What is the law that describes (a x b) x c = a x (b x c)?

What is the law that describes (a x b) x c = a x (b x c)?

• A. Associative Law for Addition
• B. Commutative Law for Multiplication
• C. Distributive Law
• D. Associative Law for Multiplication

Answer: (D)

The law that describes the equation (a x b) x c = a x (b x c) is the Associative Law for Multiplication. This law states that when multiplying three or more numbers, the way in which the numbers are grouped does not affect the product. In other words, regardless of how the numbers are grouped (whether you calculate (a x b) first or (b x c) first), the final result will be the same. This characteristic can be particularly useful when simplifying expressions or performing calculations since it allows for flexibility in how the multiplication is done. For example, if a = 2, b = 3, and c = 4, calculating (2 x 3) x 4 gives the same result as 2 x (3 x 4), both equaling 24. Understanding this law reinforces foundational properties of arithmetic and highlights the consistency of multiplication, which is critical when solving more complex mathematical problems.

The law that describes the equation (a x b) x c = a x (b x c) is the Associative Law for Multiplication. This law states that when multiplying three or more numbers, the way in which the numbers are grouped does not affect the product. In other words, regardless of how the numbers are grouped (whether you calculate (a x b) first or (b x c) first), the final result will be the same.

This characteristic can be particularly useful when simplifying expressions or performing calculations since it allows for flexibility in how the multiplication is done. For example, if a = 2, b = 3, and c = 4, calculating (2 x 3) x 4 gives the same result as 2 x (3 x 4), both equaling 24.

Understanding this law reinforces foundational properties of arithmetic and highlights the consistency of multiplication, which is critical when solving more complex mathematical problems.