Math Problem Statement

The expression was rewritten using the Associative Property of Multiplication . left parenthesis, 3, dot, 8, right parenthesis, dot, 4(3⋅8)⋅4 equals dot, 4⋅4 which equals . 3, dot, left parenthesis, 8, dot, 4, right parenthesis3⋅(8⋅4) equals 3, dot3⋅ which equals .

Solution

The given expression demonstrates how the Associative Property of Multiplication allows us to group the factors differently without changing the product.

Here’s the step-by-step breakdown:

  1. Starting with: (38)4(3 \cdot 8) \cdot 4

  2. By the Associative Property of Multiplication, we can regroup the factors: 3(84)3 \cdot (8 \cdot 4)

    The Associative Property states that the way we group numbers in a multiplication operation does not affect the result.

  3. Simplify the terms:

    • 84=328 \cdot 4 = 32 So, we get: 332=963 \cdot 32 = 96

Thus, both expressions evaluate to: (38)4=3(84)=96(3 \cdot 8) \cdot 4 = 3 \cdot (8 \cdot 4) = 96

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the Commutative Property of Multiplication?
  2. Can the Associative Property be applied to addition as well?
  3. How does the Distributive Property differ from the Associative Property?
  4. What are the other basic properties of multiplication?
  5. Why do multiplication properties work for both real numbers and integers?

Tip: The Associative Property helps in simplifying complex expressions by regrouping numbers in easier-to-multiply pairs.

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Math Problem Analysis

Mathematical Concepts

Associative Property of Multiplication
Multiplication

Formulas

(a ⋅ b) ⋅ c = a ⋅ (b ⋅ c)

Theorems

Associative Property of Multiplication

Suitable Grade Level

Grades 4-6