1. What is a Complex Fraction?

A complex fraction is a fraction where either the numerator, the denominator, or both are also fractions. The general form is (a/b)/(c/d), which represents a fraction divided by another fraction.

2. How to Simplify Complex Fractions

The standard method to simplify complex fractions is:

This works by multiplying the numerator by the reciprocal of the denominator, effectively "flipping" the denominator fraction.

3. Step-by-Step Process

Steps to simplify:

1. Identify the numerator fraction (a/b) and denominator fraction (c/d)
2. Multiply the numerator (a) by the denominator of the denominator fraction (d)
3. Multiply the denominator (b) by the numerator of the denominator fraction (c)
4. The result is (a×d)/(b×c)
5. Simplify the resulting fraction if possible

4. Practical Examples

Example 1: (2/3)/(4/5) = (2×5)/(3×4) = 10/12 = 5/6
Example 2: (1/2)/(3/4) = (1×4)/(2×3) = 4/6 = 2/3
Example 3: (5/7)/(2/3) = (5×3)/(7×2) = 15/14

5. Frequently Asked Questions (FAQ)

Q1: Why do we flip the denominator fraction?
A: Dividing by a fraction is equivalent to multiplying by its reciprocal, which makes the calculation simpler.

Q2: Can this method be used with mixed numbers?
A: Yes, but first convert mixed numbers to improper fractions before applying the method.

Q3: What if the denominator is a whole number?
A: Treat it as a fraction with denominator 1 (e.g., 5 = 5/1).

Q4: Does this work with variables?
A: Yes, the same principle applies to algebraic fractions with variables.

Q5: How do I simplify further after applying the formula?
A: Find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.