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Fraction Calculator

Enter two fractions and an operator, get the reduced fraction and its decimal value instantly, right in your browser.

How Fraction Calculator works

Fractions appear everywhere: recipe scaling, engineering ratios, school homework and financial splits. This calculator handles the four basic operations (addition, subtraction, multiplication and division) on two fractions. Enter the numerators and denominators, pick an operator, and the fully-reduced fraction plus its decimal equivalent appear immediately. All arithmetic runs locally in your browser; nothing is sent to any server.

Results are automatically reduced to lowest terms using the greatest common divisor algorithm. Invalid inputs such as a zero denominator, or dividing by a fraction whose numerator is zero, are caught immediately with a clear error message instead of returning a meaningless result.

Written by Bastien Sulyan

How to use Fraction Calculator, step by step

  1. Enter the numerator and denominator of the first fraction.
  2. Choose the operator: addition (+), subtraction (-), multiplication (x), or division (÷).
  3. Enter the numerator and denominator of the second fraction.
  4. Read the result as a reduced fraction and its decimal equivalent from the output panel.
  5. Correct any zero denominator or zero-numerator divisor before the calculation can proceed.

Common use cases

  • Checking whether 3/4 cup plus 1/3 cup of an ingredient gives more or less than one full cup.
  • Dividing a recipe in half by multiplying every fractional amount by 1/2 to see the reduced result.
  • Verifying a student's homework answer for 5/6 minus 1/4 without working through the common denominator by hand.
  • Calculating a fair split where one party contributes 2/5 of a cost and another contributes 1/3, to find the combined fraction.

Frequently asked questions

Does this fraction calculator work offline?

Yes. All arithmetic is performed locally in your browser using standard JavaScript integer math. Once the page has loaded you can disconnect from the internet and the calculator keeps working.

What is the algorithm for adding fractions?

To add a/b and c/d: compute the least common multiple (LCM) of b and d as the common denominator. Then the sum is (a times d/LCM(b,d) times b + c times b/LCM(b,d) times d) divided by LCM(b,d). The result is then divided by the GCD of the numerator and denominator to reduce to lowest terms. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

How does fraction multiplication and division work?

Multiplication: multiply the numerators together and the denominators together, then reduce. (2/3) times (3/4) = 6/12 = 1/2. Division: multiply the first fraction by the reciprocal of the second. (2/3) divided by (3/4) = (2/3) times (4/3) = 8/9.

What happens if I enter a zero denominator?

A zero denominator makes the fraction undefined. The tool validates before computing and shows an error asking you to enter a non-zero denominator. Similarly, dividing by a fraction whose numerator is zero is equivalent to dividing by zero and is flagged as invalid.

Are the results always fully reduced?

Yes. After every operation the tool computes the greatest common divisor (GCD) of the result numerator and denominator using the Euclidean algorithm and divides both by it. So 6/12 is always presented as 1/2, not left in an unreduced form.

Can I enter negative fractions or improper fractions?

Yes. Enter a negative numerator (for example, -3 over 4) to represent a negative fraction. Improper fractions where the numerator exceeds the denominator are accepted too; the result is reduced but not converted to a mixed number.

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