3rd Grade Math Printables - Entire Year! | Math properties ... - Free Printable

Let's solve this step by step. The worksheet is about identifying the properties of multiplication: Commutative, Associative, and Distributive.

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🔹 Part 1: Identify the Property Shown

#### 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 breaks down $ 6 $ into $ 5 + 1 $, and distributes 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.
- This shows that changing the order doesn't change the product.
- This is the Commutative Property.

✔ Answer: Commutative Property

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

- The grouping changes: from $ 2 \times 5 $ to $ 4 \times 2 $, but the numbers are multiplied in the same way.
- The parentheses move, but the order stays the same.
- This is the Associative Property.

✔ Answer: Associative Property

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🔹 Part 2: Use Properties to Find Missing Numbers

We’ll use the three properties to fill in the blanks.

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

- $ 8 = 4 + 4 $, so:
- $ 6 \times 8 = 6 \times (4 + 4) = (6 \times 4) + (6 \times 4) $
- So missing number is 4

✔ Answer: 4

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

- Switching order: $ 3 \times 7 = 7 \times 3 $
- Commutative Property

✔ Answer: 3

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

- Again, switching order: $ 9 \times 2 = 2 \times 9 $
- Commutative Property

✔ Answer: 2

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

- Associative Property: regrouping
- $ 4 \times (2 \times 6) = (4 \times 2) \times 6 $
- So missing number is 4

✔ Answer: 4

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

- Associative Property: $ a \times (b \times c) = (a \times b) \times c $
- So $ 3 \times (5 \times 4) = (3 \times 5) \times 4 $
- Missing number is 4

✔ Answer: 4

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

- Break 7 into $ 5 + 2 $ → $ 9 \times 7 = 9 \times (5 + 2) $
- Distribute: $ (9 \times 5) + (9 \times 2) $
- So missing number is 9

✔ Answer: 9

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

- Associative: $ 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) $
- Missing number is 4

✔ Answer: 4

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

- Commutative: $ 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) $
- Missing number is 3

✔ Answer: 3

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✔ Final Answers:

#### Part 1: Which 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

#### Part 2: Missing Numbers
| Problem | 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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