Fraction Calculator
Add, subtract, multiply, and divide proper and improper fractions with automatic least common denominator (LCD) reduction, mixed number display, and decimal conversions.
Top integer of the first fraction
Bottom integer of first fraction (non-zero)
Mathematical operation to perform
Top integer of the second fraction
Bottom integer of second fraction (non-zero)
Lowest terms representation (a / b)
How to Use This Calculator
- Enter the numerator and denominator for the first fraction.
- Select addition, subtraction, multiplication, or division.
- Enter the numerator and denominator for the second fraction.
- Observe the reduced fraction, mixed number, and decimal equivalent.
Formula & Calculation Methodology
Fraction operations combine numerators over a common denominator (for addition/subtraction), multiply directly across (for multiplication), or multiply by the reciprocal (for division).
Worked Example
Adding 3/4 + 2/5
Multiplying 2/3 × 3/4
Frequently Asked Questions
What occurs when a denominator is entered as zero?↓
Division by zero is undefined. The calculator automatically coerces a zero denominator to 1 to prevent runtime crashes.
How does division of fractions work?↓
Dividing by a fraction is equivalent to multiplying by its reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad) / (bc).
How are negative fractions reduced?↓
Negative signs are shifted to the numerator by standard convention, so 3/-4 simplifies to -3/4.
What is a limitation of floating decimal equivalents?↓
Repeating fractions like 1/3 cannot be expressed finitely in decimal form (0.3333...) and are rounded to four decimal places.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.