Properties of multiplication worksheet for Grade 3 - Free Printable

Problem Analysis:

The worksheet focuses on identifying and applying the properties of multiplication:
1. Commutative Property: $ a \times b = b \times a $
2. Associative Property: $ (a \times b) \times c = a \times (b \times c) $
3. Distributive Property: $ a \times (b + c) = (a \times b) + (a \times c) $

We will solve each part step by step.

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Part 1: Identify the Property Shown

#### 1. $ 4 \times 6 = (4 \times 5) + (4 \times 1) $
- This equation shows the Distributive Property because it distributes the multiplication over addition:
$$
4 \times 6 = 4 \times (5 + 1) = (4 \times 5) + (4 \times 1)
$$

#### 2. $ 5 \times 7 = 7 \times 5 $
- This equation shows the Commutative Property because the order of multiplication does not change the result:
$$
5 \times 7 = 7 \times 5
$$

#### 3. $ 4 \times (2 \times 5) = (4 \times 2) \times 5 $
- This equation shows the Associative Property because the grouping of factors does not change the result:
$$
4 \times (2 \times 5) = (4 \times 2) \times 5
$$

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Part 2: Use Properties of Multiplication to Identify Missing Numbers

#### 1. $ 6 \times 8 = (6 \times 4) + (6 \times \_\_) $
- Using the Distributive Property:
$$
6 \times 8 = 6 \times (4 + 4) = (6 \times 4) + (6 \times 4)
$$
Therefore, the missing number is $ 4 $.

#### 2. $ 3 \times 7 = 7 \times \_\_ $
- Using the Commutative Property:
$$
3 \times 7 = 7 \times 3
$$
Therefore, the missing number is $ 3 $.

#### 3. $ 9 \times 2 = \_\_ \times 9 $
- Using the Commutative Property:
$$
9 \times 2 = 2 \times 9
$$
Therefore, the missing number is $ 2 $.

#### 4. $ 4 \times (2 \times 6) = (\_\_ \times 2) \times 6 $
- Using the Associative Property:
$$
4 \times (2 \times 6) = (4 \times 2) \times 6
$$
Therefore, the missing number is $ 4 $.

#### 5. $ 3 \times (5 \times 4) = (3 \times 5) \times \_\_ $
- Using the Associative Property:
$$
3 \times (5 \times 4) = (3 \times 5) \times 4
$$
Therefore, the missing number is $ 4 $.

#### 6. $ 9 \times 7 = (9 \times 5) + (\_\_ \times 2) $
- Using the Distributive Property:
$$
9 \times 7 = 9 \times (5 + 2) = (9 \times 5) + (9 \times 2)
$$
Therefore, the missing number is $ 9 $.

#### 7. $ 2 \times (6 \times 5) = (\_\_ \times 6) \times 5 $
- Using the Associative Property:
$$
2 \times (6 \times 5) = (2 \times 6) \times 5
$$
Therefore, the missing number is $ 2 $.

#### 8. $ 3 \times 9 = (3 \times 5) + (3 \times \_\_) $
- Using the Distributive Property:
$$
3 \times 9 = 3 \times (5 + 4) = (3 \times 5) + (3 \times 4)
$$
Therefore, the missing number is $ 4 $.

#### 9. $ 6 \times 3 = 3 \times \_\_ $
- Using the Commutative Property:
$$
6 \times 3 = 3 \times 6
$$
Therefore, the missing number is $ 6 $.

#### 10. $ 3 \times 8 = (3 \times 5) + (3 \times \_\_) $
- Using the Distributive Property:
$$
3 \times 8 = 3 \times (5 + 3) = (3 \times 5) + (3 \times 3)
$$
Therefore, the missing number is $ 3 $.

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Final Answers:

1. Properties Shown:
- $ 4 \times 6 = (4 \times 5) + (4 \times 1) $: Distributive Property
- $ 5 \times 7 = 7 \times 5 $: Commutative Property
- $ 4 \times (2 \times 5) = (4 \times 2) \times 5 $: Associative Property

2. Missing Numbers:
- $ 6 \times 8 = (6 \times 4) + (6 \times 4) $: $ 4 $
- $ 3 \times 7 = 7 \times 3 $: $ 3 $
- $ 9 \times 2 = 2 \times 9 $: $ 2 $
- $ 4 \times (2 \times 6) = (4 \times 2) \times 6 $: $ 4 $
- $ 3 \times (5 \times 4) = (3 \times 5) \times 4 $: $ 4 $
- $ 9 \times 7 = (9 \times 5) + (9 \times 2) $: $ 9 $
- $ 2 \times (6 \times 5) = (2 \times 6) \times 5 $: $ 2 $
- $ 3 \times 9 = (3 \times 5) + (3 \times 4) $: $ 4 $
- $ 6 \times 3 = 3 \times 6 $: $ 6 $
- $ 3 \times 8 = (3 \times 5) + (3 \times 3) $: $ 3 $

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Boxed Final Answer:

$$
\boxed{
\begin{array}{l}
\text{1. Distributive Property} \\
\text{2. Commutative Property} \\
\text{3. Associative Property} \\
\text{Missing Numbers: } 4, 3, 2, 4, 4, 9, 2, 4, 6, 3
\end{array}
}
$$