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AssignmentMultiple Select

Multiplying and Dividing Rational Expressions

Question 1 • Algebra III A

Which statements are true about the multiplication and division properties of rational expressions? Check all that apply.

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 the closure property in A is true. Multiplication is commutative, but division is not: changing the order of the factors can change the result, so B is true in this multiplication-and-division context. Division is also not associative, and regrouping factors in multiplication does not change the product, so C and D are false. These properties parallel the corresponding properties of rational numbers, making E true.

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