Associative Property of Multiplication Worksheets - Math Monks - Free Printable

Let's solve this step by step based on the Associative Property of Multiplication, which states:

> A × (B × C) = (A × B) × C

This means that when multiplying three or more numbers, the way we group them does not affect the product.

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Part 1: Find the missing number based on the associative property

We are to fill in the blanks so that both sides of the equation are equivalent using grouping.

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#### 1. $ 5 × (3 × 4) = (5 × 3) × 4 $
✔ Already solved. Answer: 4

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#### 2. $ (3 × 4) × 2 = 3 × (___ × 2) $

Left side: $ (3 × 4) × 2 = 12 × 2 = 24 $

Right side: $ 3 × (x × 2) = 24 $

So: $ 3 × (x × 2) = 24 $ → $ x × 2 = 8 $ → $ x = 4 $

But wait — let’s use the associative property directly:

$ (3 × 4) × 2 = 3 × (4 × 2) $

So the missing number is 4

✔ Answer: 4

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#### 3. $ 6 × (2 × 1) = (6 × 2) × ___ $

Left: $ 6 × (2 × 1) = 6 × 2 = 12 $

Right: $ (6 × 2) × x = 12 × x $

To make it equal: $ 12 × x = 12 $ → $ x = 1 $

Using associative property:
$ 6 × (2 × 1) = (6 × 2) × 1 $

✔ Answer: 1

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#### 4. $ 8 × (4 × 2) = (___ × 4) × 2 $

Left: $ 8 × (4 × 2) = 8 × 8 = 64 $

Right: $ (x × 4) × 2 = 64 $

So: $ (x × 4) × 2 = 64 $ → $ x × 4 = 32 $ → $ x = 8 $

Using associative property:
$ 8 × (4 × 2) = (8 × 4) × 2 $

✔ Answer: 8

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#### 5. $ 12 × (10 × 2) = (12 × ___) × 2 $

Left: $ 12 × (10 × 2) = 12 × 20 = 240 $

Right: $ (12 × x) × 2 = 240 $

So: $ (12 × x) × 2 = 240 $ → $ 12 × x = 120 $ → $ x = 10 $

Using associative property:
$ 12 × (10 × 2) = (12 × 10) × 2 $

✔ Answer: 10

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#### 6. $ (20 × 2) × 24 = ___ × (2 × 24) $

Left: $ (20 × 2) × 24 = 40 × 24 = 960 $

Right: $ x × (2 × 24) = x × 48 $

So: $ x × 48 = 960 $ → $ x = 20 $

Using associative property:
$ (20 × 2) × 24 = 20 × (2 × 24) $

✔ Answer: 20

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#### 7. $ 3 × (9 × 3) = (___ × 9) × 3 $

Left: $ 3 × (9 × 3) = 3 × 27 = 81 $

Right: $ (x × 9) × 3 = 81 $

So: $ (x × 9) × 3 = 81 $ → $ x × 9 = 27 $ → $ x = 3 $

Using associative property:
$ 3 × (9 × 3) = (3 × 9) × 3 $

✔ Answer: 3

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#### 8. $ (3 × 5) × 2 = 3 × (5 × ___) $

Left: $ (3 × 5) × 2 = 15 × 2 = 30 $

Right: $ 3 × (5 × x) = 30 $

So: $ 5 × x = 10 $ → $ x = 2 $

Using associative property:
$ (3 × 5) × 2 = 3 × (5 × 2) $

✔ Answer: 2

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Part 2: Find the product using the associative property

We regroup to make multiplication easier.

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#### 9. $ (6 × 2) × 4 = 6 × (2 × 4) = 48 $ ✔ Solved

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#### 10. $ (8 × 2) × 5 $

Regroup: $ 8 × (2 × 5) = 8 × 10 = 80 $

✔ Answer: 80

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#### 11. $ 11 × (4 × 6) $

Regroup: $ (11 × 4) × 6 = 44 × 6 = 264 $

Or: $ 11 × 24 = 264 $

✔ Answer: 264

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#### 12. $ 24 × (4 × 8) $

Regroup: $ (24 × 4) × 8 = 96 × 8 = 768 $

Or: $ 24 × 32 = 768 $

✔ Answer: 768

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✔ Final Answers:

#### Part 1 (Missing Numbers):
1. 4
2. 4
3. 1
4. 8
5. 10
6. 20
7. 3
8. 2

#### Part 2 (Products):
9. 48
10. 80
11. 264
12. 768

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✔ Summary of Solutions:

| Question | Answer |
|--------|--------|
| 1 | 4 |
| 2 | 4 |
| 3 | 1 |
| 4 | 8 |
| 5 | 10 |
| 6 | 20 |
| 7 | 3 |
| 8 | 2 |
| 9 | 48 |
| 10 | 80 |
| 11 | 264 |
| 12 | 768 |

Let me know if you'd like a printed version or explanation for any specific problem!