Complex Fractions

Definition

A complex fraction is a fraction that has a fraction in either the numerator or denominator, or both. These fractions can be simplified by converting them into a single fraction with a numerator and denominator that do not contain any other fractions.

5 Must Know Facts For Your Next Test

1. Complex fractions can be encountered when adding, subtracting, multiplying, or dividing rational expressions with unlike denominators.
2. To add or subtract complex fractions, you must first find the least common denominator (LCD) of all the fractions involved.
3. Once the LCD is found, the complex fractions can be converted to equivalent fractions with the same denominator, and then the numerators can be added or subtracted.
4. Multiplying complex fractions involves multiplying the numerators together and the denominators together to obtain a single fraction.
5. Dividing complex fractions involves inverting the second fraction and then multiplying the first fraction by the inverted second fraction.

Review Questions

• Explain the process of adding or subtracting complex fractions with unlike denominators.
  • To add or subtract complex fractions with unlike denominators, you must first find the least common denominator (LCD) of all the fractions involved. Once the LCD is found, the complex fractions can be converted to equivalent fractions with the same denominator. Then, the numerators can be added or subtracted, and the resulting fraction can be simplified if necessary.
• Describe the steps involved in multiplying complex fractions.
  • To multiply complex fractions, you must multiply the numerators together and the denominators together to obtain a single fraction. This involves first simplifying any fractions within the numerator or denominator, and then performing the multiplication operation. The resulting fraction may need to be further simplified by dividing the numerator and denominator by their greatest common factor.
• Analyze the relationship between complex fractions and rational expressions, and explain how they are connected in the context of adding and subtracting fractions.
  • Complex fractions are closely related to rational expressions, as they both involve fractions with algebraic expressions in the numerator and denominator. When adding or subtracting rational expressions with unlike denominators, the process often involves converting the expressions into complex fractions and then finding the least common denominator to perform the operations. The ability to manipulate complex fractions is therefore essential for understanding and working with rational expressions, particularly in the context of addition and subtraction.

Related terms

Rational Expressions: Rational expressions are algebraic expressions that can be written as a ratio of two polynomials.

Least Common Denominator (LCD): The least common denominator is the smallest positive integer that is divisible by all the denominators of the fractions being added or subtracted.

Simplifying Fractions: Simplifying fractions involves reducing the fraction to its lowest terms by dividing the numerator and denominator by their greatest common factor.