Fraction Calculator: add, subtract, multiply and divide

This fraction calculator lets you operate on two fractions a/b and c/d through addition, subtraction, multiplication and division, simplifying the result to lowest terms using the greatest common divisor.

Formels for fraction operations

Basic fraction operations follow these rules:

• Addition: a/b + c/d = (a×d + b×c) / (b×d)
• Subtraction: a/b − c/d = (a×d − b×c) / (b×d)
• Multiplication: a/b × c/d = (a×c) / (b×d)
• Division: a/b ÷ c/d = (a×d) / (b×c)

After each operation, the result is simplified by dividing numerator and denominator by their greatest common divisor (GCD).

Example 1: adding fractions

Problem: Compute 2/3 + 1/4.

1. Apply the addition formula:
   • (2×4 + 3×1) / (3×4) = (8 + 3) / 12 = 11/12.
2. Simplify:
   • GCD(11, 12) = 1, already in lowest terms.

Answer: 2/3 + 1/4 = 11/12.

Example 2: multiplying fractions

Problem: Compute 3/8 × 4/9.

1. Apply the multiplication formula:
   • (3×4) / (8×9) = 12/72.
2. Simplify:
   • GCD(12, 72) = 12, so 12/72 = 1/6.

Answer: 3/8 × 4/9 = 1/6.

Häufige Anwendungsfälle

• Solving arithmetic exercises with fractions in school mathematics.
• Adjusting recipe proportions in cooking.
• Computing measurements in carpentry and construction using fractional inches.
• Verifying fraction operation results on exams.
• Working with proportions and percentages in financial contexts.
• Simplifying complex fractions in algebra problems.

Common mistakes when working with fractions

• Adding numerators and denominators directly (2/3 + 1/4 ≠ 3/7).
• Forgetting to simplify the final result.
• In division, not flipping the second fraction before multiplying.
• Confusing multiplication rules with addition rules.

Profi-Tipp

Before multiplying large fractions, try cross-canceling common factors between numerators and denominators. This reduces intermediate numbers and makes mental calculation easier.