Math worksheet for practicing identity properties of multiplication with problems and answer space.

Final Answer:
1. Identity
2. Commutative
3. Commutative
4. Identity
5. Distributive
6. Associative
7. Associative
8. Distributive
9. Identity
10. Identity
11. Distributive
12. Identity
13. Zero Property (or sometimes listed under Identity/Zero — but standard curriculum treats 0 × a = 0 as *Zero Property of Multiplication*; however, since only Associative, Identity, Distributive are listed as options, and this is *not* any of those strictly, but in many school worksheets, they accept Identity for 1×a=a and Zero Property is implied—wait! Rechecking: Problem 13 is 2 × (3 × 0) = (2 × 3) × 0 → both sides equal 0, and it's about regrouping with 0. This is Associative, because it’s (a × b) × c = a × (b × c), even if one value is 0. So: Associative.)
Let me carefully re-evaluate each using only the three allowed properties: Associative, Identity, Distributive.

Recall:
- Identity: multiplying by 1 → a × 1 = a or 1 × a = a
- Associative: grouping change: (a × b) × c = a × (b × c)
- Distributive: a × (b + c) = a×b + a×c (or over subtraction)

Now go one by one:

1) 4 × 1 = 4 → Identity
2) (5 × 7) × 4 = 5 × (7 × 4) → Associative
Wait! No — left is (5×7)×4, right is 5×(7×4). Yes, regrouping → Associative
But original answer I wrote “Commutative” was wrong. Let’s correct fully.

Let’s solve all 20 correctly:

1) 4 × 1 = 4 → Identity
2) (5 × 7) × 4 = 5 × (7 × 4) → Associative
3) 10 × 8 = 8 × 10 → Commutative? But options are only Associative, Identity, Distributive — wait! The instruction says: “Determine which property of multiplication is shown (Associative, Identity, Distributive, or Commutative).” So Commutative is allowed — the header lists four: Associative, Identity, Distributive, or Commutative.

So all four are options. Good.

Then:

1) 4 × 1 = 4 → Identity
2) (5 × 7) × 4 = 5 × (7 × 4) → Associative
3) 10 × 8 = 8 × 10 → Commutative
4) 6 ×1 = 1 × 6 → Both sides have ×1, but order changed: 6×1 vs 1×6 → Commutative (also involves identity element, but the *property shown* is swapping order → Commutative)
However, some curricula say if it’s a×1 = a, it’s Identity; but here it’s a×1 = 1×a, so it demonstrates both, but the key change is order → Commutative.

But let’s check standard answer keys for such worksheets. In most elementary worksheets:
- a × 1 = a → Identity
- a × 1 = 1 × a → Commutative (since order swapped)
Yes.

5) 4 × (5 + 6) = (4 × 5) + (4 × 6) → Distributive
6) 6 × (0 + 8) = (6 × 0) + (6 × 8) → Distributive (over addition, even with 0)
7) (8 × 3) × 6 = 8 × (3 × 6) → Associative
8) 7 × (2 + 3) = (7 × 2) + (7 × 3) → Distributive
9) 8 × 1 = 8 → Identity
10) 1 × 1 = 1 → Identity
11) 9 × 2 = 2 × 9 → Commutative
12) 2 × 1 = 2 → Identity
13) 2 × (3 × 0) = (2 × 3) × 0 → Associative (regrouping, even with 0)
14) (1 × 10) + (1 × 3) = 1 × (10 + 3) → Distributive (reverse form)
15) (10 × 3) + (10 × 0) = 10 × (3 + 0) → Distributive
16) 9 × 1 = 1 × 9 → Commutative
17) 3 × 1 = 3 → Identity
18) 5 × 2 = 2 × 5 → Commutative
19) 1 × (2 × 4) = (1 × 2) × 4 → Associative (grouping change; 1 is just a number here)
20) (0 × 3) + (0 × 9) = 0 × (3 + 9) → Distributive

Now list final answers 1–20:

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

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