Question

which of the following demonstrates the associative property of multiplication?

select one:
a. \\((a \cdot 4) \cdot 7 = a \cdot (4 \cdot 7)\\)
b. \\(3(8 + 3) = 3 \cdot 8 + 3 \cdot 3\\)
c. \\(8 \cdot 0 = 0\\)
d. \\(x \cdot 7 = 7 \cdot x\\)

Explanation:

Define the associative property

The associative property states grouping does not change the product: \((x \cdot y) \cdot z = x \cdot (y \cdot z)\).

Analyze option a

Option a shows \((a \cdot 4) \cdot 7 = a \cdot (4 \cdot 7)\). This matches the associative property.

Analyze option b

Option b shows \(3(8 + 3) = 3 \cdot 8 + 3 \cdot 3\). This is the distributive property.

Analyze option c

Option c shows \(8 \cdot 0 = 0\). This is the Zero Property of Multiplication.

Analyze option d

Option d shows \(x \cdot 7 = 7 \cdot x\). This is the commutative property.

Answer:

• a. \((a \cdot 4) \cdot 7 = a \cdot (4 \cdot 7)\) (Correct answer)
• b. \(3(8 + 3) = 3 \cdot 8 + 3 \cdot 3\)
• c. \(8 \cdot 0 = 0\)
• d. \(x \cdot 7 = 7 \cdot x\)