Associative property of multiplication | TPT - Free Printable

Problem Description:

The task involves solving multiplication problems using the Associative Property of Multiplication. The associative property states that when multiplying three or more numbers, the way in which the numbers are grouped does not affect the product. Mathematically, this is expressed as:

\[
(a \times b) \times c = a \times (b \times c)
\]

The goal is to compute the products for each problem listed and demonstrate how the associative property can be applied.

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Solution:

#### Left Column:

1. Problem 1: \( 3 \times 4 \times 5 \)
- Grouping: \( (3 \times 4) \times 5 \)
- First, calculate \( 3 \times 4 = 12 \).
- Then, calculate \( 12 \times 5 = 60 \).
- Answer: \( 60 \)

2. Problem 2: \( 3 \times 2 \times 3 \)
- Grouping: \( (3 \times 2) \times 3 \)
- First, calculate \( 3 \times 2 = 6 \).
- Then, calculate \( 6 \times 3 = 18 \).
- Answer: \( 18 \)

3. Problem 3: \( 5 \times 4 \times 2 \)
- Grouping: \( (5 \times 4) \times 2 \)
- First, calculate \( 5 \times 4 = 20 \).
- Then, calculate \( 20 \times 2 = 40 \).
- Answer: \( 40 \)

4. Problem 4: \( 3 \times 5 \times 3 \)
- Grouping: \( (3 \times 5) \times 3 \)
- First, calculate \( 3 \times 5 = 15 \).
- Then, calculate \( 15 \times 3 = 45 \).
- Answer: \( 45 \)

5. Problem 5: \( 8 \times 3 \times 2 \)
- Grouping: \( (8 \times 3) \times 2 \)
- First, calculate \( 8 \times 3 = 24 \).
- Then, calculate \( 24 \times 2 = 48 \).
- Answer: \( 48 \)

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#### Right Column:

6. Problem 6: \( 4 \times 2 \times 8 \)
- Grouping: \( (4 \times 2) \times 8 \)
- First, calculate \( 4 \times 2 = 8 \).
- Then, calculate \( 8 \times 8 = 64 \).
- Answer: \( 64 \)

7. Problem 7: \( 5 \times 2 \times 7 \)
- Grouping: \( (5 \times 2) \times 7 \)
- First, calculate \( 5 \times 2 = 10 \).
- Then, calculate \( 10 \times 7 = 70 \).
- Answer: \( 70 \)

8. Problem 8: \( 2 \times 7 \times 2 \)
- Grouping: \( (2 \times 7) \times 2 \)
- First, calculate \( 2 \times 7 = 14 \).
- Then, calculate \( 14 \times 2 = 28 \).
- Answer: \( 28 \)

9. Problem 9: \( 4 \times 6 \times 5 \)
- Grouping: \( (4 \times 6) \times 5 \)
- First, calculate \( 4 \times 6 = 24 \).
- Then, calculate \( 24 \times 5 = 120 \).
- Answer: \( 120 \)

10. Problem 10: \( 9 \times 4 \times 2 \)
- Grouping: \( (9 \times 4) \times 2 \)
- First, calculate \( 9 \times 4 = 36 \).
- Then, calculate \( 36 \times 2 = 72 \).
- Answer: \( 72 \)

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Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 60 \\
2. & 18 \\
3. & 40 \\
4. & 45 \\
5. & 48 \\
6. & 64 \\
7. & 70 \\
8. & 28 \\
9. & 120 \\
10. & 72 \\
\end{array}
}
\]

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Explanation:

The associative property allows us to group the numbers in any order without changing the final result. This property simplifies calculations by letting us choose the most convenient grouping. For example, in Problem 1 (\( 3 \times 4 \times 5 \)), we chose to first multiply \( 3 \times 4 \) because it results in a smaller intermediate number, making the next multiplication easier. The same principle applies to all other problems.