Properties of Multiplication Worksheets - Free Printable

Let's solve the worksheet on the Associative Property of Multiplication step by step.

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🔷 What is the Associative Property of Multiplication?

The associative property states that when multiplying three or more numbers, the way the numbers are grouped does not change the product. In other words:

> $$(a \times b) \times c = a \times (b \times c)$$

So, no matter how you group the numbers with parentheses, the result stays the same.

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Now, let’s go through each problem.

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✔ Problem a:

(4 × 2) × 6 = 4 × (2 × 6)

#### Step 1: Solve the left side:
(4 × 2) × 6 = 8 × 6 = 48

#### Step 2: Solve the right side:
4 × (2 × 6) = 4 × 12 = 48

✔ Both sides equal 48, so the property holds.

Now write a new multiplication fact using the same numbers and write the product:

- New fact: 4 × 2 × 6 = 48
- Product: 48

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✔ Problem b:

(2 × 5) × 3 = 2 × (5 × 3)

Left: (2 × 5) × 3 = 10 × 3 = 30
Right: 2 × (5 × 3) = 2 × 15 = 30

✔ Same product.

New fact: 2 × 5 × 3 = 30
Product: 30

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✔ Problem c:

(4 × 5) × 2 = 4 × (5 × 2)

Left: (4 × 5) × 2 = 20 × 2 = 40
Right: 4 × (5 × 2) = 4 × 10 = 40

✔ Same.

New fact: 4 × 5 × 2 = 40
Product: 40

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✔ Problem d:

(4 × 7) × 1 = 4 × (7 × 1)

Left: (4 × 7) × 1 = 28 × 1 = 28
Right: 4 × (7 × 1) = 4 × 7 = 28

✔ Same.

New fact: 4 × 7 × 1 = 28
Product: 28

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✔ Problem e:

(6 × 2) × 5 = 6 × (2 × 5)

Left: (6 × 2) × 5 = 12 × 5 = 60
Right: 6 × (2 × 5) = 6 × 10 = 60

✔ Same.

New fact: 6 × 2 × 5 = 60
Product: 60

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✔ Problem f:

(3 × 3) × 4 = 3 × (3 × 4)

Left: (3 × 3) × 4 = 9 × 4 = 36
Right: 3 × (3 × 4) = 3 × 12 = 36

✔ Same.

New fact: 3 × 3 × 4 = 36
Product: 36

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✔ Problem g:

(3 × 2) × 2 = 3 × (2 × 2)

Left: (3 × 2) × 2 = 6 × 2 = 12
Right: 3 × (2 × 2) = 3 × 4 = 12

✔ Same.

New fact: 3 × 2 × 2 = 12
Product: 12

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⭐ Problem h:

(2 × 2) × (4 × 1) = 2 × (2 × 4) × 1

This one has two groups. Let's simplify both sides.

#### Left side:
(2 × 2) × (4 × 1) = 4 × 4 = 16

#### Right side:
2 × (2 × 4) × 1 = 2 × 8 × 1 = 16 × 1 = 16

✔ Same.

Now, write a new multiplication fact using all the numbers:
We have: 2, 2, 4, 1 → So: 2 × 2 × 4 × 1 = 16

Product: 16

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✔ Final Answers:

| Problem | Product | New Fact | Product |
|--------|--------|----------|--------|
| a | 48 | 4 × 2 × 6 = 48 | 48 |
| b | 30 | 2 × 5 × 3 = 30 | 30 |
| c | 40 | 4 × 5 × 2 = 40 | 40 |
| d | 28 | 4 × 7 × 1 = 28 | 28 |
| e | 60 | 6 × 2 × 5 = 60 | 60 |
| f | 36 | 3 × 3 × 4 = 36 | 36 |
| g | 12 | 3 × 2 × 2 = 12 | 12 |
| h | 16 | 2 × 2 × 4 × 1 = 16 | 16 |

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📌 Summary:

All problems demonstrate the Associative Property of Multiplication — changing the grouping doesn’t change the product. The key idea is that multiplication is associative, meaning we can regroup factors without affecting the final answer.

Let me know if you'd like this turned into a printable answer sheet!