1. What Are Complex Fractions?

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), where a, b, c, and d can be any numbers (with b and d not zero).

2. How to Simplify Complex Fractions

The fundamental rule for simplifying complex fractions is:

This is equivalent to multiplying the numerator (a/b) by the reciprocal of the denominator (d/c).

3. Step-by-Step Simplification

Example: Simplify (3/4)/(5/6)

1. Identify numerator (3/4) and denominator (5/6)
2. Find reciprocal of denominator (6/5)
3. Multiply numerator by reciprocal: (3/4) × (6/5)
4. Multiply numerators: 3 × 6 = 18
5. Multiply denominators: 4 × 5 = 20
6. Simplify 18/20 to 9/10 by dividing numerator and denominator by 2

4. Practical Applications

Complex fractions appear in various mathematical and real-world contexts:

• Physics calculations involving rates and ratios
• Engineering problems with nested proportions
• Financial calculations with compound interest rates
• Probability problems with conditional probabilities

5. Frequently Asked Questions (FAQ)

Q1: What if the denominator is zero?
A: Division by zero is undefined. The calculator will not accept zero for denominators b or d.

Q2: Can this handle mixed numbers?
A: Convert mixed numbers to improper fractions first (e.g., 2½ becomes 5/2).

Q3: How does the simplification work?
A: The calculator finds the greatest common divisor (GCD) to reduce the fraction to simplest form.

Q4: What about negative fractions?
A: Negative signs can be in numerator, denominator, or before the fraction. The calculator preserves the sign.

Q5: Can I enter decimal numbers?
A: Yes, the calculator accepts decimal inputs (e.g., 0.5 for ½).