Associative Property of Addition Worksheets - Free Printable

Let's solve this step by step.

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Part 1: Identify the Property Shown

We are given three equations and asked to identify which property of multiplication is shown in each.

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#### 1. $ 4 \times 6 = (4 \times 5) + (4 \times 1) $

- Left side: $ 4 \times 6 = 24 $
- Right side: $ (4 \times 5) + (4 \times 1) = 20 + 4 = 24 $
- This shows that multiplying 4 by 6 is the same as breaking 6 into 5 + 1 and distributing the 4 over both parts.
- This is the Distributive Property.

✔ Answer: Distributive Property

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#### 2. $ 5 \times 7 = 7 \times 5 $

- The order of the numbers is switched, but the product remains the same.
- This is the Commutative Property of multiplication.

✔ Answer: Commutative Property

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#### 3. $ 4 \times (2 \times 5) = (4 \times 2) \times 5 $

- The grouping changes: from $ 4 \times (2 \times 5) $ to $ (4 \times 2) \times 5 $
- But the product stays the same.
- This is the Associative Property.

✔ Answer: Associative Property

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Part 2: Use Properties to Find Missing Numbers

Now we'll fill in the blanks using the properties.

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#### 1. $ 6 \times 8 = (6 \times 4) + (6 \times \_\_) $

- Break 8 into 4 + 4 → $ 6 \times 8 = 6 \times (4 + 4) = (6 \times 4) + (6 \times 4) $
- So the missing number is 4

✔ Answer: 4

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#### 2. $ 3 \times 7 = 7 \times \_\_ $

- This is commutative property: switch order → $ 3 \times 7 = 7 \times 3 $
- Missing number is 3

✔ Answer: 3

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#### 3. $ 9 \times 2 = \_\_ \times 9 $

- Again, commutative property: $ 9 \times 2 = 2 \times 9 $
- Missing number is 2

✔ Answer: 2

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#### 4. $ 4 \times (2 \times 6) = (\_\_ \times 2) \times 6 $

- Associative property: change grouping
- Original: $ 4 \times (2 \times 6) $
- We want: $ (\_\_ \times 2) \times 6 $
- So, the missing number must be 4, so it becomes $ (4 \times 2) \times 6 $
- That matches the associative property.

✔ Answer: 4

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#### 5. $ 3 \times (5 \times 4) = (3 \times 5) \times \_\_ $

- Associative property: group differently
- $ 3 \times (5 \times 4) = (3 \times 5) \times 4 $
- So missing number is 4

✔ Answer: 4

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#### 6. $ 9 \times 7 = (9 \times 5) + (\_\_ \times 2) $

- Think: $ 7 = 5 + 2 $, so distribute 9:
- $ 9 \times 7 = 9 \times (5 + 2) = (9 \times 5) + (9 \times 2) $
- So the missing number is 9

✔ Answer: 9

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#### 7. $ 2 \times (6 \times 5) = (\_\_ \times 6) \times 5 $

- Associative property: $ 2 \times (6 \times 5) = (2 \times 6) \times 5 $
- So missing number is 2

✔ Answer: 2

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#### 8. $ 3 \times 9 = (3 \times 5) + (3 \times \_\_) $

- $ 9 = 5 + 4 $, so $ 3 \times 9 = 3 \times (5 + 4) = (3 \times 5) + (3 \times 4) $
- So missing number is 4

✔ Answer: 4

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#### 9. $ 6 \times 3 = 3 \times \_\_ $

- Commutative property: $ 6 \times 3 = 3 \times 6 $
- Missing number is 6

✔ Answer: 6

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#### 10. $ 3 \times 8 = (3 \times 5) + (3 \times \_\_) $

- $ 8 = 5 + 3 $, so $ 3 \times 8 = 3 \times (5 + 3) = (3 \times 5) + (3 \times 3) $
- So missing number is 3

✔ Answer: 3

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✔ Final Answers:

#### Identify the Property:
1. $ 4 \times 6 = (4 \times 5) + (4 \times 1) $ → Distributive
2. $ 5 \times 7 = 7 \times 5 $ → Commutative
3. $ 4 \times (2 \times 5) = (4 \times 2) \times 5 $ → Associative

#### Fill in the Blanks:
| Expression | Answer |
|----------|--------|
| $ 6 \times 8 = (6 \times 4) + (6 \times \underline{4}) $ | 4 |
| $ 3 \times 7 = 7 \times \underline{3} $ | 3 |
| $ 9 \times 2 = \underline{2} \times 9 $ | 2 |
| $ 4 \times (2 \times 6) = (\underline{4} \times 2) \times 6 $ | 4 |
| $ 3 \times (5 \times 4) = (3 \times 5) \times \underline{4} $ | 4 |
| $ 9 \times 7 = (9 \times 5) + (\underline{9} \times 2) $ | 9 |
| $ 2 \times (6 \times 5) = (\underline{2} \times 6) \times 5 $ | 2 |
| $ 3 \times 9 = (3 \times 5) + (3 \times \underline{4}) $ | 4 |
| $ 6 \times 3 = 3 \times \underline{6} $ | 6 |
| $ 3 \times 8 = (3 \times 5) + (3 \times \underline{3}) $ | 3 |

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