Simplify complex fractions of the form (a/b)/(c/d) to lowest terms
Numerator (a/b)
a =, b =
Denominator (c/d)
c =, d =
Calculation Result
Original
↓
Simplified
Step-by-Step Derivation
Complex Fraction Formula
(a/b) ÷ (c/d) = (a/b) × (d/c) = ad / bc
A complex fraction represents division of two fractions. Multiply the numerator by the reciprocal of the denominator, then reduce to lowest terms.
⚠Note: b and d cannot be zero. c cannot be zero. The result is automatically reduced using the greatest common divisor (GCD).
What Is a Complex Fraction?
A complex fraction is a fraction whose numerator or denominator contains another fraction, written in the form (a/b)/(c/d). It is essentially a division of two fractions that can be simplified into a regular fraction and then reduced.
Reciprocal Method
(a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc. Then reduce using the GCD.
Cross-Reduction
In ad/bc, you can cancel common factors between a and c, and between b and d, before multiplying to keep numbers smaller.
Simplest Form
Divide numerator and denominator by their GCD. Once they are coprime (no common factors), the fraction is fully reduced.
Sign Rules
If numerator and denominator have the same sign, the result is positive. Different signs give a negative result.
💡 Example: Simplify (3/4) ÷ (5/6). Multiply by the reciprocal: (3/4) × (6/5) = 18/20. GCD(18,20) = 2, so reduce: 18/20 = 9/10.
A fraction with another fraction in its numerator or denominator, such as (3/4)/(5/6). It represents a division of two fractions.
How do I simplify a complex fraction?▼
(a/b)/(c/d) = (a/b) × (d/c) = ad/bc, then reduce to lowest terms. Example: (3/4)/(5/6) = 18/20 = 9/10.
Can I cross-reduce before multiplying?▼
Yes. Cancel common factors between a and c, and between b and d, before multiplying. This keeps numbers smaller and makes the calculation easier.
Can the result be a mixed number?▼
Yes, improper fractions (where numerator > denominator) can be written as mixed numbers. This tool displays the result as a simplified fraction along with its decimal equivalent.
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