Question

which of the following demonstrates the associative property of multiplication?
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 in a multiplication problem does not change their product. In other words, \( (a \cdot b) \cdot c = a \cdot (b \cdot c) \).

Looking at the options provided:

A. \( (3 \cdot 5) \cdot 2 = (3 \cdot 5) \cdot 2 \) - This simply reiterates the same expression and does not demonstrate the associative property.

B. \( (3 \cdot 5) + 2 = (3 + 5) \cdot 2 \) - This is not demonstrating the associative property of multiplication; instead, it mixes addition and multiplication incorrectly.

C. \( (3 \cdot 5) \cdot 2 = 3 \cdot (5 \cdot 2) \) - This correctly demonstrates the associative property of multiplication because it shows that you can regroup the numbers in multiplication.

D. \( (3 + 5) \cdot 2 = 3 + (5 \cdot 2) \) - This demonstrates the distributive property, not the associative property.

Therefore, the correct answer is **C. \( (3 \cdot 5) \cdot 2 = 3 \cdot (5 \cdot 2) \)**.