Sure! Let’s solve this worksheet step by step.
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## 📘
Part 1: Find the missing number according to the associative property.
The
Associative Property of Multiplication says:
> When multiplying three or more numbers, the way you group them doesn’t change the product.
> That is:
>
a × (b × c) = (a × b) × c
We’ll use this to fill in the blanks.
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🔹 Problem 1:
3 × (5 × 2) = (3 × 5) × _
→ Left side: 3 × (5 × 2) = 3 × 10 = 30
→ Right side: (3 × 5) × ? = 15 × ?
→ To get 30, ? must be
2
✔ Answer: 2
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🔹 Problem 2:
8 × (1 × 6) = (_ × 1) × 6
→ Left side: 8 × (1 × 6) = 8 × 6 = 48
→ Right side: (? × 1) × 6 = ? × 6
→ So ? × 6 = 48 → ? =
8
✔ Answer: 8
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🔹 Problem 3:
7 × (5 × 3) = (7 × _) × 3
→ Left side: 7 × (5 × 3) = 7 × 15 = 105
→ Right side: (7 × ?) × 3 = 7×?×3
→ So 21 × ? = 105 → ? =
5
✔ Answer: 5
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🔹 Problem 4:
2 × (4 × 1) = (2 × _) × 1
→ Left side: 2 × (4 × 1) = 2 × 4 = 8
→ Right side: (2 × ?) × 1 = 2×?
→ So 2×? = 8 → ? =
4
✔ Answer: 4
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🔹 Problem 5:
7 × (3 × 5) = (_ × 3) × 5
→ Left side: 7 × (3 × 5) = 7 × 15 = 105
→ Right side: (? × 3) × 5 = 15 × ?
→ So 15×? = 105 → ? =
7
✔ Answer: 7
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🔹 Problem 6:
6 × (3 × 2) = (6 × 3) × _
→ Left side: 6 × (3 × 2) = 6 × 6 = 36
→ Right side: (6 × 3) × ? = 18 × ?
→ So 18×? = 36 → ? =
2
✔ Answer: 2
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##
✔ Part 1 Answers Summary:
1.
2
2.
8
3.
5
4.
4
5.
7
6.
2
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## 📗
Part 2: Match according to the associative property.
We need to match expressions that are equal due to the associative property — meaning they have the same numbers multiplied, just grouped differently.
Let’s list the left column and right column, then match.
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🔸 Left Column:
1.
5 × (7 × 6)
→ This equals (5 × 7) × 6 → matches with
(5 × 7) × 6 on the right
2.
(7 × 3) × 2
→ This equals 7 × (3 × 2) → matches with
7 × (3 × 2)
3.
3 × (9 × 1)
→ This equals (3 × 9) × 1 → matches with
(3 × 9) × 1
4.
(4 × 3) × 2
→ This equals 4 × (3 × 2) → matches with
4 × (3 × 2)
5.
(3 × 4) × 6
→ This equals 3 × (4 × 6) → matches with
3 × (4 × 6)
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✔ Matching Pairs:
-
5 × (7 × 6) ↔
(5 × 7) × 6
-
(7 × 3) × 2 ↔
7 × (3 × 2)
-
3 × (9 × 1) ↔
(3 × 9) × 1
-
(4 × 3) × 2 ↔
4 × (3 × 2)
-
(3 × 4) × 6 ↔
3 × (4 × 6)
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## 🎯 Final Answer Summary:
Part 1: Missing Numbers
1.
2
2.
8
3.
5
4.
4
5.
7
6.
2
Part 2: Matching Pairs
- 5 × (7 × 6) → (5 × 7) × 6
- (7 × 3) × 2 → 7 × (3 × 2)
- 3 × (9 × 1) → (3 × 9) × 1
- (4 × 3) × 2 → 4 × (3 × 2)
- (3 × 4) × 6 → 3 × (4 × 6)
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✔ All done! The associative property lets us regroup multiplication without changing the result — that’s the key idea here.
Parent Tip: Review the logic above to help your child master the concept of associative worksheet.
