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Sure! Let’s go through each problem and identify which property of multiplication is being shown. The properties to choose from are:

- Associative Property: When multiplying three or more numbers, the way you group them doesn’t change the product.
→ (a × b) × c = a × (b × c)

- Identity Property: Any number multiplied by 1 stays the same.
→ a × 1 = a

- Distributive Property: Multiplication distributes over addition or subtraction.
→ a × (b + c) = (a × b) + (a × c)
→ a × (b – c) = (a × b) – (a × c)

- Commutative Property: The order of multiplication doesn’t matter.
→ a × b = b × a

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Now let’s solve each one:

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1) 4 × 1 = 4
→ Multiplying by 1 gives the same number → Identity

2) (5 × 7) × 4 = 5 × (7 × 4)
→ Grouping changed, but result same → Associative

3) 10 × 8 = 8 × 10
→ Order switched → Commutative

4) 6 × 1 = 1 × 6
→ Order switched → Commutative
*(Note: Also involves identity, but the property shown is commutative since both sides are equal due to order change.)*

5) 4 × (5 + 6) = (4 × 5) + (4 × 6)
→ Multiplication distributed over addition → Distributive

6) 6 × (0 + 8) = (6 × 0) + (6 × 8)
→ Again, distribution over addition → Distributive

7) (8 × 3) × 6 = 8 × (3 × 6)
→ Grouping changed → Associative

8) 7 × (2 × 3) = (7 × 2) × 3
→ Grouping changed → Associative

9) 8 × 1 = 8
→ Multiplied by 1 → Identity

10) 1 × 1 = 1
→ 1 × 1 = 1 → still Identity (since 1 is the multiplicative identity)

11) 9 × 2 = 2 × 9
→ Order switched → Commutative

12) 2 × 1 = 2
→ Multiplied by 1 → Identity

13) 2 × (3 × 0) = (2 × 3) × 0
→ Grouping changed → Associative
*(Note: Even though 0 is involved, the property shown is associative grouping.)*

14) (1 × 10) + (1 × 3) = 1 × (10 + 3)
→ This is distributive property written backwards → Distributive

15) (10 × 3) + (10 × 0) = 10 × (3 + 0)
→ Again, distributive → Distributive

16) 9 × 1 = 1 × 9
→ Order switched → Commutative

17) 3 × 1 = 3
→ Multiplied by 1 → Identity

18) 5 × 2 = 2 × 5
→ Order switched → Commutative

19) 1 × (2 × 4) = (1 × 2) × 4
→ Grouping changed → Associative
*(Also involves identity, but the structure shows associative property.)*

20) (0 × 3) + (0 × 9) = 0 × (3 + 9)
→ Distributive property → Distributive

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✔ Final Answers:

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

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Let me know if you’d like a printable version or flashcards for these properties!