Complex Fractions
Complex fractions are a Grade 7 math skill from Yoshiwara Intermediate Algebra involving fractions that contain fractions in the numerator, denominator, or both. Students simplify complex fractions by finding the LCD of all sub-fractions and multiplying through, or by dividing numerator by denominator.
Key Concepts
Property A fraction that contains one or more fractions in either its numerator or its denominator or both is called a complex fraction . Like simple fractions, complex fractions represent quotients. For example, $\frac{\frac{2}{3}}{\frac{5}{6}} = \frac{2}{3} \div \frac{5}{6}$.
To simplify a complex fraction: 1. Find the LCD of all the fractions contained in the complex fraction. 2. Multiply the numerator and the denominator of the complex fraction by the LCD. 3. Reduce the resulting simple fraction, if possible.
Examples To simplify $\frac{\frac{3}{4}}{\frac{7}{8}}$, we can treat it as a division: $\frac{3}{4} \div \frac{7}{8} = \frac{3}{4} \cdot \frac{8}{7} = \frac{24}{28} = \frac{6}{7}$.
Common Questions
What is a complex fraction?
A complex fraction is a fraction where the numerator or denominator (or both) contain fractions. For example, (1/2)/(3/4) is a complex fraction.
How do you simplify a complex fraction?
Method 1: Multiply numerator and denominator by the LCD of all sub-fractions to clear them. Method 2: Treat it as division — multiply the numerator fraction by the reciprocal of the denominator fraction.
How do you simplify (x/2)/((x+1)/4)?
Multiply by the reciprocal: (x/2) × (4/(x+1)) = 4x/(2(x+1)) = 2x/(x+1).
Where are complex fractions used in algebra?
Complex fractions appear in rational expressions, rate problems (like average speed), and simplifying formulas with multiple fractional parts.