

17) $ 0 \times 8 = 8 \times 0 $
→ Order changed, but both sides equal 0 → This is Commutative, even though it involves zero.

18) $ 4 \times (10 + 6) = (4 \times 10) + (4 \times 6) $
→ Distributing 4 → Distributive

19) $ 0 + 5 = 5 $
→ Adding zero doesn’t change the number → Identity (Additive)

20) $ 11 \times 1 = 11 $
→ Multiplying by 1 → Identity (Multiplicative)

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Final Answers:

1) Commutative
2) Commutative
3) Commutative
4) Identity
5) Identity
6) Associative
7) Associative
8) Distributive
9) Distributive
10) Commutative
11) Distributive
12) Associative
13) Associative
14) Associative
15) Identity
16) Distributive
17) Commutative
18) Distributive
19) Identity
20) Identity

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✔ Summary of Properties Used:
- Commutative: 1, 2, 3, 10, 17
- Associative: 6, 7, 12, 13, 14
- Distributive: 8, 9, 11, 16, 18
- Identity: 4, 5, 15, 19, 20

Let me know if you'd like this formatted as a printable answer sheet!