Which expression shows the associative property for multiplication?

Which expression shows the associative property for multiplication?

• A. (A×B)×C = A×(B×C)
• B. A×B + C = B×A + C
• C. A + B = B + A
• D. (A×B) + C = A×(B+C)

Answer: (A)

Multiplying several numbers, the grouping doesn’t matter. For three numbers, you can first multiply A and B and then multiply by C, or first multiply B and C and then multiply by A, and you’ll get the same product. The expression (A×B)×C = A×(B×C) shows exactly this idea, illustrating the associativity of multiplication. The other forms mix different operations or appeal to a different property. A plus B equaling B plus A is the commutative property of addition, not about how multiplication groups. The remaining option combines multiplication and addition in a way that isn’t a standard rule for handling products, and the distributive rule would look different (A×(B+C) = A×B + A×C), not the given form.

Multiplying several numbers, the grouping doesn’t matter. For three numbers, you can first multiply A and B and then multiply by C, or first multiply B and C and then multiply by A, and you’ll get the same product. The expression (A×B)×C = A×(B×C) shows exactly this idea, illustrating the associativity of multiplication.

The other forms mix different operations or appeal to a different property. A plus B equaling B plus A is the commutative property of addition, not about how multiplication groups. The remaining option combines multiplication and addition in a way that isn’t a standard rule for handling products, and the distributive rule would look different (A×(B+C) = A×B + A×C), not the given form.