Which of the following demonstrates the Associative Property of Multiplication?(1 point) Responses

Question

A. (3⋅5)⋅2=3⋅(5⋅2)
B. (3⋅5)⋅2=(3⋅5)⋅2
C. (3⋅5)+2=(3+5)⋅2
D. (3+5)⋅2=3+(5⋅2)

Answer 1

The Associative Property of Multiplication states that the way in which factors are grouped does not affect the product. This can be expressed as \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \).

In the options provided:

A. \((3 \cdot 5) \cdot 2 = 3 \cdot (5 \cdot 2)\) — This demonstrates the Associative Property of Multiplication.

B. \((3 \cdot 5) \cdot 2 = (3 \cdot 5) \cdot 2\) — This is an identity and does not demonstrate the associative property.

C. \((3 \cdot 5) + 2 = (3 + 5) \cdot 2\) — This does not involve multiplication in a manner that applies the associative property.

D. \((3 + 5) \cdot 2 = 3 + (5 \cdot 2)\) — This demonstrates the Distributive Property, not the Associative Property.

So, the correct answer is A.