Grade 3 Associative Property of Multiplication Worksheets 2024 - Free Printable

Let’s solve each problem step by step using the Associative Property of Multiplication.

This property says:
When multiplying three or more numbers, you can group them in different ways — but the answer stays the same.
For example:
(a × b) × c = a × (b × c)

We’ll use this to find missing numbers or match expressions.

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Part 1: Find the missing number

#### Problem 1:
3 • (5 • 2) = (3 • 5) • ___

Left side: 3 • (5 • 2) → first do 5•2=10, then 3•10=30
Right side: (3 • 5) • ? → 3•5=15, so we need 15 • ? = 30 → ? = 2
✔ Missing number is 2

*(Already filled in image — correct!)*

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#### Problem 2:
8 • (1 • 6) = (___ • 1) • 6

Left side: 8 • (1 • 6) → 1•6=6, then 8•6=48
Right side: (? • 1) • 6 → whatever ? is, times 1 is still ?, then times 6 must equal 48
So: ? • 6 = 48 → ? = 8
✔ Missing number is 8

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#### Problem 3:
7 • (5 • 3) = (7 • ___) • 3

Left side: 7 • (5 • 3) → 5•3=15, then 7•15=105
Right side: (7 • ?) • 3 → let’s say 7•? = X, then X•3=105 → X=35 → so 7•?=35 → ?=5
✔ Missing number is 5

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#### Problem 4:
2 • (4 • 1) = (2 • ___) • 1

Left side: 2 • (4 • 1) → 4•1=4, then 2•4=8
Right side: (2 • ?) • 1 → anything times 1 is itself, so (2•?) must equal 8 → 2•?=8 → ?=4
✔ Missing number is 4

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#### Problem 5:
7 • (3 • 5) = (___ • 3) • 5

Left side: 7 • (3 • 5) → 3•5=15, then 7•15=105
Right side: (? • 3) • 5 → let’s call ?•3 = Y, then Y•5=105 → Y=21 → so ?•3=21 → ?=7
✔ Missing number is 7

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#### Problem 6:
6 • (3 • 2) = (6 • 3) • ___

Left side: 6 • (3 • 2) → 3•2=6, then 6•6=36
Right side: (6 • 3) • ? → 6•3=18, then 18•?=36 → ?=2
✔ Missing number is 2

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Part 2: Match according to associative property

We need to pair expressions that are equal because of grouping change.

Remember:
(a × b) × c = a × (b × c) — just regrouping, order doesn’t change.

Let’s list all left-side expressions and find their matches on the right.

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Left column:

1. 5 • (7 • 6) → This means multiply 7 and 6 first, then multiply by 5.
Equivalent to: (5 • 7) • 6 → which is in the right column! ✔ Match with last one: (5 • 7) • 6

2. (7 • 3) • 2 → Multiply 7 and 3 first, then by 2.
Same as: 7 • (3 • 2) → which is in right column! ✔ Match with fourth one: 7 • (3 • 2)

3. 3 • (9 • 1) → Multiply 9 and 1 first, then by 3.
Same as: (3 • 9) • 1 → which is in right column! ✔ Match with second one: (3 • 9) • 1

4. (4 • 3) • 2 → Multiply 4 and 3 first, then by 2.
Same as: 4 • (3 • 2) → which is in right column! ✔ Match with third one: 4 • (3 • 2)

5. (3 • 4) • 6 → Multiply 3 and 4 first, then by 6.
Same as: 3 • (4 • 6) → which is in right column! ✔ Match with first one: 3 • (4 • 6)

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Now let’s write the matching pairs clearly:

- 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)

All matched correctly!

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Final Answer:

Part 1 Missing Numbers:
- Problem 2: 8
- Problem 3: 5
- Problem 4: 4
- Problem 5: 7
- Problem 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)