Complex Fraction Calculator

Simplify complex fractions with multi-term expressions in the numerator and denominator. Build expressions like (1/2 + 1/3) / (3/4) and see the step-by-step solution.

📐 Complex Fraction Calculator
Result
Visual Diagram
Definition

What is a Complex Fraction?

A complex fraction is a fraction whose numerator, denominator, or both contain fractions or fraction expressions. Unlike a simple fraction like 3/4, a complex fraction has fractions stacked inside fractions — for example, (1/2 + 1/3) / (3/4).

The simplest complex fraction is (a/b) / (c/d), which equals a single division. But real-world complex fractions often have sums, differences, products, or quotients of fractions in the numerator or denominator. This calculator handles all of those cases.

Complex fractions appear in algebra (rational expressions), calculus (derivatives of fractions), physics (compound unit conversions), electrical engineering (parallel resistance: 1/(1/R₁ + 1/R₂)), and recipe scaling.

Interactive Visualization
Formula

How to Simplify Complex Fractions

Step 1: Evaluate the numerator expression — combine all fractions in the numerator into a single fraction using addition, subtraction, multiplication, or division as needed.

Step 2: Evaluate the denominator expression — do the same for the denominator.

Step 3: Divide the numerator result by the denominator result — multiply by the reciprocal.

Step 4: Simplify — reduce the final fraction to lowest terms.

Example: (1/2 + 1/3) / (3/4)

  1. Numerator: 1/2 + 1/3 = 3/6 + 2/6 = 5/6
  2. Denominator: 3/4
  3. Divide: (5/6) ÷ (3/4) = (5/6) × (4/3) = 20/18
  4. Simplify: 20/18 = 10/9 = 1 1/9
Examples

Worked Examples

(1/2 + 1/3) / (3/4)

Numerator: 1/2 + 1/3 = 5/6. Then (5/6) ÷ (3/4) = (5/6) × (4/3) = 20/18 = 10/9.

(3/4 − 1/6) / (2/3 + 1/4)

Numerator: 3/4 − 1/6 = 7/12. Denominator: 2/3 + 1/4 = 11/12. Then (7/12) ÷ (11/12) = 7/11.

(2/5 × 3/7) / (1/2)

Numerator: 2/5 × 3/7 = 6/35. Then (6/35) ÷ (1/2) = (6/35) × (2/1) = 12/35. Result: 12/35.

(1/3) / (1/3 + 1/4)

Denominator: 1/3 + 1/4 = 7/12. Then (1/3) ÷ (7/12) = (1/3) × (12/7) = 12/21 = 4/7.

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FAQ

Frequently Asked Questions

Common questions about the complex fraction calculator.

A complex fraction is a fraction where the numerator, denominator, or both contain fraction expressions — not just single numbers. Examples: (1/2 + 1/3) / (3/4), or (3/8) / (1/4 − 1/6). The "big" fraction bar separates two expressions that may themselves involve sums, differences, products, or quotients of fractions.

Simple fraction division computes (a/b) ÷ (c/d), which is a special case. A complex fraction calculator handles expressions with multiple terms — like (1/2 + 1/3) in the numerator — by first evaluating each expression into a single fraction, then dividing.

This calculator evaluates each expression left to right. If you enter 1/2 + 1/3 × 1/4, it computes (1/2 + 1/3) first, then multiplies by 1/4. For standard order of operations (PEMDAS), break your expression into separate calculations.

Yes. Start with a single fraction in each slot — the calculator works like a simple complex fraction solver. Use the + Add Term button only when you need expressions with multiple fractions.

Complex fractions appear in parallel resistance (1/(1/R₁ + 1/R₂)), unit rate calculations (miles per hour per minute), recipe scaling, and algebra (simplifying rational expressions).