Let’s go through each problem one by one and identify which multiplication property is being used.
We’ll use these common properties:
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Commutative Property: Order doesn’t matter → a × b = b × a
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Associative Property: Grouping doesn’t matter → (a × b) × c = a × (b × c)
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Identity Property: Multiplying by 1 gives the same number → a × 1 = a
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Zero Property: Multiplying by 0 gives 0 → a × 0 = 0
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Distributive Property: Multiplication over addition → (a + b) × c = (a × c) + (b × c)
Now let’s solve each:
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① 2 × (5 × 2) = (2 × 5) × 2
→ The grouping changed: left side groups 5×2 first, right side groups 2×5 first. But the order of numbers also changed? Wait — actually, look closely:
Left: 2 × (5 × 2) → that’s 2 × 10 = 20
Right: (2 × 5) × 2 → that’s 10 × 2 = 20
But notice: on the right, it’s (2 × 5) × 2 — so we’re multiplying 2×5 first, then ×2. On the left, it’s 2 × (5×2). So the *grouping* of the operations changed — but also the order of the factors? Actually, no — the numbers are still 2, 5, 2 — just grouped differently.
Wait — this is tricky. Let’s rewrite:
Original: 2 × (5 × 2)
Rewritten: (2 × 5) × 2
This is changing the grouping — from grouping the last two to grouping the first two. That’s the
Associative Property.
BUT — in associative property, the order of the numbers should stay the same. Here, the numbers are 2, 5, 2 — same on both sides. Just parentheses moved.
✔ So:
Associative Property
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② 2 × 7 = 7 × 2
→ Order switched. Classic commutative.
✔ Commutative Property
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③ 10 × 1 = 10
→ Multiplying by 1 leaves it unchanged.
✔ Identity Property
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④ 2 × 0 = 0
→ Anything times zero is zero.
✔ Zero Property
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⑤ 4 × (8 × 6) = (4 × 8) × 6
→ Again, grouping changed: left groups 8×6, right groups 4×8. Numbers are same: 4,8,6.
✔ Associative Property
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4 × 8 = 8 × 4
→ Order switched.
✔ Commutative Property
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⑦ (3 + 4) × 6 = (3 × 6) + (4 × 6)
→ This is distributing the ×6 over the sum (3+4).
✔ Distributive Property
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⑧ 5 × 0 = 0
→ Zero property again.
✔ Zero Property
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⑨ 11 × 1 = 11
→ Identity property.
✔ Identity Property
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⑩ 12 × (14 × 11) = (12 × 14) × 11
→ Grouping changed: left groups 14×11, right groups 12×14. Same numbers: 12,14,11.
✔ Associative Property
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⑪ 20 × 0 = 0
→ Zero property.
✔ Zero Property
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⑫ 31 × 1 = 31
→ Identity property.
✔ Identity Property
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Final Answer:
① Associative Property
② Commutative Property
③ Identity Property
④ Zero Property
⑤ Associative Property
⑥ Commutative Property
⑦ Distributive Property
⑧ Zero Property
⑨ Identity Property
⑩ Associative Property
⑪ Zero Property
⑫ Identity Property
Parent Tip: Review the logic above to help your child master the concept of multiplication properties worksheet 4th grade.
