Complex Fractions

Definition

A complex fraction is a fraction that has a fraction in the numerator, denominator, or both. They are used to represent and manipulate more complicated fractional expressions involving multiple levels of division.

5 Must Know Facts For Your Next Test

1. Complex fractions can be simplified by converting them to an equivalent fraction with a polynomial in the numerator and denominator.
2. Multiplying or dividing rational expressions that contain complex fractions requires applying the rules for multiplying and dividing fractions.
3. The reciprocal of a complex fraction is obtained by flipping the numerator and denominator of the entire complex fraction.
4. Complex fractions can be used to represent and solve more advanced fractional equations and inequalities.
5. Proficiency in working with complex fractions is essential for success in advanced algebra and calculus courses.

Review Questions

• How can a complex fraction be simplified?
  • To simplify a complex fraction, the first step is to convert it to an equivalent fraction with a polynomial in the numerator and denominator. This can be done by multiplying the numerator and denominator of the complex fraction by the least common denominator of the fractions within the complex fraction. Once the complex fraction is in this form, it can be simplified using the standard rules for simplifying fractions, such as canceling common factors in the numerator and denominator.
• Explain the process of multiplying or dividing rational expressions that contain complex fractions.
  • When multiplying or dividing rational expressions that contain complex fractions, you must first simplify the complex fractions by converting them to equivalent fractions with polynomials in the numerator and denominator. Then, you can apply the standard rules for multiplying or dividing rational expressions. This may involve finding common denominators, factoring, and canceling common factors in the numerator and denominator.
• How can the reciprocal of a complex fraction be determined?
  • To find the reciprocal of a complex fraction, you simply need to flip the numerator and denominator of the entire complex fraction. This means that the numerator of the reciprocal will be the denominator of the original complex fraction, and the denominator of the reciprocal will be the numerator of the original complex fraction. The reciprocal of a complex fraction can be useful when solving more advanced fractional equations or inequalities.

Related terms

Rational Expression: A rational expression is a quotient of two polynomial expressions, which can be simplified using the rules of fractions.

Simplifying Fractions: The process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common factor.

Reciprocal: The reciprocal of a number is the value obtained by flipping the numerator and denominator of a fraction.