What is the law represented by a x b = b x a?

What is the law represented by a x b = b x a?

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

Answer: (B)

The equation \( a \times b = b \times a \) represents the Commutative Law for Multiplication. This law states that the order in which two numbers are multiplied does not affect the product. Understanding this principle is fundamental in arithmetic, as it allows for flexibility in calculations and simplifies operations. For instance, if you have the numbers 3 and 5, according to the Commutative Law, multiplying them together will yield the same result regardless of their order, i.e., \( 3 \times 5 = 15 \) and \( 5 \times 3 = 15 \). This property holds for any pair of numbers. In contrast, the Associative Law for Multiplication pertains to how numbers are grouped in multiplication (e.g., \( (a \times b) \times c = a \times (b \times c) \)), while the Identity Law for Multiplication specifies that any number multiplied by one remains unchanged (e.g., \( a \times 1 = a \)). The Distributive Law combines addition and multiplication and states that \( a \times (b + c) = a \times b + a \times c \). Thus, recognizing the specifics of each mathematical law

The equation ( a \times b = b \times a ) represents the Commutative Law for Multiplication. This law states that the order in which two numbers are multiplied does not affect the product. Understanding this principle is fundamental in arithmetic, as it allows for flexibility in calculations and simplifies operations.

For instance, if you have the numbers 3 and 5, according to the Commutative Law, multiplying them together will yield the same result regardless of their order, i.e., ( 3 \times 5 = 15 ) and ( 5 \times 3 = 15 ). This property holds for any pair of numbers.

In contrast, the Associative Law for Multiplication pertains to how numbers are grouped in multiplication (e.g., ( (a \times b) \times c = a \times (b \times c) )), while the Identity Law for Multiplication specifies that any number multiplied by one remains unchanged (e.g., ( a \times 1 = a )). The Distributive Law combines addition and multiplication and states that ( a \times (b + c) = a \times b + a \times c ).

Thus, recognizing the specifics of each mathematical law