In the equation a + b = b + a, which law is represented?

In the equation a + b = b + a, which law is represented?

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

Answer: (C)

The equation \( a + b = b + a \) illustrates the principle that the order in which two numbers are added does not affect the sum. This fundamental property of addition is known as the Commutative Law for Addition. According to this law, you can switch the order of the operands (the numbers being added) without changing the result. For instance, whether you add 3 + 5 or 5 + 3, the result will always be 8. This characteristic is foundational in arithmetic and is applicable to all real numbers. Therefore, when encountering an equation that can be rearranged in this way, it demonstrates the Commutative Law for Addition accurately. The other laws mentioned are related to addition and its properties, but they do not pertain directly to the fact that adding in different orders yields the same result. For example, the Associative Law refers to how numbers are grouped in addition, the Distributive Law connects multiplication with addition, and the Identity Law specifies that adding zero to a number does not change its value.

The equation ( a + b = b + a ) illustrates the principle that the order in which two numbers are added does not affect the sum. This fundamental property of addition is known as the Commutative Law for Addition. According to this law, you can switch the order of the operands (the numbers being added) without changing the result.

For instance, whether you add 3 + 5 or 5 + 3, the result will always be 8. This characteristic is foundational in arithmetic and is applicable to all real numbers. Therefore, when encountering an equation that can be rearranged in this way, it demonstrates the Commutative Law for Addition accurately.

The other laws mentioned are related to addition and its properties, but they do not pertain directly to the fact that adding in different orders yields the same result. For example, the Associative Law refers to how numbers are grouped in addition, the Distributive Law connects multiplication with addition, and the Identity Law specifies that adding zero to a number does not change its value.