Math & Education

Fraction Calculator

Add, subtract, multiply, or divide fractions instantly.

Enter two fractions and choose an operation to get the simplified result instantly.

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Result

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How to Use This Tool

  1. Enter the numerator and denominator for both fractions.
  2. Choose the operation — add, subtract, multiply, or divide.
  3. Click Calculate for the simplified result.

Fraction Operation Formulas

Addition/Subtraction: a/b ± c/d = (ad ± cb) ÷ bd

Multiplication: a/b × c/d = ac ÷ bd

Division: a/b ÷ c/d = a/b × d/c = ad ÷ bc

Simplifying the Result

After computing the raw result, this calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by it, ensuring the fraction is always presented in its simplest form.

Why Common Denominators Matter for Addition

Fractions can only be directly added or subtracted once they share a common denominator — cross-multiplying (as this calculator does) is a shortcut that finds a common denominator (bd) automatically without needing to find the least common multiple manually.

Frequently Asked Questions

Does this always give the simplest form?

Yes, the calculator automatically finds the greatest common divisor of the result and simplifies accordingly, so the fraction shown is always in its lowest terms.

Can I use negative numbers?

Yes, both numerators and denominators can be negative, and the calculator correctly handles the sign in the simplified result.

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This calculator is provided for general informational and estimation purposes only. Results should not be treated as professional financial, tax, legal, medical, or engineering advice. Always verify critical calculations with a qualified professional or official source before making decisions.