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Math tool

Fraction Calculator

Combine two fractions with exact integer arithmetic, then inspect the simplified fraction, mixed-number form, and decimal check.

Free · Private · Runs in your browser

Exact fraction arithmetic

Enter two fractions

Add, subtract, multiply, or divide signed whole-number fractions. Values and results stay in your browser.

Fraction values

Each entry must be a whole number from −1,000,000 through 1,000,000. Denominators cannot be zero.

Your exact simplified result will appear here after you submit valid fractions.

Formulas and calculation method

For fractions a/b and c/d, addition uses (ad + bc)/bd; subtraction uses (ad − bc)/bd; multiplication uses ac/bd; and division uses ad/bc when c is not zero.

The exact result is reduced by the greatest common divisor of its numerator and denominator. A negative sign is kept on the numerator, the denominator is normalized as positive, and a zero result is written as 0 rather than 0 over another value.

Exact operations and simplification use safe integer arithmetic. The input limit keeps every intermediate integer exact. The decimal is derived only after the exact result and rounded to ten places.

Conventions and boundaries

  • Inputs: two signed numerators, two nonzero signed denominators, and one of four operations.
  • Outputs: an exact simplified result, an optional mixed number, a decimal check, and the normalized denominator.
  • Input bounds: every entry must be a whole number from −1,000,000 through 1,000,000.
  • Zero behavior: zero numerators are allowed; zero denominators are invalid; division by a zero-valued second fraction is invalid.
  • Negative values: accepted and normalized to one leading negative sign. Mixed numbers use truncation toward zero, so −7/3 appears as −2 1/3.
  • Fixed versus changing information: the calculator uses settled arithmetic and user entries only. It has no live data, rates, jurisdictional defaults, or external lookups.

Limitations

This tool accepts integer numerators and denominators only. It does not parse typed mixed numbers, decimals, expressions, units, measurements, significant figures, repeating-decimal notation, or algebraic fractions. The decimal is an approximation and may display zero for a very small nonzero exact result. The calculator supplies arithmetic, not tutoring, grading, financial guidance, or another individualized recommendation.

Worked example

For 2/3 divided by 4/5, multiply 2/3 by the reciprocal 5/4. The result 10/12 reduces by a greatest common divisor of 2 to 5/6. Its ten-place decimal approximation is 0.8333333333.

Common questions

Why is the exact result simplified?

Dividing the numerator and denominator by their greatest common divisor produces an equivalent fraction with no remaining common factor greater than one.

Why can a denominator be entered as negative?

A negative denominator represents the same rational value as moving that sign to the numerator. The calculator accepts either form and always displays a positive denominator.

Is the decimal the authoritative result?

No. The simplified fraction is exact. The decimal is a rounded convenience limited to ten places.

Use the Percentage Calculator for part-to-whole questions, or the Descriptive Statistics Calculator to summarize a list of numbers.

Version and verification

Calculation version 1.0.0; formulas and deterministic fixtures last verified 2026-08-10. Authority pages were retrieved 2026-08-10. Automated tests cover arithmetic, simplification, bounds, metadata, privacy, keyboard use, responsive layout, contrast, and Axe behavior. Manual VoiceOver remains waived and is not claimed as passed.