Which law is associated with the operation a + b = b + a?

Which law is associated with the operation a + b = b + a?

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

Answer: (B)

The operation \( a + b = b + a \) illustrates the Commutative Law for Addition. This law states that the order in which two numbers are added does not affect the sum. In other words, whether you add \( a \) to \( b \) or \( b \) to \( a\), the result will always be the same. This property is fundamental in arithmetic and algebra as it allows for flexibility in computation. It assures us that when rearranging numbers in addition, the outcome remains unchanged. Understanding this law can simplify calculations and facilitate problem-solving, as it provides the freedom to reorder terms for ease of computation or to group numbers conveniently. The other laws mentioned relate to different properties. The Associative Law pertains to how numbers are grouped (e.g., \( (a + b) + c = a + (b + c) \)), the Identity Law establishes that adding zero to a number does not change its value (e.g., \( a + 0 = a \)), and the Distributive Law connects addition and multiplication (e.g., \( a(b + c) = ab + ac \)). Each of these laws serves a specific purpose in arithmetic and algebra but does not apply to the scenario described

The operation ( a + b = b + a ) illustrates the Commutative Law for Addition. This law states that the order in which two numbers are added does not affect the sum. In other words, whether you add ( a ) to ( b ) or ( b ) to ( a), the result will always be the same.

This property is fundamental in arithmetic and algebra as it allows for flexibility in computation. It assures us that when rearranging numbers in addition, the outcome remains unchanged. Understanding this law can simplify calculations and facilitate problem-solving, as it provides the freedom to reorder terms for ease of computation or to group numbers conveniently.

The other laws mentioned relate to different properties. The Associative Law pertains to how numbers are grouped (e.g., ( (a + b) + c = a + (b + c) )), the Identity Law establishes that adding zero to a number does not change its value (e.g., ( a + 0 = a )), and the Distributive Law connects addition and multiplication (e.g., ( a(b + c) = ab + ac )). Each of these laws serves a specific purpose in arithmetic and algebra but does not apply to the scenario described