Which property is being demonstrated when rearranging terms in an expression?

Which property is being demonstrated when rearranging terms in an expression?

• A. Commutative Property
• B. Associative Property
• C. Distributive Property
• D. Identity Property

Answer: (A)

The Commutative Property is demonstrated when rearranging terms in an expression because it states that the order in which two numbers are added or multiplied does not change the result. For addition, for instance, \(a + b = b + a\); similarly, for multiplication, \(a \times b = b \times a\). This property allows for flexibility in rearranging the terms without affecting the overall value of the expression. In contrast, the Associative Property involves the grouping of numbers rather than their order. It states that the way in which numbers are grouped in addition or multiplication does not affect the sum or product, such as \((a + b) + c = a + (b + c)\). The Distributive Property refers to distributing a factor across terms in parentheses, while the Identity Property defines that adding zero or multiplying by one yields the same number, \(a + 0 = a\) or \(a \times 1 = a\).

The Commutative Property is demonstrated when rearranging terms in an expression because it states that the order in which two numbers are added or multiplied does not change the result. For addition, for instance, (a + b = b + a); similarly, for multiplication, (a \times b = b \times a). This property allows for flexibility in rearranging the terms without affecting the overall value of the expression.

In contrast, the Associative Property involves the grouping of numbers rather than their order. It states that the way in which numbers are grouped in addition or multiplication does not affect the sum or product, such as ((a + b) + c = a + (b + c)). The Distributive Property refers to distributing a factor across terms in parentheses, while the Identity Property defines that adding zero or multiplying by one yields the same number, (a + 0 = a) or (a \times 1 = a).