Question

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 1

The correct options are:

Rational expressions are closed under multiplication.

The commutative property states that changing the order of two or more factors does not change the value of the product.

The properties of rational expression multiplication are parallel to the properties of rational number multiplication.

Answer 2

The correct options are:

• 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 properties of rational expression multiplication and division are parallel to the properties of rational number multiplication and division.

Explanation:

We know that if a and b are two rational expression than :

Closure property of multiplication states that:

a.b is also an rational expression.

Commutative property under multiplication is given by:

a.b=b.a

The commutative property holds only under multiplication and not division since, if a=0 then,

a/b=0

but b/a is not defined.

Also, the property of rational expression are parallel to the properties of rational number.