Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which of the following defines a rational expression?

1. Any fraction

2. Fractions with polynomials in the numerator and denominator

3. Fractions with integers only

4. Expressions without variables

The correct answer is: Fractions with polynomials in the numerator and denominator

A rational expression is defined specifically as a fraction where both the numerator and the denominator are polynomials. This definition is rooted in algebraic principles, where polynomials can include variables raised to non-negative integer powers. Thus, the critical aspect is that both parts of the expression, the numerator and denominator, must consist of polynomial terms, allowing for the inclusion of variables and entire polynomial structures. Other options, such as any fraction, do not accurately define a rational expression because they could include fractions containing non-polynomial numerators or denominators, such as those involving roots or irrational numbers. Fractions with integers only represent a narrower case of rational expressions, which are indeed rational but do not encompass the full range of polynomials that might be present in more complex rational expressions. Finally, expressions without variables lack the polynomial component and thus cannot qualify as rational expressions. Therefore, the distinction lies in the requirement for both numerator and denominator to be polynomials, solidifying option B as the accurate definition.