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Question 4 • RS AZ-US History A

Which statements are true about the multiplication and division properties of rational expressions? Check all that apply.The closure property of multiplication states that the product of two rational expressions is a rational expression.The commutative property only holds true for the multiplication of rational expressions.The associative property holds true for both the multiplication and division of rational expressions.The associative property states that the way in which two or more factors are grouped in a product changes the value of the product.The properties of rational expression multiplication and division are parallel to the properties of rational number multiplication and division.

Answer
A
The closure property of multiplication states that the product of two rational expressions is a rational expression.
B
The commutative property only holds true for the multiplication of rational expressions.
C
The associative property holds true for both the multiplication and division of rational expressions.
D
The associative property states that the way in which two or more factors are grouped in a product changes the value of the product.
E
The properties of rational expression multiplication and division are parallel to the properties of rational number multiplication and division.

Explanation

Multiplying two rational expressions gives another rational expression, so multiplication has the closure property. Multiplication is commutative, meaning the factors can switch order without changing the product; division is not commutative. Division is also not associative, and associativity means regrouping factors does not change a product’s value. These properties parallel those for rational numbers.

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